Program

× Ross Duncan

Quantinuum

www.quantinuum.com

Ariel Bendersky

Technology Innovation Institute

www.tii.ae

Nicolas Heurtel

Quandela

www.quandela.com

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Excursion to Delta de Tigre

Tickets to be paid on registration

The Delta de Tigre is a beautiful area located 30 km north of Buenos Aires. The delta is formed by the Paraná River, which splits into several smaller rivers and streams.

• 3:00 pm - Departure from the conference venue
• 3:30 pm - Arrival at Tigre
• 4:30 pm - Boat trip through the delta, including navigation through the Río de la Plata and the Paraná River.
• 6:30 pm - Arrival at Puerto Madero

Bar at Puerto Madero

You do not need an excursion ticket to join us at the bar. Please note that drinks are not complimentary

We arrive at Puerto Madero in Buenos Aires City around 6:30 pm. Puerto Madero is one of the most modern and exclusive neighborhoods in Buenos Aires, with a wide variety of bars and pubs. The excursion ends here, and you can stay in the area to have dinner or return to the hotel. We will provide you with a map of some pubs and bars in the area, so those who do not participate in the excursion can join us for a drink.

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Conference dinner

Tickets to be paid on registration

The conference dinner will be at Galidon, a traditional Argentine restaurant.
Address: Av. Guillermo Udaondo 1470

Menu example (it may have little changes)

All options include one bottle of Argentinian Malbec wine for every 2 persons, and complimentary non-alcoholic drinks.

Gluten and dairy free options can be asked on site.

Standard: A typical Argentinian asado
Starter	Empanada and Chorizo Small meat pie & Argentinian sausage
Main dish	Parrillada A selection of grilled meats served with salads
Desert	Dulce de leche ice cream

Vegetarian: Italian pasta
Starter	Grilled provoleta cheese
Main dish	Spaghetti with tomato sauce and basil
Desert	Dulce de leche ice cream

Vegan: Italian pasta
Starter	Green salad with tomato, carrot, arugula, and seeds
Main dish	Egg-free spaghetti with tomato sauce and basil
Desert	Fruit salad

× Emmanuel Hainry, Romain Péchoux, and Mário Silva

A Programming Language Characterizing Quantum Polynomial Time

We introduce a first-order quantum programming language, named FOQ, whose terminating programs are reversible. We restrict FOQ to a strict and tractable subset, named PFOQ, of terminating programs with bounded width, that provides a first programming-language-based characterization of the quantum complexity class FBQP. We finally present a tractable semantics-preserving algorithm compiling a PFOQ program to a quantum circuit of size polynomial in the number of input qubits.

Extended abstract

× Eleftherios Tselentis and Ämin Baumeler

The Mobius game and other Bell test for relativity

We derive multiparty games that, if the winning chance exceeds a certain limit, prove the incompatibility of the parties' causal relations with any partial order. This, in turn, means that the parties exert a back-action on the causal relations; the causal relations are dynamical. The games turn out to be representable by directed graphs, for instance by an orientation of the Möbius ladder. We discuss these games as device-independent tests of spacetime's dynamical nature in general relativity. To do so, we design a relativistic setting where, in the Minkowski spacetime, the winning chance is bound to the limits. In contrast, we find otherwise tame processes with classical control of causal order that win the games deterministically. These suggest a violation of the bounds in gravitational implementations. We obtain these games by uncovering a "pairwise central symmetry" of the correlations in question. This symmetry allows us to recycle the facets of the acyclic subgraph polytope studied by Grötschel, Jünger, and Reinelt in the mid-80s for combinatorial optimization. In addition, we derive multiparty games in a scenario where the polytope dimension grows only linearly in the number of parties. Here, exceeding the limits not only proves the dynamical nature of the causal relations, but also that the correlations are incompatible with any global causal order.

× Maarten Grothus and V. Vilasini

Characterizing Signalling: Connections between Causal Inference and Space-time Geometry

Causality is pivotal to our understanding of the world, presenting itself in various forms: information-theoretic and relativistic, the former linked to the flow of information, and the latter to the structure of spacetime. Leveraging a framework introduced in PRA, 106, 032204 (2022), which formally connects these two notions in general physical theories, we study their interplay. Here, information-theoretic causality is defined through a causal modelling approach, which enables the inference of causal connections through agents' interventions and correlations. First, we improve the characterization of information-theoretic signalling as defined through so-called affects relations. Specifically, we provide conditions for identifying redundancies in different parts of such a relation, introducing techniques for causal inference in unfaithful causal models (where the observable data does not “faithfully” reflect the causal dependences). In particular, this demonstrates the possibility of causal inference using the absence of signalling between certain nodes. Second, we define an order-theoretic property called conicality, showing that it is satisfied for light cones in Minkowski space-times with d > 1 spatial dimensions but violated for d = 1. Finally, we study the embedding of information-theoretic causal models in spacetime without violating relativistic principles such as no superluminal signalling (NSS). In general, we observe that constraints imposed by NSS in a spacetime and those imposed by purely information-theoretic causal inference behave differently. We then prove a correspondence between conical space-times and faithful causal models: in both cases, there emerges a parallel between these two types of constraints. This indicates a connection between informational and geometric notions of causality, and offers new insights and tools for studying the relations between the principles of NSS and no causal loops in different spacetime geometries and theories of information processing.

Extended abstract

× Urs Schreiber

Topological Quantum Programming via Linear Homotopy Types

We explain that there is a closer relation between Quantum Computing and Homotopy Type Theory (HoTT) than might superficially be expected.
First, we observe that the specification of topological quantum gates based on anyon braiding is essentially a native construct in HoTT, being given by type transport in the 0-truncation of a certain dependent function type into dependent Eilenberg MacLane types. This follows by a neat synthetic encoding of “Gauss-Manin connections” into HoTT, combined with a theorem by Feigin, Schechtmann & Varchenko (1991) on conformal quantum field theory. Arguably, this reveals (certified) topological quantum computing as the first use-case of genuinely “homotopical computation”.
Moreover, we observe that HoTT admits conservative extensions by dependent linear homotopy types (LHoTT) which constitute genuine quantum data types much as familiar from the Quipper quantum programming language. Semantically this reflects the remarkable observation by Biedermann et al. that ∞-categories of parameterized module spectra (interpreting dependent linear homotopy types) are ∞-toposes. Specifically, LHoTT verifies the Grothendieck-Wirthmüller “motivic yoga of operations” on parameterized spectra, and we observe that this implies admissible inference rules for whole a system of (co)monads on linear homotopy types which naturally express quantum effects both on pure as well as on mixed states. In particular this recovers (hence certifies) Coecke et al.'s quantum measurement monads now used in the zx-Caclulus, and it provides “dynamic lifting” of measurement results as envisioned by the Quipper community.

Extended abstract

× Robert Allen and Dominic Verdon

CP-infinity and beyond: 2-categorical dilation theory

The problem of extending the insights and techniques of categorical quantum mechanics to infinite-dimensional systems was considered in (Coecke and Heunen, 2016 - In Proceedings QPL 2011). In that work the CP-infinity construction, which recovers the category of Hilbert spaces and quantum operations from the category of Hilbert spaces and bounded linear maps, was defined. Here we show that by a 'horizontal categorification' of the CP∞-construction, one can recover the category of all von Neumann algebras and channels (normal unital completely positive maps) from the 2-category [W*] of von Neumann algebras, bimodules and intertwiners. As an application, we extend Choi's characterisation of extremal channels between finite-dimensional matrix algebras to a characterisation of extremal channels between arbitrary von Neumann algebras.

Extended abstract

× Raman Choudhary, Rui Soares Barbosa, and Adán Cabello

Lifting noncontextuality inequalities

Kochen-Specker contextuality is a fundamental feature of quantum mechanics and a crucial resource for quantum computational advantage and reduction of communication complexity. Its presence is witnessed in empirical data by the violation of noncontextuality inequalities. However, all known noncontextuality inequalities corresponding to facets of noncontextual polytopes are either Bell inequalities or refer to cyclic or state-independent contextuality scenarios.
We introduce a general method for lifting noncontextuality inequalities, deriving facets of noncontextual polytopes for more complex scenarios from known facets of simpler sub-scenarios. Concretely, starting from an arbitrary scenario, the addition of a new measurement or a new outcome preserves the facet-defining nature of any noncontextuality inequality. This extends the results of Pironio [J. Math. Phys. 46, 062112 (2005)] from Bell nonlocality scenarios to contextuality scenarios and unifies liftings of Bell and noncontextuality inequalities. We show that our method produces facet-defining noncontextuality inequalities in all scenarios with contextual correlations, and we present examples of facet-defining noncontextuality inequalities for scenarios where no examples were known.
Our results shed light on the structure of noncontextuality polytopes and the relationship between such polytopes across different scenarios.

Extended abstract

× Satoshi Yoshida, Akihito Soeda, and Mio Murao

Optimal protocols for universal adjointation of isometry operations

Identification of possible transformations of quantum objects including quantum states and quantum operations is indispensable in developing quantum algorithms.
Universal transformations, defined as input-independent transformations, appear in various quantum applications. Such is the case for universal transformations of unitary operations. However, extending these transformations to non-unitary operations is nontrivial and largely unresolved. Addressing this, we introduce isometry adjointation protocols that convert an input isometry operation into its adjoint operation, which include both unitary operation and quantum state transformations. The paper details the construction of parallel and sequential isometry adjointation protocols, derived from unitary inversion protocols using quantum combs, and achieving optimal approximation error. This error is shown to be independent of the output dimension of the isometry operation. In particular, we explicitly obtain an asymptotically optimal parallel protocol achieving an approximation error ε = θ(d^2/n), where d is the input dimension of the isometry operation and n is the number of calls of the isometry operation.

Extended abstract

× John van de Wetering, Richie Yeung, Tuomas Laakkonen, and Aleks Kissinger

Optimal compilation of parametrised quantum circuits

Parametrised quantum circuits contain phase gates whose phase is determined by a classical algorithm prior to running the circuit on a quantum device. Such circuits are used in variational algorithms like QAOA and VQE. In order for these algorithms to be as efficient as possible it is important that we use the fewest number of parameters. We show that, while the general problem of minimising the number of parameters is NP-hard, when we restrict to circuits that are Clifford apart from parametrised phase gates and where each parameter is used just once, we can efficiently find the optimal parameter count. We show that when parameter transformations are required to be sufficiently well-behaved that the only rewrites that reduce parameters correspond to simple 'fusions'. Using this we find that a previous circuit optimisation strategy by some of the authors [Kissinger, van de Wetering. PRA (2019)] finds the optimal number of parameters.
Our proof uses the ZX-calculus. We also prove that the standard rewrite rules of the ZX-calculus suffice to prove any equality between parametrised Clifford circuits.

× Haruki Emori and Hiroyasu Tajima

Error and Disturbance as Irreversibility with Applications: Unified Definition, Wigner--Araki--Yanase Theorem and Out-of-Time-Order Correlator

Error and disturbance are fundamental concepts in quantum measurements. Here we show that these two concepts can be formulated as special cases of irreversibility of quantum processes. Our formulation provides fruitful byproducts: First, we unify the existing formulations of error and disturbance and derive them from ours by constructing the corresponding quantum processes. Second, we extend the quantitative Wigner–Araki–Yanase theorem—a universal restriction on measurement implementation under a conservation law—to error and disturbance of arbitrary definitions and processes. Third, we give a novel treatment of out-of-time-orderd-correlator (OTOC)—a measure of quantum chaos in a quantum many-body system—as irreversibility in analogy with the measurement context, and its experimental evaluation method.

× Alexandre Clément, Noé Delorme, and Simon Perdrix

Minimal Equational Theories for Quantum Circuits

We introduce the first minimal and complete equational theory for quantum circuits. Hence, we show that any true equation on quantum circuits can be derived from simple rules, all of them being standard except a novel but intuitive one which states that a multi-control 2π rotation is nothing but the identity. Our work improves on the recent complete equational theories for quantum circuits, by getting rid of several rules including a fairly unpractical one. One of our main contributions is to prove the minimality of the equational theory, i.e. none of the rules can be derived from the other ones. More generally, we demonstrate that any complete equational theory on quantum circuits (when all gates are unitary) requires rules acting on an unbounded number of qubits. Finally, we also simplify the complete equational theories for quantum circuits with ancillary qubits and/or qubit discarding.

Extended abstract

× Martin Avanzini, Georg Moser, Romain Péchoux, and Simon Perdrix

On the Hardness of Analyzing Quantum Programs Quantitatively

We study quantitative properties of quantum programs such as (positive) almost-sure termination, expected runtime or expected cost, that is, for example, the expected number of applications of a given quantum gate, etc.
After studying the completeness of these problems in the arithmetical hierarchy over the Clifford+T fragment of quantum mechanics, we express these problems using a variation of a quantum pre-expectation transformer, a weakest pre-condition based technique that allows to symbolically compute these quantitative properties. Under a smooth restriction—a restriction to polynomials of bounded degree over a real closed field—we show that the quantitative problem, which consists in finding an upper-bound to the pre-expectation, can be decided in time double-exponential in the size of a program. Finally, we sketch how the latter can be transformed into an efficient synthesis method.

Extended abstract

× Nadish de Silva and Imin Chen

Characterising semi-Clifford gates using algebraic sets

Motivated by their central role in fault-tolerant quantum computation, we study the sets of gates of the third-level of the Clifford hierarchy and their distinguished subsets of 'nearly diagonal' semi-Clifford gates. The Clifford hierarchy gates can be implemented via gate teleportation given appropriate magic states. The vast quantity of these resources states required for achieving fault-tolerance is a significant bottleneck for experimental implementations of universal quantum computers. Semi-Clifford gates are important because they can be implemented with far more efficient use of these resource states.
We prove that every third-level gate of up to two qudits is semi-Clifford. We thus generalise results of Zeng-Chen-Chuang (2008) in the qubit case and of the second author (2020) in the qutrit case to the case of qudits of arbitrary prime dimension d.
Earlier results relied on exhaustive computations whereas our present work leverages tools of algebraic geometry which can be applied more widely within quantum information. Specifically, we construct two schemes corresponding to the sets of third-level Clifford hierarchy gates and third-level semi-Clifford gates. We then show that the two algebraic sets resulting from reducing these schemes modulo d share the same set of rational points.

Extended abstract

× Massy Khoshbin, Lorenzo Catani, and Matthew Leifer

Alternative robust ways of witnessing nonclassicality in the simplest scenario

In this work we relate notions of nonclassicality in what is known as the simplest nontrivial scenario (a prepare and measure scenario composed of four preparations and two binary-outcome tomographically complete measurements). Specifically, we relate the established method developed in [Pusey, PRA 98,022112(2018)] to witness a violation of preparation noncontextuality, that is not suitable in experiments where the operational equivalences to be tested are specified in advance, with a novel approach based on the notion of bounded ontological distinctness for preparations, defined in [Chaturvedi and Saha, Quantum 4, 345 (2020)]. In our approach, we test bounded ontological distinctness for two particular preparations that are relevant in certain information processing tasks in that they are associated with the even and odd parity of the bits to communicate. When there exists an ontological model where this distance is preserved we talk of parity preservation. Our main result provides a noise threshold under which violating parity preservation (and so bounded ontological distinctness) agrees with the established method for witnessing preparation contextuality in the simplest nontrivial scenario. This is achieved by first relating the violation of parity preservation to the quantification of contextuality in terms of inaccessible information as developed in [Marvian, arXiv:2003.05984(2020)], that we also show, given the way we quantify noise, to be more robust in witnessing contextuality than Pusey's noncontextuality inequality. As an application of our findings, we treat the case of 2-bit parity oblivious multiplexing in the presence of noise. In particular, given that we have a noise threshold below which preparation contextuality holds, we use it to establish a condition for which preparation contextuality is present in the case where the probability of success exceeds that achieved by any classical strategy.

× Léo Colisson, Damian Markham, and Raja Yehia

All graph state verification protocols are composably secure

Graph state verification protocols allow multiple parties to share a graph state while checking that the state is honestly prepared, even in the presence of malicious parties. Since graph states are the starting point of numerous quantum protocols, it is crucial to ensure that graph state verification protocols can safely be composed with other protocols, this property being known as composable security. Previous works conjectured that such a property could not be proven within the abstract cryptography framework: we disprove this conjecture by showing that all graph state verification protocols can be turned into a composably secure protocol with respect to the natural functionality for graph state preparation. Moreover, we show that any unchanged graph state verification protocol can also be considered as composably secure for a slightly different, yet useful, functionality. Finally, we show that these two results are optimal, in the sense that any such generic result, considering arbitrary black-box protocols, must either modify the protocol or consider a different functionality.
Along the way, we show a protocol to generalize entanglement swapping to arbitrary graph states that might be of independent interest. We derive our results using the scalable ZX-calculus formalism, providing one of the first application of this formalism to cryptography.

Extended abstract

× David Schmid, Yìlè Ying, and Matthew Leifer

A review and analysis of six extended Wigner's friend arguments

The Wigner's friend thought experiment was intended to illustrate the difficulty one has in describing an agent as a quantum system when that agent performs a measurement. While it does pose a challenge to the orthodox interpretation of quantum theory, most modern interpretations have no trouble in resolving the difficulty. Recently, a number of extensions of Wigner's ideas have been proposed. We provide a gentle introduction to six such arguments, modifying the specifics of many of them so that they are as simple and unified as possible. In particular, we show that all of the arguments hinge on assumptions about correlations between measurement outcomes that are not accessible to any observer, even in principle. We then provide a critical analysis of each argument, focusing especially on how well one can motivate the required assumptions regarding these inaccessible correlations. Although we argue that some of these assumptions are not entirely well-motivated, all of the arguments do shed light on the nature of quantum theory, especially when concerning the description of agents and their measurements.

× Zixuan Liu and Giulio Chiribella

Tsirelson bounds for quantum correlations with indefinite causal order

Quantum theory is in principle compatible with processes that violate causal inequalities, an analogue of Bell inequalities that constrain the correlations observed by a set of parties operating in a definite order. Since the introduction of causal inequalities, determining their maximum quantum violation, analogue to Tsirelson's bound, has remained an open problem. Here we provide a general method for bounding the violation of causal inequalities by arbitrary quantum processes with indefinite causal order. We prove that the maximum violation is generally smaller than the algebraic maximum, and determine a Tsirelson-like bound for the paradigmatic example of the Oreshkov-Brukner-Costa causal inequality. Surprisingly, we find that the algebraic maximum of arbitrary causal inequalities can be achieved by a new type of processes that allow for information to flow in an indefinite direction within the parties' laboratories. In the classification of the possible correlations, these processes play a similar role as the no-signalling processes in Bell scenarios.

Extended abstract

× Samson Abramsky, Serban Cercelescu, and Carmen Maria Constantin

Commutation Groups and State-Independent Contextuality

We introduce an algebraic structure for studying state-independent contextuality arguments, a key form of quantum non-classicality exemplified by the well-known Peres-Mermin magic square, and used as a source of quantum advantage.
We introduce commutation groups presented by generators and relations, and analyse them in terms of a string rewriting system. There is also a linear algebraic construction, a directed version of the Heisenberg group. We introduce contextual words as a general form of contextuality witness. We characterise when contextual words can arise in commutation groups, and explicitly construct non-contextual value assignments in other cases. Generalized Pauli n-groups are commutation groups. Every commutation group has a unitary representation as a sub-group of a generalized Pauli n-group.

× Robert Booth, Titouan Carette, and Cole Comfort

A graphical language for Gaussian quantum processes

We give a simple, complete graphical language for Gaussian quantum processes. Our graphical language extends Menicucci et al.'s graphical calculus for Gaussian pure states with a representation for processes, including measurements. We also interpret the LOv-calculus, a graphical language for reasoning about passive linear-optical quantum circuits in our language; extending the LOv-calculus with both active squeezing and shearing. Constructing our graphical language requires us to formally extend Gaussian quantum mechanics with infinitely-squeezed states. We do this by showing that Gaussian quantum processes can always be though of as special kinds of relations between the phase spaces of the systems involved. In this setting, infinite squeezing is completely natural; therefore, our work provides a rigorous justification for many common yet informal calculations in the quantum optics literature involving infinite-squeezing. We demonstrate this utility by providing a graphical proof of the continuous-variable quantum teleportation protocol, which would not be possible if we took the conventional approach of describing infinite squeezing using distributions.

× Cihan Okay and Walker Stern

Twisted simplicial distributions

Bell's notion of non-locality and its generalization quantum contextuality are fundamental features of quantum theory. In addition to its foundational importance to quantum theory, contextuality is the source of significant advantages in quantum computation. Simplicial distributions provide a topological way of capturing this non-classical phenomenon. The theory of simplicial distributions combines the earlier sheaf-theoretic and cohomological approaches by modeling measurements and their outcomes as simplicial sets — a combinatorial avatar of topological spaces. One novel feature of the theory is that contextuality proofs can be done using arguments that rely on topological intuition. In this work, we introduce simplicial distributions which are 'twisted' by local algebraic constraints — a notion which has immediate applications to studying naturally appearing twisted quantum probabilities. Our framework is based on the theory of principal bundles from simplicial homotopy theory. The powerful techniques introduced in this framework provide valuable tools and new insights for the vertex enumeration problem of non-signaling polytopes of quantum foundations and simulation polytopes with applications for studying quantum advantage. In addition, our approach is well suited to categorical construction for developing a resource theory of contextuality.

× Yìlè Yīng, Marina Maciel Ansanelli, Andrea Di Biagio, Elie Wolfe, and Eric Gama Cavalcanti

Relating Wigner's Friend Scenarios to Nonclassical Causal Compatibility, Monogamy Relations, and Fine Tuning

Nonclassical causal modeling was developed in order to explain violations of Bell inequalities while adhering to relativistic causal structure and faithfulness — that is, avoiding fine-tuned causal explanations. Recently, a no-go theorem stronger than Bell's theorem has been derived, based on extensions of Wigner's friend thought experiment: the Local Friendliness (LF) no-go theorem. Here we show that the LF no-go theorem poses formidable challenges for the field of causal modeling, even when nonclassical and/or cyclic causal explanations are considered. We first recast the LF inequalities, one of the key elements of the LF no-go theorem, as special cases of monogamy relations stemming from a statistical marginal problem; we then further recast LF inequalities as causal compatibility inequalities stemming from a nonclassical causal marginal problem, for a causal structure implied by well-motivated causal-metaphysical assumptions. We find that the LF inequalities emerge from the causal modeling perspective even when allowing the latent causes of observed events to admit post-quantum descriptions, such as Generalised Probabilistic Theories (GPT) or even more exotic theories. We further prove that no nonclassical causal model can explain violations of LF inequalities without violating the No Fine-Tuning principle. Finally, we note that these obstacles cannot be overcome even if one were to appeal to cyclic causal models.

× Shuyang Meng, Fionnuala Curran, Gabriel Senno, Victoria J. Wright, Máté Farkas, Valerio Scarani, and Antonio Acín

Maximal intrinsic randomness of a quantum state

One of the most counterintuitive aspects of quantum theory is its claim that there is 'intrinsic' randomness in the physical world. Arising from the quantum phenomenon of superposition, this randomness has no classical counterpart. It ensures, for instance, that the outcomes of an unbiased measurement on a pure quantum state cannot be predicted by even the most powerful eavesdropper. By contrast, mixed quantum states also possess an apparent, classical form of randomness, as the 'actual' state of the system in each round of measurement may be unknown to the experimentalist, but known to a nefarious eavesdropper. We ask, then, how much intrinsic randomness can be extracted from a quantum state? We solve this problem for three common quantifiers of randomness, the conditional min-, von Neumann and max-entropies, and we derive necessary and sufficient conditions for the projective measurements that achieve the bound in each case. While all of the bounds can be reached by measuring in a basis unbiased to the diagonal basis of the state, we find other, less intuitive measurements that achieve them. Interestingly, we find measurements that saturate one of the entropies but not the other two, highlighting the inequivalence between these three characterisations of intrinsic randomness.

× Shashaank Khanna, Marina Maciel Ansanelli, Matthew Pusey, and Elie Wolfe

Classifying Causal Structures: Ascertaining when Classical Correlations are Constrained by Inequalities

The classical causal relations between a set of variables, some observed and some latent, can induce both equality constraints (typically conditional independencies) as well as inequality constraints (Instrumental and Bell inequalities being prototypical examples) on their compatible distribution over the observed variables. Enumerating a causal structure's implied inequality constraints is generally far more difficult than enumerating its equalities. Furthermore, only inequality constraints ever admit violation by quantum correlations. For both those reasons, it is important to classify causal scenarios into those which impose inequality constraints versus those which do not. Here we develop methods for detecting such scenarios by appealing to d-separation, e-separation, and incompatible supports. Many (perhaps all?) scenarios with exclusively equality constraints can be detected via a condition articulated by Henson, Lal and Pusey (HLP). Considering all scenarios with up to 4 observed variables, which number in the thousands, we are able to resolve all but three causal scenarios, providing evidence that the HLP condition is, in fact, exhaustive.

× Marco Erba, Paolo Perinotti, Davide Rolino, and Alessandro Tosini

A minimalist approach to operational theories

We explore the concept of minimalism within the frameworks of operational theories by developing two classes of theories: Minimal Operational Probabilistic Theories (MOPTs) and Minimal Strongly causal Operational Probabilistic Theories (MSOPTs). These classes of Operational Probabilistic Theories (OPTs) are characterized by the fact that the set of allowed operations with non-trivial input and output systems is restricted to the minimum possible. We show that these OPTs, even when allowing for conditioning if entanglement is present, satisfy the properties of no-information without disturbance, the fact that extracting information from a system irreversibly alters its state, and irreversibility, and that they do not admit a broadcasting channel. Furthermore, we show that this holds true even when classicality is assumed by explicitly building two theories, termed Minimal Classical Theory (MCT), a MOPT, and Minimal Strongly causal Bilocal Classical Theory (MSBCT), a MSOPT.
Our results also imply that simpliciality, strong causality and local discriminability represent a minimal set of axioms characterizing Classical Theory.

Extended abstract

× Michael Zurel and Arne Heimendahl

Efficient classical simulation of quantum computation beyond Wigner positivity

We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits. By introducing new CNC-type phase space point operators, we construct a quasiprobability representation for quantum computation which is covariant with respect to the Clifford group and positivity preserving under Pauli measurements, and whose nonnegative sector strictly contains the subtheory of quantum theory described by nonnegative Wigner functions. This allows for a broader class of magic state quantum circuits to be efficiently classically simulated than those covered by the stabilizer formalism and Wigner function methods.

× Shiv Akshar Yadavalli, Nikola Andrejić, and Ravi Kunjwal

Qualitative equivalence between incompatibility and Bell nonlocality

Measurements in quantum theory can fail to be jointly measurable. Like entanglement, this incompatibility of measurements is necessary but not sufficient for violating Bell inequalities. The (in)compatibility relations among a set of measurements can be represented by a joint measurability structure, i.e., a hypergraph whose vertices denote measurements and hyperedges denote all and only compatible sets of measurements. Since incompatibility is necessary for a Bell violation, the joint measurability structure on each wing of a Bell experiment must necessarily be non-trivial, i.e., it must admit a subset of incompatible vertices. Here we show that for any non-trivial joint measurability structure with a finite set of vertices, there exists a quantum realization with a set of measurements that enables a Bell violation, i.e., given that Alice has access to this incompatible set of measurements, there exists a set of measurements for Bob and an entangled state shared between them such that they can jointly violate a Bell inequality. Hence, a non-trivial joint measurability structure is not only necessary for a Bell violation, but also sufficient. We also provide a partial characterization of qubit measurements that are useful for Bell inequality violations in the simplest joint measurability structure of interest, i.e., Specker's scenario, which consists of three pairwise compatible but triplewise incompatible measurements.

× Vivien Vandaele

Qubit-count optimization using ZX-calculus

We propose methods for optimizing the number of qubits in a quantum circuit while preserving the number of non-Clifford gates. One of our approaches consists in reversing, as much as possible, the gadgetization of Hadamard gates, which is a procedure used by some T-count optimizers to circumvent Hadamard gates at the expense of additional qubits. We prove the NP-hardness of this problem and we present an algorithm for solving it. We also propose a more general approach to optimize the number of qubits by showing how it relates to well-known graph-theoretical problems. This approach can be used to optimize the number of qubits for any computational model that can natively be depicted in ZX-calculus, such as the Pauli Fusion computational model which can represent lattice surgery operations. We also show how this method can be used to optimize the number of qubits in a quantum circuit by using the ZX-calculus as an intermediate representation.

× Kinnari Dave, Louis Lemonnier, Romain Pechoux, and Vladimir Zamdzhiev

Combining Quantum and Classical Control

The two main notions of control in quantum programming languages are often referred to as "quantum" control and "classical" control. With the latter, the control flow is based on classical information (potentially resulting from a quantum measurement) and this paradigm is well-suited to mixed-state quantum computation. Whereas with quantum control, we are primarily focused on pure quantum computation and there the "control" is based on superposition. The two paradigms have not mixed well traditionally and they are almost always treated separately. In this work, we show that the paradigms may be combined within the same system. The key ingredients for achieving this are: (1)syntactically: a modality for incorporating pure quantum types into a mixed-state quantum type system; (2) operationally: an adaptation of the notion of "quantum configuration" from quantum lambda calculi, where the quantum data is replaced with pure quantum primitives; (3) denotationally: suitable (sub)categories of Hilbert spaces (for pure computation) and von Neumann algebras (for mixed-state computation in the Heisenberg picture of quantum mechanics).

× Daniel McNulty, Susane Calegari, Joanna Majsak, and Michał Oszmaniec

A Simple and Efficient Joint Measurement Strategy for Estimating Non-Commuting Fermionic Observables and Hamiltonians

We propose a simple scheme to estimate fermionic observables and Hamiltonians relevant in quantum chemistry and correlated fermionic systems. Our approach is based on implementing a joint measurement of a modified (noisy) collection of Majorana monomials of degree-2k in an n mode fermionic system, whose outcome statistics can be reproduced from the (parent) measurement together with an efficient classical post-processing. To realize our measurement we use: (i) a randomization over a set of unitaries that realize products of Majorana fermion operators; (ii) a unitary, sampled at random from a constant-size set of suitably chosen fermionic Gaussian unitaries; (iii) a measurement of fermionic occupation numbers; (iv) suitable post-processing. For any constant k, our scheme can estimate expectation values of all degree-2k Majorana monomials to ε precision using O(n^klog(n)/ε²) measurement rounds, matching the performance offered by fermionic shadow tomography. Furthermore, we prove that our joint measurement is asymptotically optimal, in the sense that no parent POVM exists that reduces the sample complexity by more than a constant factor. In certain settings, such as a rectangular lattice of qubits realizing an n mode fermionic system via the Jordan-Wigner transformation, our parent measurement for Majorana pairs and quadruples can be implemented in circuit depth O(n^1/2) with O(n^3/2) two-qubit gates, offering an improvement over fermionic and matchgate classical shadows that require depth O(n) and O(n²) two-qubit gates. We also benchmark our method on molecular Hamiltonians and observe performances comparable to those offered by fermionic classical shadows.

× Boseong Kim and Samson Abramsky

State Independence of Quantum Contextuality on a Pauli Abelian Partial Group

Contextuality is a key feature of quantum information that challenges classical intuitions, providing the basis for constructing explicit proofs of quantum advantage. Among the definitions of quantum contextuality, Kochen and Specker's definition stands out for its state-independent nature, making it particularly effective for applications to quantum algorithmic scenarios. However, it is questionable if Kochen-Specker contextuality indeed implies sheaf-theoretic contextuality, which captures contextuality in a more general sense. Furthermore, it induces another natural question about the condition where the two definitions become equivalent. In this talk, we first review a state-independent all-versus-nothing(AvN) argument and an abelian partial group. Then, we establish the equivalence between Kochen-Specker contextuality and state-independent AvN on an abelian partial group. This equivalence extends to an arbitrary set of measurements through the concept of partial closure. The partial closure formalism is what we have conjectured as a bridge between sheaf-theoretic contextuality and Kochen-Specker contextuality, making those two definitions equivalent. We present a proof of this conjecture on a Pauli abelian partial group and discuss its generalisability to an arbitrary abelian partial group. Overall, an abelian partial group structure can provide a basis for state-independent analysis of quantum contextuality. This state-independent framework will pave the way for a shortcut to applications of contextuality and an intuition into the fundamental attributes of quantum mechanics.

× Alejandro Díaz-Caro, Gilles Dowek, and Octavio Malherbe

From linear logic to quantum control

This talk explores several recent papers by the authors in the quest for a quantum logic founded on the Curry-Howard-Lambek correspondence. We stand in the quantum control paradigm, where the control flow of programs can follow a quantum particle. Our starting point is intuitionistic multiplicative additive linear logic (IMALL) with an extended proof language, the L^S-calculus, allowing to represent matrices, vectors, and measurement-free quantum programs. We then introduce a new logical connective, sup, to express superposition and measurement. Finally, we model this non-deterministic proof-language for IMALL in the category of semimodules over a semiring.

Extended abstract

× Albert Aloy, Thomas Galley, Caroline Jones, Stefan Ludescher, and Markus Müller

Spin-bounded correlations: rotation boxes within and beyond quantum theory

How can detector click probabilities respond to spatial rotations around a fixed axis, in any possible physical theory? Here, we give a thorough mathematical analysis of this question in terms of "rotation boxes", which are analogous to the well-known notion of non-local boxes. We prove that quantum theory admits the most general rotational correlations for spins 0, 1/2, and 1, but we describe a metrological game where beyond-quantum resources of spin 3/2 outperform all quantum resources of the same spin. We prove a multitude of fundamental results about these correlations, including an exact convex characterization of the spin-1 correlations, a Tsirelson-type inequality for spins 3/2 and higher, and a proof that the general spin-J correlations provide an efficient outer SDP approximation to the quantum set. Furthermore, we review and consolidate earlier results that hint at a wealth of applications of this formalism: a theory-agnostic semi-device-independent randomness generator, an exact characterization of the quantum (2,2,2)-Bell correlations in terms of local symmetries, and the derivation of multipartite Bell witnesses. Our results illuminate the foundational question of how space constrains the structure of quantum theory, they build a bridge between semi-device-independent quantum information and spacetime physics, and they demonstrate interesting relations to topics such as entanglement witnesses, spectrahedra, and orbitopes.

× Lorenzo Catani, Thomas Galley, and Tomáš Gonda

Resource-Theoretic Hierarchy of Contextuality for General Probabilistic Theories

In this work we present a hierarchy of generalized contextuality. It refines the traditional binary distinction between contextual and noncontextual theories, and facilitates their comparison based on how contextual they are. Our approach focuses on the contextuality of prepare-and-measure scenarios, described by general probabilistic theories (GPTs). To motivate the hierarchy, we define it as the resource ordering of a novel resource theory of GPT-contextuality. The building blocks of its free operations are classical systems and GPT-embeddings. The latter are simulations of one GPT by another, which preserve the operational equivalences and thus cannot generate contextuality. Noncontextual theories can be recovered as least elements in the hierarchy. We then define a new contextuality monotone, called classical excess, given by the minimal error of embedding a GPT within an infinite classical system. In addition, we show that the optimal success probability in the parity oblivious multiplexing game also defines a monotone in our resource theory. We end with a discussion of a potential interpretation of the non-free operations of the resource theory of GPT-contextuality as expressing a kind of information erasure.

× Quanlong Wang, Boldizsár Poór, and Razin A. Shaikh

Completeness of qufinite ZXW calculus, a graphical language for finite-dimensional quantum theory

Finite-dimensional quantum theory serves as the theoretical foundation for quantum information and computation. Mathematically, it is formalized in the category FHilb, comprising all finite-dimensional Hilbert spaces and linear maps between them. However, there has not been a graphical language for FHilb which is both universal and complete and thus incorporates a set of rules rich enough to derive any equality of the underlying formalism solely by rewriting. In this paper, we introduce the qufinite ZXW calculus - a graphical language for reasoning about finite-dimensional quantum theory. We set up a unique normal form to represent an arbitrary tensor and prove the completeness of this calculus by demonstrating that any qufinite ZXW diagram can be rewritten into its normal form. This result implies the equivalence of the qufinite ZXW calculus and the category FHilb, leading to a purely diagrammatic framework for finite-dimensional quantum theory with the same reasoning power. In addition, we identify several domains where the application of the qufinite ZXW calculus holds promise. These domains include spin networks, interacting mixed-dimensional systems in quantum chemistry, quantum programming, high-level description of quantum algorithms, and mixed-dimensional quantum computing. Our work paves the way for a comprehensive diagrammatic description of quantum physics, opening the doors of this area to the wider public.

× Uta Meyer, Ivan Supic, Frédéric Grosshans, and Damian Markham

Bell Nonlocality from Wigner Negativity in Qudit Stabilizer States

Nonlocality is an essential concept that distinguishes quantum from classical models and has been extensively studied in systems of qubits.
For higher-dimensional systems, certain results for their two-level counterpart, like Bell violations with stabilizer states and Clifford operators, do not generalize.
However, similar to systems with infinite dimension, Wigner negativity is necessary for nonlocality in qudit systems.
We propose a family of Bell inequalities that inquire correlations related to the Wigner negativity of stabilizer states under the adjoint action of a generalization of the qubit π/8 gate, which, in the bipartite case, is an abstraction of the CHSH inequality.
The classical bound is simple to compute, and a specified stabilizer state maximally violates the inequality among all qudit states based on the Wigner negativity and the inequality between the square and the maximum norm.
Moreover, the Bell operator not only serves as a measure for the singlet fraction but also quantifies the volume of Wigner negativity.
Additionally, we demonstrate deterministic violations and violations with a constant number of measurements for the Bell state, relying on operators innate to higher-dimensional systems than the qudit at hand.

Extended abstract

× Francisco J. R. Ruiz, Tuomas Laakkonen, Johannes Bausch, Matej Balog, Mohammadamin Barekatain, Francisco J. H. Heras, Alexander Novikov, Nathan Fitzpatrick, Bernardino Romera-Paredes, John van de Wetering, Alhussein Fawzi, Konstantinos Meichanetzidis, and Pushmeet Kohli

Quantum Circuit Optimization with AlphaTensor

A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e., minimizing the number of T gates that are needed to implement a given circuit. To achieve this, we develop AlphaTensor-Quantum, a method based on deep reinforcement learning that exploits the relationship between optimizing T-count and tensor decomposition. Unlike existing methods for T-count optimization, AlphaTensor-Quantum can incorporate domain-specific knowledge about quantum computation and leverage gadgets, which significantly reduces the T-count of the optimized circuits. AlphaTensor-Quantum outperforms the existing methods for T-count optimization on a set of arithmetic benchmarks (even when compared without making use of gadgets). Remarkably, it discovers an efficient algorithm akin to Karatsuba's method for multiplication in finite fields. AlphaTensor-Quantum also finds the best human-designed solutions for relevant arithmetic computations used in Shor's algorithm and for quantum chemistry simulation, thus demonstrating it can save hundreds of hours of research by optimizing relevant quantum circuits in a fully automated way.

× Samson Abramsky, Rui Soares Barbosa, and Amy Searle

Combining Contextuality and Causality: a game semantics approach

We develop an approach to combining contextuality with causality, which is general enough to cover causal background structure, adaptive measurement-based quantum computation, and causal networks. The key idea is to view contextuality as arising from a game played between Experimenter and Nature, allowing for causal dependencies in the actions of both the Experimenter (choice of measurements) and Nature (choice of outcomes).

Extended abstract

× James Hefford and Matt Wilson

A Profunctorial Semantics for Quantum Supermaps

We identify morphisms of strong profunctors as a categorification of quantum supermaps. These black-box generalisations of diagrams-with-holes are hence placed within the broader field of profunctor optics, as morphisms in the category of copresheaves on concrete networks. This enables the first construction of abstract logical connectives such as tensor products and negations for supermaps in a totally theory-independent setting. These logical connectives are found to be all that is needed to abstractly model the key structural features of the quantum theory of supermaps: black-box indefinite causal order, black-box definite causal order, and the factorisation of definitely causally ordered supermaps into concrete circuit diagrams. We demonstrate that at the heart of these factorisation theorems lies the Yoneda lemma and the notion of representability.

× Adrian Lehmann, Ben Caldwell, Bhakti Shah, and Robert Rand

VyZX: Formal Verification of a Graphical Quantum Language with automated structural rewrites

ZX-diagrams are typically represented as adjacency-based graphs, reflecting the guiding principle that “only connectivity matters”. In the context of formal theorem provers like Coq, however, such graphs are difficult to reason about, especially when we seek to give them semantics. To address this gap, we build VyZX, a verified library for reasoning about the ZX-calculus, using inductive constructs that arise naturally from category theoretic definitions. One of the issues arising from this representation is that we explicitly encode associativity information that can be an obstacle to reasoning about connectivity. To address this, we present DC⇕AC, a solver to automatically reason about associativity structures built on top of the e-graph solver egg. egg performs equivalence saturation with all possible structural rewrites in an efficient manner. We incorporate egg into VyZX to allow easy rewriting with the rules of the ZX-calculus.

Extended abstract

× Amy Searle, Rui Soares Barbosa, and Samson Abramsky

Mapping temporal correlations to contextuality correlations

We study temporal correlations in a simple setup using a sheaf-theoretic framework in the spirit of Abramsky and Brandenburger's sheaf-theoretic approach to contextuality; the setup consists of a system and a set of measurement sequences which are performed in turn on the system, thereby producing outcomes with a particular probability. Nonclassicality then coincides with obstructions to the existence of a global section—or of a global strategy, as we will prefer to call them—as in the case of contextuality. We limit the amount of information that can be signalled; in particular, when a deterministic system is measured the outcome can only depend upon a subset of previous measurement choices (which for Bell scenarios becomes previous measurement settings). This can be thought of as a restricted type of memory, and we show that in the case that no measurements are stored we recover the macrorealistic correlations which were advocated, for example, by Leggett and Garg, and that when all measurements are stored this corresponds to a system with maximal memory, and obtain the setup studied by Gogioso and Pinzani. We then show that for each signalling depth, there exists a map from the temporal setup to a contextuality setup, such that every set of nonclassical temporal correlations on the former corresponds to a set of contextual correlations on the latter. Doing so allows us to utilise a result from Vorob'ev, originating in the realm of game theory, in order to say, for any temporal setup, whether nonclassical correlations can arise. We demonstrate that this Vorob'ev-type result can be extended to the case in which outcomes as well as measurements can be stored in memory.

Extended abstract

× Matt Wilson and Nick Ormrod

On the Origin of Linearity and Unitarity in Quantum Theory

We reconstruct the transformations of quantum theory using a physically motivated postulate. This postulate states that transformations should be locally applicable, and recovers the linear unitary maps from pure quantum theory, as well as the completely positive, trace-preserving maps from mixed quantum theory. Notably, in the pure case, linearity with respect to the superposition rule on Hilbert spaces is derived rather than assumed (and without any continuity assumptions).

× Nicolas Heurtel

A Complete Graphical Language for Linear Optical Circuits with Finite-Photon-Number Sources and Detectors

Linear optical circuits can be used to manipulate the quantum states of photons as they pass through components including beam splitters and phase shifters. Those photonic states possess a particularly high level of expressiveness, as they reside within the bosonic Fock space, an infinite-dimensional Hilbert space. However, these basic components may not be sufficient to efficiently perform all computations of interest, such as universal quantum computation. To address this limitation it is common to add auxiliary sources and detectors, which enable projections onto auxiliary photonic states and thus increase the versatility of the processes. In this paper, we introduce the LOfi-calculus, a graphical language to reason on the infinite-dimensional bosonic Fock space with circuits composed of four core elements of linear optics: the phase shifter, the beam splitter, and auxiliary sources and detectors with bounded photon number. We present an equational theory that we prove to be complete: two LOfi-circuits represent the same quantum process if and only if one can be transformed into the other with the rules of the LOfi-calculus. We give a unique and compact universal form for such circuits.

× Hector Bombin, Daniel Litinski, Naomi Nickerson, Fernando Pastawski, and Sam Roberts

Unifying flavors of fault tolerance with the ZX calculus

There are several models of quantum computation which exhibit shared fundamental fault-tolerance properties. This article makes commonalities explicit by presenting these different models in a unifying framework based on the ZX calculus. We focus on models of topological fault tolerance — specifically surface codes — including circuit-based, measurement-based and fusion-based quantum computation, as well as the recently introduced model of Floquet codes. We find that all of these models can be viewed as different flavors of the same underlying stabilizer fault-tolerance structure, and sustain this through a set of local equivalence transformations which allow mapping between flavors. We anticipate that this unifying perspective will pave the way to transferring progress among the different views of stabilizer fault-tolerance and help researchers familiar with one model easily understand others.

Extended abstract

× Amin Karamlou and Nihil Shah

First Steps in Quantum Finite Model Theory

Spoiler-Duplicator games such as the Ehrenfeucht-Fraïssé and pebble games are of central importance in finite model theory. In this work we study a quantum variant of these game. Our approach is guided by the recent categorical characterisation of the games in terms of comonads on the category of relational structures. We show that it is possible to define a distributive law of game comonads over the quantum monad, whose Kleisli morphisms correspond to perfect winning strategies in the non-local structure homomorphism game. In order to prove this result we must introduce and work with a generalisation of relational structures, which we dub commeasurable structures. The existence of a distributive law provides a positive answer to an open question of Abramsky et al. and allows us to define a biKleisli category, whose morphisms we characterise as winning strategies for Duplicator in a quantum version of the existential positive versions of the Ehrenfeucht-Fraïssé and pebble games. We also introduce a notion of quantum satisfiability for first-order logic formulas and extend the well-known correspondence between spoiler-duplicator games and fragments of first-order logic to a quantum setting.

× Kathleen Barsse, Paolo Perinotti, Alessandro Tosini, and Leonardo Vaglini

Causal influence versus signalling for interacting quantum channels

A causal relation between quantum agents, say Alice and Bob, is necessarily mediated by an interaction. Modelling the last one as a reversible quantum channel, an intervention of Alice can have causal influence on Bob's system, modifying correlations between Alice and Bob's systems. Causal influence between quantum systems necessarily allows for signalling. Here we prove a mismatch between causal influence and signalling via direct computation of the two quantities for the Cnot gate. Finally we show a continuity theorem for causal effects of unitary channels: a channel has small causal influence iff it allows for small signalling.

Extended abstract

× Pieter Claeys, Austen Lamacraft, and Jamie Vicary

From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics

Dual-unitary brickwork circuits are an exactly-solvable model for many-body chaotic quantum systems, based on 2-site gates which are unitary in both the time and space directions. Prosen has recently described an alternative model called 'dual-unitary interactions round-a-face', which we here call 'clockwork', based on 2-controlled 1-site unitaries composed in a non-brickwork structure, yet with many of the same attractive global properties. We present a 2-categorical framework that simultaneously generalizes these two existing models, and use it to show that brickwork and clockwork circuits can interact richly, yielding new types of generalized heterogeneous circuits. We show that these interactions are governed by quantum combinatorial data, which we precisely characterize. These generalized circuits remain exactly-solvable and we show that they retain the attractive features of the original models such as single-site correlation functions vanishing everywhere except on the causal light-cone. Our presented framework allows us to directly extend the notion of solvable initial states to these biunitary circuits, which are shown to result in maximal entanglement growth and exact thermalization after finitely many time steps under biunitary circuit dynamics.

Extended abstract

× Min-Hsiu Hsieh, Leandro Mendes, Michael de Oliveira, and Sathyawageeswar Subramanian

Quantum Circuits surpass Biased Threshold Circuits in Constant-Depth

Shallow-depth quantum circuits with gates of bounded fan-in have been demonstrated to achieve computational advantages over shallow-depth classical circuits, even allowing for unbounded fan-in (AC⁰). Despite their versatility, these computational models are known to be less powerful than Polynomial Threshold Function (PTF) circuits, which serve as a natural model for neural networks and exhibit enhanced expressivity and computational capabilities. We prove that PTF circuits with a constant number of layers, when biased (having the activation region of their gates limited), fail to solve certain computational (relational) problems that quantum circuits of constant depth can solve. Furthermore, we prove such a separation for a family of problems, one for each prime qudit dimension. We prove all of these separations via correlation bounds for average-case hardness. We also establish a tight lower bound on the size of biased PTF circuits that can solve a specific relational problem exactly. This allows us to significantly reduce the estimated resource requirements for potential demonstrations of quantum advantage.
The main challenges in this area of research arise in establishing the classical lower bounds, and in designing non-local games with quantum-classical gaps in the winning strategy in order to go beyond qubits to higher dimensions. To address the former, we have formulated novel switching lemmas specifically designed for multi-output biased PTF circuits, and have developed a way to assess the difficulty of deriving exact solutions. Our contribution towards the latter is grounded in a novel assortment of non-local games, characterized by an exponential difference between their classical and quantum success probabilities. Finally, our technical developments could be of more general and independent interest.

Extended abstract

× Nick Ormrod and Jonathan Barrett

Quantum Influences and Event Relativity

We develop an approach to decoherence that is entirely based on quantum causal structures, and not on quantum states. We show that, relative to subsets of unitarily interacting subsystems, unique classical structures emerge from causal decoherence. This allows us to propose a precise and realistic interpretation of quantum theory as a description of relational events and their emergence from causal structure. The interpretation recovers the statistics from standard quantum theory, while providing clear resolutions to various quantum paradoxes. Our framework brings together ideas from quantum causal models, relational quantum mechanics, and consistent histories.
(This talk would be based on https://arxiv.org/pdf/2401.18005.pdf, but would focus a bit more on the idea of causal decoherence that underpins the interpretation, and a bit less on the interpretation itself — hence the slightly different abstract.)

× Tatsuki Odake, Hlér Kristjánsson, Philip Taranto, and Mio Murao

Universal algorithm for transforming Hamiltonian eigenvalues

Manipulating Hamiltonians governing physical systems has found a broad range of applications, from quantum chemistry to semiconductor design. In this work, we provide a new way of manipulating Hamiltonians, by transforming their eigenvalues while keeping their eigenstates unchanged. We develop a universal algorithm that deterministically implements any desired (suitably differentiable) function on the eigenvalues of any unknown Hamiltonian, whose positive-time and negative-time dynamics are given as a black box. Our algorithm uses correlated randomness to efficiently combine two subroutines—namely controlization and Fourier series simulation—exemplifying a general compilation procedure that we develop. The time complexity of our algorithm is significantly reduced using compilation compared to a naive concatenation of the subroutines and outperforms similar methods based on the quantum singular value transformation. Finally, to circumvent the need for the negative-time dynamics, we present a universal algorithm to transform positive-time to negative-time dynamics without adding an auxiliary qubit, which could also be of standalone interest.

Extended abstract

× Danilo Fucci and Renato Angelo

Theory-Independent Realism

The distinctive features of quantum mechanics, which set it apart from other physical theories, challenge our notions of realism. Recovering realism from purely philosophical grounds, a quantitative and operational criterion was proposed in the past, but solely for the context of quantum mechanics. We use a framework of generalized probabilistic theories to expand the notion of realism for a theory-independent context, providing a criterion uniquely based on the probabilities assigned to measurement outcomes. More so, using robustness and the Kullback-Leibler divergence, we propose quantifiers for the realism of arbitrary physical properties given a particular state of a generic physical theory. These theory-independent quantifiers are then employed in quantum mechanics and we investigate their relation with another well-established irrealism measure.

× Stefano Gogioso and Nicola Pinzani

Local fraction in Static Causal Orders

In this talk, we introduce a notion of local fraction for experiments taking place against arbitrary static causal backgrounds—greatly generalising previous results on no-signalling scenarios—and we explicitly formulate a linear program to compute this quantity. We derive a free characterisation of causal functions which allows us to efficiently construct the matrices required to perform concrete calculations. We demonstrate our techniques by analysing the local fraction of a novel example involving two Bell tests in interleaved causal order.

× Lorenzo Giannelli and Giulio Chiribella

Information-theoretic derivation of energy and speed bounds

Information-theoretic insights have proven fruitful in many areas of quantum physics. But can the fundamental dynamics of quantum systems be derived from purely information-theoretic principles, without resorting to Hilbert space structures such as unitary evolution and self-adjoint observables? Here we provide a model where the dynamics originates from a condition of informational non-equilibrium, the deviation of the system's state from a reference state associated to a field of identically prepared systems. Combining this idea with three basic information-theoretic principles, we derive a notion of energy that captures the main features of energy in quantum theory: it is observable, bounded from below, invariant under time-evolution, in one-to-one correspondence with the generator of the dynamics, and quantitatively related to the speed of state changes. Our results provide an information-theoretic reconstruction of the Mandelstam-Tamm bound on the speed of quantum evolutions, thus establishing a bridge between dynamical and information-theoretic notions.

Extended abstract

× Farid Shahandeh, Theodoros Yianni, and Mina Doosti

Contextuality of Cloning via Dimensional Witnesses

The no-cloning theorem, a fundamental principle in quantum information processing and cryptography, states that an unknown quantum state cannot be exactly and deterministically cloned. Due to the lack of such limitation for copying classical bits, no-cloning is often considered a genuinely nonclassical property of quantum mechanics. While perfect quantum cloning is impossible, certain quantum cloning machines can produce approximate copies with bounded fidelities. On the other hand, generalized contextuality is also known to be a bona fide quantum features. In this work, we address the relationship between approximate cloning and contextuality, demonstrating that all main classes of approximate cloning do not admit a noncontextual ontological model.

× Giovanni de Felice, Boldizsár Poór, and Lia Yeh

Fusion and flow: formal protocols to reliably build photonic graph states

Photonics has been the platform of reference for implementations of measurement-based quantum computing (MBQC), with recently proposed fusion-based architectures promising to achieve fault-tolerance. In these approaches, graph states are constructed by performing probabilistic entangling measurements on a supply of small resource states. Modeling the different levels in this architecture requires the interplay of linear algebraic, stochastic, and control flow structures, that have yet to be put together into a unified formal language to verify and simulate optical protocols that implement fusion-based computations. This paper develops a framework for reasoning about different levels of photonic quantum computing by bringing together linear optics, MBQC, and dataflow programming. We start by defining a graphical language combining linear optical circuits and the ZX calculus to reason about dual-rail qubits. We use it to fully characterize the kinds of fusion measurements which induce Pauli errors and are thus correctable using flow structure on a target MBQC graph. We then define a dataflow programming language for optical protocols that construct photonic cluster states. Protocols can be efficiently verified by graphical rewriting and recursive reasoning. We use the language to prove the correctness of new repeat-until-success protocols for the realization of arbitrary fusions. We present an entirely graphical proof that linear optics, entangled photon sources, active switching, and classical feed-forward suffice to build arbitrary MBQC patterns and hence achieve universal quantum computation. Our results pave the way for developing verified compilation algorithms for photonic quantum computing.

× Jacopo Surace

A theory of Inaccessible Information

Out of the many lessons quantum mechanics seems to teach us, one is that it seems there are things we cannot experimentally have access to. There is, indeed, a fundamental limit to our ability to experimentally explore the world. In this work we accept this lesson as a fact and we build a general theory based on this principle. We start by assuming the existence of statements whose truth value is not experimentally accessible. That is, there is no way, not even in theory, to directly test if these statements are true or false. We further develop a theory in which experimentally accessible statements are a union of a fixed minimum number of inaccessible statements. For example, the value of truth of the statements A and B is not accessible, but the value of truth of the statement “A or B" is accessible. We do not directly assume probability theory, we exclusively define experimentally accessible and inaccessible statements and build on these notions using the rules of classical logic. We find that an interesting structure emerges. Developing this theory, we relax the logical structure, naturally obtaining a derivation of a constrained quasi-probabilistic theory rich in structure that we name theory of inaccessible information. Surprisingly, the simplest model of theory of inaccessible information is the qubit in quantum mechanics. Along the path for the construction of this theory, we characterise and study a family of multiplicative information measures that we call inaccessibility measures.

× Aleks Kissinger, Neil J. Ross, and John van de Wetering

Catalysing Completeness and Universality

A catalysis state is a quantum state that is used to make some desired operation possible or more efficient, while not being consumed in the process. Recent years have seen catalysis used in state-of-the-art protocols for implementing magic state distillation or small angle phase rotations. In this paper we will see that we can also use catalysis to prove that certain gate sets are computationally universal, and that we can use them to extend completeness results of graphical languages to larger fragments. In particular, we give a simple proof of the computational universality of the CS+Hadamard gate set using the catalysis of a T gate using a CS gate, which sidesteps the more complicated analytic arguments of the original proof by Kitaev. This then also gives us a simple self-contained proof of the computational universality of Toffoli+Hadamard. Additionally, We show that the phase-free ZH-calculus can be extended to a larger complete fragment, just by using a single catalysis rule (and one scalar rule).

× Marco Erba, David Schmid, John Selby, and Sina Soltani

A noncontextual ontological model for bilocal classical theory

In this paper we construct a generalised noncontextual ontological model for the theory known as bilocal classical theory. From the point of view of research into generalised noncontextuality, this is interesting as it is, to our knowledge, only the second time that such a model has been constructed for an entire theory of physics, as opposed to just some simple scenario within the theory. Moreover, it is the first time that such a model has been constructed for a theory which fails to be locally tomographic. In particular, this shows that the assumption of local tomography underpinning the structure theorem in [1] is a genuine limitation of the theorem. From the point of view of research into generalised probabilistic theories and bilocal clasical theory in particular, this result is interesting in that it refutes the conjecture of [2] which states that there is no local-realist ontological model for the theory. Moreover, the ontological model underpinning bilocal classical theory is in many ways much simpler to work with than the original formulation of the theory, which, in particular, opens the door to generalisations to applying this idea to other generalised probabilistic theories.
1- Schmid, D., Selby, J. H., Pusey, M. F., & Spekkens, R. W. (2020). A structure theorem for generalized-noncontextual ontological models. arXiv preprint arXiv:2005.07161.
2- D'Ariano, G. M., Erba, M., & Perinotti, P. (2020). Classicality without local discriminability: Decoupling entanglement and complementarity. Physical Review A, 102(5), 052216.

× Alexander Wilce

Compounding and Coarse-Graining as Monads

Two very basic constructions involving general probabilistic models are the formation of coarse-grained versions of experiments, and the formation of branching sequential experiments. The latter allows for the conditioning of states on the results of previous measurements. When one condition on the results of different coarse-grainings of the same previous experiment, the possibility of interference effects arises. Here, I show how to formulate both constructions in terms of monads on a suitable category of (general) probabilistic models. Moreover, I show that these are connected by a distributive law, allowing for a composite monad describing the closure of a probabilistic model under both coarse-graining and sequential measurement. Algebras for these monad are discussed, some lessons are drawn regarding the formation of sequential products of effects, and some questions for further research are adduced.

Extended abstract

× Aleks Kissinger and John van de Wetering

Scalable spider nests (...or how to graphically grok transversal non-Clifford gates)

This is the second in a series of "graphical grokking" papers in which we study how stabiliser codes can be understood using the ZX-calculus. In this paper we show that certain complex rules involving ZX-diagrams, called spider nest identities, can be captured succinctly using the scalable ZX-calculus, and all such identities can be proved inductively from a single new rule using the Clifford ZX-calculus. This can be combined with the ZX picture of CSS codes, developed in the first "grokking" paper, to give a simple characterisation of the set of all transversal diagonal gates at the third level of the Clifford hierarchy implementable in an arbitrary CSS code.

EPTCS 406:79-95, 2024

× Matthew Amy, Neil J. Ross, and Scott Wesley

A Sound and Complete Equational Theory for 3-qubit Toffoli-Hadamard Circuits

We give a sound and complete equational theory for 3-qubit quantum circuits over the Toffoli-Hadamard gate set { X, CX, CCX, H }. That is, we introduce a collection of true equations among Toffoli-Hadamard circuits on three qubits that is sufficient to derive any other true equation between such circuits. To obtain this equational theory, we first consider circuits over the Toffoli-K gate set { X, CX, CCX, K }, where K = HxH. The Toffoli-Hadamard and Toffoli-K gate sets appear similar, but they are crucially different on exactly three qubits. Indeed, in this case, the former generates an infinite group of operators, while the latter generates the finite group of automorphisms of the well-known E8 lattice. We take advantage of this fact, and of the theory of automorphism groups of lattices, to obtain a sound and complete collection of equations for Toffoli-K circuits. We then extend this equational theory to one for Toffoli-Hadamard circuits by leveraging prior work of Li et al. on Toffoli-Hadamard operators.

EPTCS 406:1-43, 2024

× Piotr Mitosek

Pauli flow on open graphs with unknown measurement labels

One-way quantum computation, or measurement-based quantum computation, is a universal model of quantum computation alternative to the circuit model. The computation progresses by measurements of a pre-prepared resource state together with corrections of undesired outcomes via applications of Pauli gates to yet unmeasured qubits. The fundamental question of this model is determining whether computation can be implemented deterministically. Pauli flow is one of the most general structures guaranteeing determinism. It is also essential for polynomial time ancilla-free circuit extraction. It is known how to efficiently determine the existence of Pauli flow given an open graph together with a measurement labelling (a choice of measurements to be performed).
In this work, we focus on the problem of deciding the existence of Pauli flow for a given open graph when the measurement labelling is unknown. We show that this problem is in RP by providing a random polynomial time algorithm. To do it, we extend previous algebraic interpretations of Pauli flow, by showing that, in the case of X and Z measurements only, flow existence corresponds to the right-invertibility of a matrix derived from the adjacency matrix. We also use this interpretation to show that the number of output qubits can always be reduced to match the number of input qubits while preserving the existence of flow.

EPTCS 406:117-136, 2024

× Andrew N. Glaudell, Neil J. Ross, John van de Wetering, and Lia Yeh

Exact Synthesis of Multiqutrit Clifford-cyclotomic Circuits

It is known that the matrices that can be exactly represented by a multiqubit circuit over the Toffoli+Hadamard, Clifford+T , or, more generally, Clifford-cyclotomic gate set are precisely the unitary matrices with entries in the ring Z[1/2, ζ_k], where k is a positive integer that depends on the gate set and ζ_k is a primitive 2^k-th root of unity. In the present paper, we establish an analogous correspondence for qutrits. We define the multiqutrit Clifford-cyclotomic gate set of degree 3^k by extending the classical qutrit gates X, CX, and CCX with the Hadamard gate H and the Tk gate Tk = diag(1, ω_k, ω_k²), where ω_k is a primitive 3^k-th root of unity. This gate set is equivalent to the qutrit Toffoli+Hadamard gate set when k=1, and to the qutrit Clifford+Tk gate set when k > 1. We then prove that a 3ⁿ×3ⁿ unitary matrix U can be represented by an n-qutrit circuit over the Clifford-cyclotomic gate set of degree 3^k if and only if the entries of U lie in the ring Z[1/3, ω_k].

EPTCS 406:44-62, 2024

× Dichuan Gao

The Qudit ZH Calculus for Arbitrary Finite Fields: Universality and Application

We propose a generalization of the graphical ZH calculus to qudits of prime-power dimensions q = p^t, implementing field arithmetic in arbitrary finite fields. This is an extension of a previous result by Roy et.al. which implemented arithmetic of prime-sized fields; and an alternative to a result by de Beaudrop which extended the ZH to implement cyclic-ring arithmetic in ℤ / qℤ rather than field arithmetic in 𝔽_q. We show this generalized ZH calculus to be universal over matrices ℂ^qn → ℂ^qm with entries in the ring ℤ[ω] where &omega, is a pth (not qth!) root of unity. As an illustration of the necessity of such an extension of ZH for field rather than cyclic-ring arithmetic, we offer a graphical description and proof for a quantum algorithm for polynomial interpolation. This algorithm relies on the invertibility of multiplication in non-prime-sized fields, and therefore can only be described in a graphical language that implements field, rather than ring, multiplication.

× Matthew Sutcliffe and Aleks Kissinger

Procedurally Optimised ZX-Diagram Cutting for Efficient T-Decomposition in Classical Simulation

A quantum circuit may be strongly classically simulated with the aid of ZX-calculus by decomposing its t T-gates into a sum of 2^αt classically computable stabiliser terms. In this paper, we introduce a general procedure to find an optimal pattern of vertex cuts in a ZX-diagram to maximise its T-count reduction at the cost of the fewest cuts. Rather than reducing a Clifford+T diagram based on a fixed routine of decomposing its T-gates directly (as is the conventional approach), we focus instead on taking advantage of certain patterns and structures common to such circuits to, in effect, design by automatic procedure an arrangement of spider decompositions that is optimised for the particular circuit. In short, this works by assigning weights to vertices based on how many T-like gates they are blocking from fusing/cancelling and then appropriately propagating these weights through any neighbours which are then blocking weighted vertices from fusing, and so on. Ultimately, this then provides a set of weightings on relevant nodes, which can then each be cut, starting from the highest weighted down. While this is a heuristic approach, we show that, for circuits small enough to verify, this method achieves the most optimal set of cuts possible 71% of the time. Furthermore, there is no upper bound for the efficiency achieved by this method, allowing, in principle, an effective decomposition efficiency α → 0 for highly structured circuits. Even applied to random pseudo-structured circuits (produced from CNOTs, phase gates, and Toffolis), we record the number of stabiliser terms required to reduce all T-gates, via our method as compared to that of the more conventional T-decomposition approaches (namely that of Kissinger and van de Wetering, with α ≈ 0.47), and show consistent improvements of orders of magnitude, with an effective efficiency 0.1 ≲ α ≲ 0.2.

EPTCS 406:63-78, 2024

× Lorenzo Ceragioli, Fabio Gadducci, Giuseppe Lomurno, and Gabriele Tedeschi

Effect Semantics for Quantum Process Calculi

Along with the development of quantum communication protocols, quantum extensions of process calculi have been explored for modelling communicating systems featuring both non-determinism and quantum capabilities. However, recent works have shown that it is surprisingly difficult to define a behavioural equivalence that matches the observational properties prescribed by quantum theory. Moreover, the two proposals explicitly addressing this issue, namely qCCS and lqCCS, do not define an algorithm for deciding equivalence: in order to equate two processes, one has to compare their behaviour under any possible input state. We introduce a new semantic model based on effects, i.e. probabilistic predicates on quantum states that represent their observable properties. We define and investigate the properties of effect distributions and effect labelled transition systems (eLTS), generalizing probability distributions and probabilistic labelled transition systems (pLTS), respectively. We give an eLTS-based semantics for a minimal quantum process calculus, featuring concurrent and non-deterministic behaviour, quantum measurements and unitaries. We give a behavioural equivalence in the form of a bisimilarity relation, and we prove it sound and complete with respect to the purely probabilistic observable behaviour of quantum processes. To the best of our knowledge, ours is the first algorithmically verifiable proposal that abides to the properties of quantum theory.

Extended abstract

× Korbinian Staudacher, Ludwig Schmid, Johannes Zeiher, Robert Wille, and Dieter Kranzlmüller

Multi-controlled Phase Gate Synthesis with ZX-calculus applied to Neutral Atoms Hardware

Quantum circuit synthesis describes the process of converting arbitrary unitary operations into a gate sequence of a fixed universal gate set, usually defined by the operations native to a given hardware platform. Most current synthesis algorithms are designed to synthesize towards a set of single qubit rotations and an additional entangling two qubit gate, such as CX, CZ, or the Molmer Sorensen gate. However, with the emergence of neutral atom based hardware and their native support for gates with more than two qubits, synthesis approaches tailored to these new gate sets become necessary. In this work, we present an approach to synthesize multi controlled phase gates using ZX calculus. By representing quantum circuits as graph like ZX diagrams, one can utilize the distinct graph structure of diagonal gates to identify multi controlled phase gates inherently present in some quantum circuits even if none were explicitly defined in the original circuit. We evaluate the approach on a wide range of benchmark circuits and compare them to the standard Qiskit synthesis regarding its circuit execution time for neutral atom based hardware with native support of multi controlled gates. Our results show possible advantages for current state of the art hardware and represent the first exact synthesis algorithm supporting arbitrary sized multi controlled phase gates.

EPTCS 406:96-116, 2024

× Tuomas Laakkonen, Konstantinos Meichanetzidis, and Bob Coecke

Compositional Quantum Algorithms for Text Processing

Quantum computing and AI have found a fruitful intersection in the field of natural language processing. We focus on the recently proposed DisCoCirc framework for natural language, and propose a quantum adaptation, QDisCoCirc. This is motivated by a compositional approach to rendering AI interpretable: the behavior of the whole can be understood in terms of the behavior of parts, and the way they are put together. For the model-native primitive operation of text similarity, we derive quantum algorithms for fault-tolerant quantum computers to solve the task of question-answering within QDisCoCirc, and show that this is BQP-hard; note that we do not consider the complexity of question-answering in other natural language processing models. Assuming widely-held conjectures, implementing the proposed model classically would require super-polynomial resources. Therefore, it could provide a meaningful demonstration of the power of practical quantum processors. The model construction builds on previous work in compositional quantum natural language processing. Word embeddings are encoded as parameterized quantum circuits, and compositionality here means that the quantum circuits compose according to the linguistic structure of the text. We outline a method for evaluating the model on near-term quantum processors, and elsewhere we report on a recent implementation of this on quantum hardware. In addition, we adapt a quantum algorithm for the closest vector problem to obtain a Grover-like speedup in the fault-tolerant regime for our model. This provides an unconditional quadratic speedup over any classical algorithm in certain circumstances, which we will verify empirically in future work.

EPTCS 406:162-196, 2024

× Tuomas Laakkonen, Konstantinos Meichanetzidis, and John van de Wetering

A Graphical #SAT Algorithm for Formulae with Small Clause Density

We study the counting version of the Boolean satisfiability problem #SAT using the ZH-calculus, a graphical language originally introduced to reason about quantum circuits. Using this, we generalize #SAT to a weighted variant we call #SAT_±, which is complete for the class GapP. We show there is an efficient linear-time reduction from #SAT to #2SAT_±, unlike previous reductions from #SAT to #2SAT which blow up the size of the formula by a polynomial factor. Our main conceptual contribution is that introducing weights to #SAT allows for more efficient translations, and we use this to remove the dependence on clause width k in this case. We observe that DPLL-style algorithms for #2SAT can be adapted to #2SAT_± directly and hence the best-known upper bounds for #2SAT apply. Applying an upper bound for #2SAT in terms of variables gives us upper bounds for #SAT in terms of clauses and variables that are better than O^*(2ⁿ) for small clause densities of m⁄n < 2.25, and improve on previous average-case and worst-case bounds for k ≥ 6 and k ≥ 4, respectively. Applying a similar bound in terms of clauses produces a bound of O^*(1.1740^L) in terms of the length of the formula. These are, to our knowledge, the first non-trivial upper bounds for #SAT that is independent of clause size, and in terms of formula length, respectively. Based on a result of Kutzkov, we find an improved bound on #3SAT for 1.2577 < m⁄n ≤ 7⁄3. Finally, we use this technique to find an upper bound on the complexity of calculating amplitudes of quantum circuits in terms of the total number of gates. Our results demonstrate that graphical reasoning can lead to new algorithmic insights, even outside the domain of quantum computing that the calculus was intended for.

EPTCS 406:137-161, 2024

× Jay Owers, Ekaterina Shutova, and Martha Lewis

Density Matrices for Metaphor Understanding

In physics, density matrices are used to represent mixed states, i.e. probabilistic mixtures of pure states. This concept has previously been used to model lexical ambiguity. In this paper, we consider metaphor as a type of lexical ambiguity, and examine whether metaphorical meaning can be effectively modelled using mixtures of word senses. We find that modelling metaphor is significantly more difficult than other kinds of lexical ambiguity, but that our best-performing density matrix method outperforms simple baselines as well as some neural language models.

EPTCS 406:197-215, 2024

× Anurudh Peduri, Tim Bittner, Luca Witt, Luke Southall, Ina Schaefer, and Michael Walter

Qubrabench: Quantum Benchmarking without Quantum Computers

Quantum algorithms promise significant asymptotic speedups compared to their classical counterparts in several areas such as search, solving linear systems and factoring.
However we find ourselves in the NISQ era, and these speedups are only expected in the future in a fault-tolerant regime.
To better understand which algorithms show promising speedups, we are forced to rely on purely theoretical analyses.
These often capture worst-case complexities, and we are unable to gain insights into how these algorithms would perform on real-world problem instances and data.
To remedy this, one does "hybrid benchmarking", an instrumentation methodology of obtaining quantum costs by using known formulas for basic primitive routines, while computing the expected output of each step by using a state-of-the-art classical implementation.
So far, this has only been done by hand, on a case-by-case basis for each application.
We present Qubrabench, a novel python library that supports hybrid benchmarking to estimate expected quantum and classical query costs for arbitrary programs that use primitives with quantum counterparts.
This enables one to use these primitives in their existing code, by replacing the default primitives, and mark the oracles and data-structures that they would like to obtain query costs for.
Qubrabench supports computing query costs for arbitrarily nested quantum subroutines, by internally using well known theoretical query composition models.
This enables users to gain insights into when and where they could expect quantum speedups for their state-of-the-art algorithms and heuristics.

Extended abstract

× Nadish de Silva, Wilfred Salmon, and Ming Yin

Fast algorithms for classical specifications of stabiliser states and Clifford gates

The stabiliser formalism plays a central role in quantum computing, error correction, and fault-tolerance. Stabiliser states are used to encode quantum data. Clifford gates are those which can be easily performed fault-tolerantly in the most common error correction schemes. Their mathematical properties are the subject of significant research interest.
Numerical experiments are critical to formulating and testing conjectures involving the stabiliser formalism. Conversions between different specifications of stabiliser states and Clifford gates are also important components of classical algorithms for simulating quantum circuits.
In this work, we develop novel mathematical insights concerning stabiliser states and Clifford gates that significantly clarify their descriptions. We then utilise these to provide fast methods for verifying that a vector is a stabiliser state, and interconverting between its specification as amplitudes, a quadratic form, and a check matrix. These methods are in turn leveraged to rapidly check if a given unitary matrix is a Clifford gate and to interconvert between the matrix of a Clifford gate and its compact specification as a stabiliser tableau.
For example, we extract the stabiliser tableau of a Clifford gate matrix with N² entries in O(NlogN) time. Remarkably, it is not necessary to read all the elements of a Clifford matrix to extract its stabiliser tableau. This represents a superexponential speedup over the best known methods.
Our methods outperform the best-known brute force methods by some orders of magnitude with asymptotic improvements that are exponential in the number of qubits. We provide example implementations of our algorithms in Python.

×

List of posters

1. Adriano Lusso and Victor Onofre: Simulating unknown qubit-unitary inversion with zero-noise extrapolation
2. Alejandro Díaz-Caro, Gilles Dowek, Malena Ivnisky, and Octavio Malherbe: Polymorphic intuitionistic linear logic and its connection to quantum computing
3. Alejandro Díaz-Caro, Octavio Malherbe, and Rafael Romero: A multiple-basis quantum lambda calculus
4. Amanda Maria Fonseca, Vinicius Rossi, John Selby, and Ana Belén Sainz: Robustness of contextuality under different types of noise with a linear program and an application for parity-oblivious multiplexing tasks
5. Amrapali Sen, Matthias Salzger, and Łukasz Rudnicki: An operational analysis of superluminal observers
6. Ana Belén Sainz: Postquantum steering in multipartite characterised situations
7. Beata Zjawin, Matty Hoban, Paul Skrzypczyk, and Ana Belén Sainz: Activation of post-quantumness in generalized EPR scenarios
8. Carlos Miguel Soto and Alejandro Díaz-Caro: Soundness and Completeness for a Linear Logic Calculus Designed for Quantum Computing
9. Dohun Kim, Minyoung Kim, Sarah Meng Li, and Michele Mosca: Improving the Fidelity of CNOT Circuits on NISQ Hardware
10. Dongho Lee: Simulating Boolean Logic in Category of Halfspaces and Linear Maps
11. Ignacio Perito, María Balanzó-Juandó, Máté Farkas, and Antonio Acín: Robust self-testing of bipartite entanglement
12. Jakob Murauer, Korbinian Staudacher, Wolfgang Gehrke, and Michaela Geierhos: Towards Masked Language Modeling in Quantum Natural Language Processing
13. Jiaxin Huang, Aleks Kissinger, Sarah Meng Li, John van de Wetering, and Lia Yeh: Repping Stabilizer Codes in ZX: Stabilizer Tableaus, Encoder Circuits, and Code Transformations
14. Laura Henderson, Rishi Goel, and Sally Shrapnel: Quantum kernel machine learning with continuous variables
15. Lorenzo Saraiva, Hermann Haeusler, and Vaston Costa: Quantum Algorithm for Multiplicative Linear Logic
16. Maiyuren Srikumar, Angela Karanjai, and Stephen D. Bartlett: Contextuality implies the antidistinguishability of states
17. Marco Erba: Are local-classicality and generalised-noncontextuality equivalent notions of classical explainability?
18. Masanao Ozawa: Operational Meanings of Conjunction and Disjunction for Incompatible Quantum Propositions
19. Matthias Salzger and John H. Selby: A decompositional framework for process theories in spacetime
20. Naim Elias Comar, Danilo Cius, Luis Felipe Santos da Silva, Rafael Wagner, and Bárbara Lopes Amaral: Transformation contextuality witness in heat flow inversion
21. Nicolás Monzón and Alejandro Díaz-Caro: An extension of Lambda-S for multiple basis
22. Patrick Andriolo, Danilo Cius, and Naim Comar: Quantifying Bell nonlocality on gravitationally entangled qudits
23. Paulo Cavalcanti, Vinicius Rossi, Amanda Fonseca, John Selby, and Ana Belén Sainz: An open-source Pyhon importation of a linear program for testing nonclassicality
24. Quanlong Wang, Richard D. P. East, Razin A. Shaikh, Lia Yeh, and Boldizsár Poór: Penrose Spin Calculus: ZX for SU(2)
25. Richie Yeung, Konstantinos Meichanetzidis, Alexandre Krajenbrink, and François Charton: Teaching small transformers to rewrite ZX diagrams
26. Santiago Cifuentes, Nicolás Ciancaglini, Guido Bellomo, Santiago Figueira, and Ariel Bendersky: Towards exact algorithmic proofs of maximal mutually unbiased bases sets in arbitrary integer dimension
27. Sauradeep Sasmal, Som Kanjilal, and Alok Kumar Pan: Unbounded Sharing of Nonlocality Using local randomness assisted Projective measurement
28. Tom Williams and Andrei Constantin: Maximal Non-Kochen-Specker Sets and a Lower Bound on the Size of Kochen-Specker Sets
29. Vanessa Brzić, Satoshi Yoshida, Mio Murao, and Marco Túlio Quintino: Higher order quantum transformations for known input state
30. William Schober: Circuits as a self-contained graphical language