Publications (46)
A bundle perspective on contextuality: Empirical models and simplicial distributions on bundle scenarios
Rui Soares Barbosa, Aziz Kharoof, Cihan Okay
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…
Simulating quantum computation: how many "bits" for "it"?
Michael Zurel, Cihan Okay, Robert Raussendorf
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…
Homotopy colimits of classifying spaces of abelian subgroups of a finite group
Cihan Okay
The classifying space BG of a topological group can be filtered by a sequence of subspaces , using the descending central series of free groups. If is finite, descr…
Classifying space for quantum contextuality
Cihan Okay, Daniel Sheinbaum
We construct a topological space to study contextuality in quantum mechanics. The resulting space is a classifying space in the sense of algebraic topology. Cohomological invariant…
Phase space tableau simulation for quantum computation
Selman Ipek, Atak Talay Yucel, Farzad Shahi +2
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-…
Vertex structure of fiber products of probability polytopes
Aziz Kharoof, Cihan Okay
We develop tools for characterizing vertices of fiber products of polytopes and apply them to simplicial distribution polytopes, a class of probability polytopes arising in quantum…
Topological methods for studying contextuality: -cycle scenarios and beyond
Aziz Kharoof, Selman Ipek, Cihan Okay
Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize non-signaling distributions on contextuality scena…
Simplicial quantum contextuality
Cihan Okay, Aziz Kharoof, Selman Ipek
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 approa…
Commutative classifying space for simplicial groups
Cihan Okay, Pál Zsámboki
In this paper, we introduce a simplicial analog of classifying spaces for commutativity which classify principal bundles with commutativity structure on their transition functions.…
Polyhedral Classical Simulators for Quantum Computation
Cihan Okay
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 c…
Equivalence between contextuality and negativity of the Wigner function for qudits
Nicolas Delfosse, Cihan Okay, Juan Bermejo-Vega +2
Contextuality and negativity of the Wigner function are two notions of non-classicality for quantum systems. Howard, Wallman, Veitch and Emerson proved recently that these two noti…
The cohomological and the resource-theoretic perspective on quantum contextuality: common ground through the contextual fraction
Cihan Okay, Emily Tyhurst, Robert Raussendorf
We unify the resource-theoretic and the cohomological perspective on quantum contextuality. At the center of this unification stands the notion of the contextual fraction. For both…
No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords
Markus Frembs, Cihan Okay, Ho Yiu Chung
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 re…
Phase space simulation method for quantum computation with magic states on qubits
Robert Raussendorf, Juani Bermejo-Vega, Emily Tyhurst +2
We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our…
Contextuality and Wigner function negativity in qubit quantum computation
Robert Raussendorf, Dan E. Browne, Nicolas Delfosse +2
We describe a scheme of quantum computation with magic states on qubits for which contextuality is a necessary resource possessed by the magic states. More generally, we establish…
Simplicial methods in the resource theory of contextuality
Aziz Kharoof, Cihan Okay
We develop a resource theory of contextuality within the framework of symmetric monoidal categories, extending recent simplicial approaches to quantum contextuality. Building on th…
Hidden variable model for quantum computation with magic states on qudits of any dimension
Michael Zurel, Cihan Okay, Robert Raussendorf +1
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,…
Possibilistic collapse and extremality of simplicial distributions
Aziz Kharoof, Cihan Okay
Consistent families of locally defined probability distributions that do not admit a joint global distribution are known as contextual, with primary examples arising in quantum the…
Simplicial techniques for operator solutions of linear constraint systems
Ho Yiu Chung, Cihan Okay, Igor Sikora
A linear constraint system is specified by linear equations over the group $\ZZ_d$ of integers modulo . Their operator solutions play an important role in the study of quantum c…
Classical simulation of universal measurement-based quantum computation using multipartite Bell scenarios
Cihan Okay, Atak Talay Yucel, Selman Ipek
We introduce a new classical simulation algorithm based on non-signaling polytopes of multipartite Bell scenarios, capable of simulating universal measurement-based quantum computa…
The role of cohomology in quantum computation with magic states
Robert Raussendorf, Cihan Okay, Michael Zurel +1
A web of cohomological facts relates quantum error correction, measurement-based quantum computation, symmetry protected topological order and contextuality. Here we extend this we…
Simplicial distributions, convex categories and contextuality
Aziz Kharoof, Cihan Okay
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 obtain…
Double categories for adaptive quantum computation
Cihan Okay, Walker Stern, Redi Haderi +1
Quantum computation admits several models that emphasize different computational primitives and forms of classical control. We develop a unified double categorical framework for de…
Dimension functions for spherical fibrations
Cihan Okay, Ergun Yalcin
Given a spherical fibration over the classifying space of a finite group we define a dimension function for the fold fiber join of where is some large positi…
Topological proofs of contextuality in quantum mechanics
Cihan Okay, Sam Roberts, Stephen D. Bartlett +1
We provide a cohomological framework for contextuality of quantum mechanics that is suited to describing contextuality as a resource in measurement-based quantum computation. This…
Colimits of abelian groups
Cihan Okay
In this paper we study the colimit N_2(G) of abelian subgroups of a discrete group G. This group is the fundamental group of a subspace B(2,G) of the classifying space BG. We descr…
Homotopical approach to quantum contextuality
Cihan Okay, Robert Raussendorf
We consider the phenomenon of quantum mechanical contextuality, and specifically parity-based proofs thereof. Mermin's square and star are representative examples. Part of the info…
Contextuality as a resource for models of quantum computation on qubits
Juan Bermejo-Vega, Nicolas Delfosse, Dan E. Browne +2
A central question in quantum computation is to identify the resources that are responsible for quantum speed-up. Quantum contextuality has been recently shown to be a resource for…
The Bloch--Kato conjecture, decomposing fields, and generating cohomology in degree one
Sunil K. Chebolu, Ján MináÄ, Cihan Okay +2
The famous Bloch--Kato conjecture implies that for a field containing a primitive th root of unity, the cohomology ring of the absolute Galois group of with $\math…
Equivariant simplicial distributions and quantum contextuality
Cihan Okay, Igor Sikora
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 const…
On the rank of two-dimensional simplicial distributions
Cihan Okay
Simplicial distributions provide a framework for studying quantum contextuality, a generalization of Bell's non-locality. Understanding extremal simplicial distributions is of fund…
On the mod- homology of the classifying space for commutativity
Cihan Okay, Ben Williams
We study the mod- homotopy type of classifying spaces for commutativity, , at a prime . We show that the mod- homology of dep…
Simplicial effects and weakly associative partial groups
Cihan Okay, Victor Castillo, Walker H. Stern
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…
The operadic theory of convexity
Redi Haderi, Cihan Okay, Walker H. Stern
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…
Extremal simplicial distributions on cycle scenarios with arbitrary outcomes
Aziz Kharoof, Cihan Okay, Selman Ipek
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 i…
The degenerate vertices of the -qubit -polytope and their update rules
Selman Ipek, Cihan Okay
Recently, a class of objects, known as -polytopes, were introduced for classically simulating universal quantum computation with magic states. In -simulation, the probabili…
No quantum solutions to linear constraint systems from monomial measurement-based quantum computation in odd prime dimension
Markus Frembs, Cihan Okay, Ho Yiu Chung
We combine the study of resources in measurement-based quantum computation (MBQC) with that of quantum solutions to linear constraint systems (LCS). Contextuality of the input stat…
Twisted simplicial distributions
Cihan Okay, Walker H. Stern
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 con…
Commutative d-Torsion K-Theory and Its Applications
Cihan Okay
Commutative -torsion -theory is a variant of topological -theory constructed from commuting unitary matrices of order dividing . Such matrices appear as solutions of li…
Homotopical characterization of strongly contextual simplicial distributions on cone spaces
Aziz Kharoof, Cihan Okay
This paper offers a novel homotopical characterization of strongly contextual simplicial distributions with binary outcomes, specifically those defined on the cone of a 1-dimension…
A computationally universal phase of quantum matter
Robert Raussendorf, Cihan Okay, Dong-Sheng Wang +2
We provide the first example of a symmetry protected quantum phase that has universal computational power. Throughout this phase, which lives in spatial dimension two, the ground s…
Mermin polytopes in quantum computation and foundations
Cihan Okay, Ho Yiu Chung, Selman Ipek
Mermin square scenario provides a simple proof for state-independent contextuality. In this paper, we study polytopes obtained from the Mermin scenario, parametrized…
A hidden variable model for universal quantum computation with magic states on qubits
Michael Zurel, Cihan Okay, Robert Raussendorf
We show that every quantum computation can be described by Bayesian update of a probability distribution on a finite state space. When applied to the model of quantum computation w…
On the extremal points of the -polytopes and classical simulation of quantum computation with magic states
Cihan Okay, Michael Zurel, Robert Raussendorf
We investigate the -polytopes, a convex-linear structure recently defined and applied to the classical simulation of quantum computation with magic states by sampling. There is…
Quasi-exact quantum computation
Dong-Sheng Wang, Guanyu Zhu, Cihan Okay +1
We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling pa…
Spherical posets from commuting elements
Cihan Okay
In this paper we study the homotopy type of the partially ordered set of left cosets of abelian subgroups in an extraspecial -group. We prove that the universal cover of its ner…