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View article: Polyhedral Classical Simulators for Quantum Computation
Polyhedral Classical Simulators for Quantum Computation Open
Quantum advantage in computation refers to the existence of computational tasks that can be performed efficiently on a quantum computer but cannot be efficiently simulated on any classical computer. Identifying the precise boundary of effi…
View article: Extremal simplicial distributions on cycle scenarios with arbitrary outcomes
Extremal simplicial distributions on cycle scenarios with arbitrary outcomes Open
Cycle scenarios are a significant class of contextuality scenarios, with the Clauser–Horne–Shimony–Holt scenario being a notable example. While binary outcome measurements in these scenarios are well understood, the generalization to arbit…
View article: Phase space tableau simulation for quantum computation
Phase space tableau simulation for quantum computation Open
We introduce a novel tableau-based classical simulation method for quantum computation, formulated within the phase space framework of the extended stabilizer theory of closed non-contextual operators. This method enables the efficient cla…
View article: Simplicial methods in the resource theory of contextuality
Simplicial methods in the resource theory of contextuality Open
We develop a resource theory of contextuality within the framework of symmetric monoidal categories, extending recent simplicial approaches to quantum contextuality. Building on the theory of simplicial distributions, which integrates homo…
View article: Simplicial effects and weakly associative partial groups
Simplicial effects and weakly associative partial groups Open
In this paper, we introduce a new category of simplicial effects that extends the categories of effect algebras and their multi-object counterpart, effect algebroids. Our approach is based on relaxing the associativity condition satisfied …
View article: No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords
No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords Open
Linear constraint systems (LCS) have proven to be a surprisingly prolific tool in the study of non-classical correlations and various related issues in quantum foundations. Many results are known for the Boolean case, yet the generalisatio…
View article: Classical simulation of universal measurement-based quantum computation using multipartite Bell scenarios
Classical simulation of universal measurement-based quantum computation using multipartite Bell scenarios Open
We introduce a new classical simulation algorithm based on non-signaling polytopes of multipartite Bell scenarios, capable of simulating universal measurement-based quantum computation with single-qubit Pauli measurements. In our model, th…
View article: Simulating Quantum Computation: How Many “Bits” for “It”?
Simulating Quantum Computation: How Many “Bits” for “It”? Open
A recently introduced classical simulation method for universal quantum computation with magic states operates by repeated sampling from probability functions [M. Zurel PRL 260404 (2020)]. This method is closely related to sampling algorit…
View article: On the rank of two-dimensional simplicial distributions
On the rank of two-dimensional simplicial distributions Open
Simplicial distributions provide a framework for studying quantum contextuality, a generalization of Bell's non-locality. Understanding extremal simplicial distributions is of fundamental importance with applications to quantum computing. …
View article: Extremal simplicial distributions on cycle scenarios with arbitrary outcomes
Extremal simplicial distributions on cycle scenarios with arbitrary outcomes Open
Cycle scenarios are a significant class of contextuality scenarios, with the Clauser-Horne-Shimony-Holt (CHSH) scenario being a notable example. While binary outcome measurements in these scenarios are well understood, the generalization t…
View article: The Bloch--Kato conjecture, decomposing fields, and generating cohomology in degree one
The Bloch--Kato conjecture, decomposing fields, and generating cohomology in degree one Open
The famous Bloch--Kato conjecture implies that for a field $F$ containing a primitive $p$ th root of unity, the cohomology ring of the absolute Galois group $G_F$ of $F$ with $\mathbb{F}_p$ coefficients is generated by degree one elements.…
View article: Hidden variable model for quantum computation with magic states on qudits of any dimension
Hidden variable model for quantum computation with magic states on qudits of any dimension Open
It was recently shown that a hidden variable model can be constructed for universal quantum computation with magic states on qubits. Here we show that this result can be extended, and a hidden variable model can be defined for quantum comp…
View article: Twisted simplicial distributions
Twisted simplicial distributions Open
We introduce a theory of twisted simplicial distributions on simplicial principal bundles, which allow us to capture Bell's non-locality, and the more general notion of quantum contextuality. We leverage the classical theory of simplicial …
View article: The operadic theory of convexity
The operadic theory of convexity Open
In this article, we characterize convexity in terms of algebras over a PROP, and establish a tensor-product-like symmetric monoidal structure on the category of convex sets. Using these two structures, and the theory of $\scr{O}$-monoidal …
View article: On the rank of two-dimensional simplicial distributions
On the rank of two-dimensional simplicial distributions Open
Simplicial distributions provide a framework for studying quantum contextuality, a generalization of Bell's non-locality. Understanding extremal simplicial distributions is of fundamental importance with applications to quantum computing. …
View article: The degenerate vertices of the $2$-qubit $Λ$-polytope and their update rules
The degenerate vertices of the $2$-qubit $Λ$-polytope and their update rules Open
Recently, a class of objects, known as $Λ$-polytopes, were introduced for classically simulating universal quantum computation with magic states. In $Λ$-simulation, the probabilistic update of $Λ$ vertices under Pauli measurement yields dy…
View article: Homotopical characterization of strongly contextual simplicial distributions on cone spaces
Homotopical characterization of strongly contextual simplicial distributions on cone spaces Open
This paper offers a novel homotopical characterization of strongly contextual simplicial distributions with binary outcomes, specifically those defined on the cone of a 1-dimensional space. In the sheaf-theoretic framework, such distributi…
View article: Equivariant simplicial distributions and quantum contextuality
Equivariant simplicial distributions and quantum contextuality Open
We introduce an equivariant version of contextuality with respect to a symmetry group, which comes with natural applications to quantum theory. In the equivariant setting, we construct cohomology classes that can detect contextuality. This…
View article: Simplicial techniques for operator solutions of linear constraint systems
Simplicial techniques for operator solutions of linear constraint systems Open
A linear constraint system is specified by linear equations over the group Zd of integers modulo d. Their operator solutions play an important role in the study of quantum contextuality and non-local games. In this paper, we use the theory…
View article: A bundle perspective on contextuality: Empirical models and simplicial distributions on bundle scenarios
A bundle perspective on contextuality: Empirical models and simplicial distributions on bundle scenarios Open
This paper provides a bundle perspective to contextuality by introducing new categories of contextuality scenarios based on bundles of simplicial complexes and simplicial sets. The former approach generalizes earlier work on the sheaf-theo…
View article: Topological Methods for Studying Contextuality: N-Cycle Scenarios and Beyond
Topological Methods for Studying Contextuality: N-Cycle Scenarios and Beyond Open
Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize nonsignaling distributions on contextuality scenarios. This paper studies simplicial distributions on two-dim…
View article: Topological methods for studying contextuality: $N$-cycle scenarios and beyond
Topological methods for studying contextuality: $N$-cycle scenarios and beyond Open
Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize non-signaling distributions on contextuality scenarios. This paper studies simplicial distributions on $2$-di…
View article: Simulating quantum computation: how many "bits" for "it"?
Simulating quantum computation: how many "bits" for "it"? Open
A recently introduced classical simulation method for universal quantum computation with magic states operates by repeated sampling from probability functions [M. Zurel et al. PRL 260404 (2020)]. This method is closely related to sampling …
View article: Simplicial quantum contextuality
Simplicial quantum contextuality Open
We introduce a new framework for contextuality based on simplicial sets, combinatorial models of topological spaces that play a prominent role in modern homotopy theory. Our approach extends measurement scenarios to consist of spaces (rath…
View article: Simplicial techniques for operator solutions of linear constraint systems
Simplicial techniques for operator solutions of linear constraint systems Open
A linear constraint system is specified by linear equations over the group $\ZZ_d$ of integers modulo $d$. Their operator solutions play an important role in the study of quantum contextuality and non-local games. In this paper, we use the…
View article: The role of cohomology in quantum computation with magic states
The role of cohomology in quantum computation with magic states Open
A web of cohomological facts relates quantum error correction, measurement-based quantum computation, symmetry protected topological order and contextuality. Here we extend this web to quantum computation with magic states. In this computa…
View article: Simplicial distributions, convex categories and contextuality
Simplicial distributions, convex categories and contextuality Open
The data of a physical experiment can be represented as a presheaf of probability distributions. A striking feature of quantum theory is that those probability distributions obtained in quantum mechanical experiments do not always admit a …
View article: Mermin polytopes in quantum computation and foundations
Mermin polytopes in quantum computation and foundations Open
Mermin square scenario provides a simple proof for state-independent contextuality. In this paper, we study polytopes $\text{MP}_β$ obtained from the Mermin scenario, parametrized by a function $β$ on the set of contexts. Up to combinatori…