Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2311.01363 · Quantum Science and Technology

Application-level benchmarking of quantum computers using nonlocal game strategies

Jim Furches, Sarah Chehade, Kathleen E. Hamilton, Nathan Wiebe, Carlos Ortiz Marrero

Published Jul 18, 2025• 0 citations
arXivHTMLPDF

Abstract

Abstract In a nonlocal game, two noncommunicating players cooperate to convince a referee that they possess a strategy that does not violate the rules of the game. Quantum strategies allow players to optimally win some games by performing joint measurements on a shared entangled state, but computing these strategies can be challenging. We present a variational quantum algorithm to compute quantum strategies for nonlocal games by encoding the rules of a nonlocal game into a Hamiltonian. We show how this algorithm can generate a short-depth optimal quantum strategy for a graph coloring game with a quantum advantage. This quantum strategy is then evaluated on fourteen different quantum hardware platforms to demonstrate its utility as a benchmark. Finally, we discuss potential sources of errors that can explain the observed decreased performance of the executed task and derive an expression for the number of samples required to accurately estimate the win rate in the presence of noise.

DOI
10.1088/2058-9565/adf1c0

Related papers

Nonlocal Games as Cross-Platform Quantum Benchmarks: Exceeding unconditional classical bounds on trapped-ion processors

Anton T. Than, Jim Furches, Debopriyo Biswas +15 more

Nonlocal games provide application-level benchmarks for quantum hardware whose classical performance bounds are information-theoretic, holding against all classical strategies regardless of computational resources. We implement a 14-vertex graph coloring game, the smallest graph exhibiting a quantum-classical separation for this game type, on four trapped-ion quantum processors across three institutions. One system achieved a win rate that surpasses the classical bound with statistical significance, marking the first violation of a classical bound in a graph coloring nonlocal game on quantum hardware. The remaining systems achieved win rates comparable to the best superconducting processors evaluated on the same game, further illustrating the potential of nonlocal games as cross-architecture quantum benchmarks.

quant-pharXiv:2603.18323•Mar 20, 2026•0 citations

Decidability of Fully Quantum Nonlocal Games with Noisy Maximally Entangled States

Minglong Qin, Penghui Yao

Abstract This paper considers the decidability of fully quantum nonlocal games with noisy maximally entangled states. Fully quantum nonlocal games are a generalization of nonlocal games, where both questions and answers are quantum and the referee performs a binary POVM measurement to decide whether they win the game after receiving the quantum answers from the players. The quantum value of a fully quantum nonlocal game is the supremum of the probability that they win the game, where the supremum is taken over all the possible entangled states shared between the players and all the valid quantum operations performed by the players. The seminal work $\mathrm{MIP}^*=\mathrm{RE}$~\cite{JNVWY'20,JNVWYuen'20} implies that it is undecidable to approximate the quantum value of a fully nonlocal game. This still holds even if the players are only allowed to share (arbitrarily many copies of) maximally entangled states. This paper investigates the case that the shared maximally entangled states are noisy. We prove that there is a computable upper bound on the copies of noisy maximally entangled states for the players to win a fully quantum nonlocal game with a probability arbitrarily close to the quantum value. This implies that it is decidable to approximate the quantum values of these games. Hence, the hardness of approximating the quantum value of a fully quantum nonlocal game is not robust against the noise in the shared states. This paper is built on the framework for the decidability of non-interactive simulations of joint distributions~\cite{7782969,doi:10.1137/1.9781611975031.174,Ghazi:2018:DRP:3235586.3235614} and generalizes the analogous result for nonlocal games in~\cite{qin2021nonlocal}. We extend the theory of Fourier analysis to the space of super-operators and prove several key results including an invariance principle and a dimension reduction for super-operators. These results are interesting in their own right and are believed to have further applications.

arXiv:2211.10613•Algorithmica•Aug 13, 2025•6 citations

Optimal, and approximately optimal, quantum strategies for $\mathrm{XOR}^{*}$ and $\mathrm{FFL}$ games

Pete Rigas

We analyze optimal, and approximately optimal, quantum strategies in two non-local settings based upon previous investigations of the XOR and CHSH games. By building upon previous arguments due to Ostrev in 2016, {\color{blue}[37]}, which characterized approximately optimal, and optimal, strategies that players Alice and Bob can adopt for increasing their respective winning probabilities, we identify additional applications of the framework for analyzing prospective quantum advantage in other game-theoretic settings. In particular, while it is possible for Alice and Bob to realize quantum advantage if they adopt strategies that are dependent upon entanglement, two-dimensional resource systems, and reversible transformations, the magnitude of the duality gap between the performance of classical and quantum strategies has not yet been classified from the perspective of error bounds. Such bounds are not only dependent upon the winning probability if Alice and Bob leverage entanglement in their strategies but also upon a suitably defined representation-theoretic intertwining operation.

arXiv:2311.12887•Nov 21, 2023•0 citations

Quantum Locality in Game Strategy

Carlos A. Melo-Luna, Cristian E. Susa, Andrés F. Ducuara +2 more

Game theory is a well established branch of mathematics whose formalism has a vast range of applications from the social sciences, biology, to economics. Motivated by quantum information science, there has been a leap in the formulation of novel game strategies that lead to new (quantum Nash) equilibrium points whereby players in some classical games are always outperformed if sharing and processing joint information ruled by the laws of quantum physics is allowed. We show that, for a bipartite non zero-sum game, input local quantum correlations, and separable states in particular, suffice to achieve an advantage over any strategy that uses classical resources, thus dispensing with quantum nonlocality, entanglement, or even discord between the players' input states. This highlights the remarkable key role played by pure quantum coherence at powering some protocols. Finally, we propose an experiment that uses separable states and basic photon interferometry to demonstrate the locally-correlated quantum advantage.

arXiv:1609.06389•Scientific Reports•Mar 22, 2017•31 citations

Extended Nonlocal Games

Russo, Vincent

The notions of entanglement and nonlocality are among the most striking ingredients found in quantum information theory. One tool to better understand these notions is the model of nonlocal games; a mathematical framework that abstractly models a physical system. The simplest instance of a nonlocal game involves two players, Alice and Bob, who are not allowed to communicate with each other once the game has started and who play cooperatively against an adversary referred to as the referee. The focus of this thesis is a class of games called extended nonlocal games, of which nonlocal games are a subset. In an extended nonlocal game, the players initially share a tripartite state with the referee. In such games, the winning conditions for Alice and Bob may depend on outcomes of measurements made by the referee, on its part of the shared quantum state, in addition to Alice and Bob's answers to the questions sent by the referee. We build up the framework for extended nonlocal games and study their properties and how they relate to nonlocal games.

arXiv:1704.07375•Apr 24, 2017•3 citations

Consequences and Limits of Nonlocal Strategies

Richard Cleve, Peter Høyer, Ben Toner +1 more

This paper investigates the powers and limitations of quantum entanglement in the context of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement outperform all possible classical strategies. One implication of these examples is that entanglement can profoundly affect the soundness property of two-prover interactive proof systems. We then establish limits on the probability with which strategies making use of entanglement can win restricted types of nonlocal games. These upper bounds may be regarded as generalizations of Tsirelson-type inequalities, which place bounds on the extent to which quantum information can allow for the violation of Bell inequalities. We also investigate the amount of entanglement required by optimal and nearly optimal quantum strategies for some games.

arXiv:quant-ph/0404076•Apr 12, 2004•0 citations
Abstract In a nonlocal game, two noncommunicating players cooperate to convince a referee that they possess a strategy that does not violate the rules of the game. Quantum strategies allow players to optimally win some games by performing joint measurements on a shared entangled state, but computing these strategies can be challenging. We present a variational quantum algorithm to compute quantum strategies for nonlocal games by encoding the rules of a nonlocal game into a Hamiltonian. We show how this algorithm can generate a short-depth optimal quantum strategy for a graph coloring game with a quantum advantage. This quantum strategy is then evaluated on fourteen different quantum hardware platforms to demonstrate its utility as a benchmark. Finally, we discuss potential sources of errors that can explain the observed decreased performance of the executed task and derive an expression for the number of samples required to accurately estimate the win rate in the presence of noise.
Nonlocal games provide application-level benchmarks for quantum hardware whose classical performance bounds are information-theoretic, holding against all classical strategies regardless of computational resources. We implement a 14-vertex graph coloring game, the smallest graph exhibiting a quantum-classical separation for this game type, on four trapped-ion quantum processors across three institutions. One system achieved a win rate that surpasses the classical bound with statistical significance, marking the first violation of a classical bound in a graph coloring nonlocal game on quantum hardware. The remaining systems achieved win rates comparable to the best superconducting processors evaluated on the same game, further illustrating the potential of nonlocal games as cross-architecture quantum benchmarks.
Abstract This paper considers the decidability of fully quantum nonlocal games with noisy maximally entangled states. Fully quantum nonlocal games are a generalization of nonlocal games, where both questions and answers are quantum and the referee performs a binary POVM measurement to decide whether they win the game after receiving the quantum answers from the players. The quantum value of a fully quantum nonlocal game is the supremum of the probability that they win the game, where the supremum is taken over all the possible entangled states shared between the players and all the valid quantum operations performed by the players. The seminal work MIP∗=RE\mathrm{MIP}^*=\mathrm{RE}MIP∗=RE~\cite{JNVWY'20,JNVWYuen'20} implies that it is undecidable to approximate the quantum value of a fully nonlocal game. This still holds even if the players are only allowed to share (arbitrarily many copies of) maximally entangled states. This paper investigates the case that the shared maximally entangled states are noisy. We prove that there is a computable upper bound on the copies of noisy maximally entangled states for the players to win a fully quantum nonlocal game with a probability arbitrarily close to the quantum value. This implies that it is decidable to approximate the quantum values of these games. Hence, the hardness of approximating the quantum value of a fully quantum nonlocal game is not robust against the noise in the shared states. This paper is built on the framework for the decidability of non-interactive simulations of joint distributions~\cite{7782969,doi:10.1137/1.9781611975031.174,Ghazi:2018:DRP:3235586.3235614} and generalizes the analogous result for nonlocal games in~\cite{qin2021nonlocal}. We extend the theory of Fourier analysis to the space of super-operators and prove several key results including an invariance principle and a dimension reduction for super-operators. These results are interesting in their own right and are believed to have further applications.
Optimal, and approximately optimal, quantum strategies for XOR∗\mathrm{XOR}^{*}XOR∗ and FFL\mathrm{FFL}FFL games
We analyze optimal, and approximately optimal, quantum strategies in two non-local settings based upon previous investigations of the XOR and CHSH games. By building upon previous arguments due to Ostrev in 2016, {\color{blue}[37]}, which characterized approximately optimal, and optimal, strategies that players Alice and Bob can adopt for increasing their respective winning probabilities, we identify additional applications of the framework for analyzing prospective quantum advantage in other game-theoretic settings. In particular, while it is possible for Alice and Bob to realize quantum advantage if they adopt strategies that are dependent upon entanglement, two-dimensional resource systems, and reversible transformations, the magnitude of the duality gap between the performance of classical and quantum strategies has not yet been classified from the perspective of error bounds. Such bounds are not only dependent upon the winning probability if Alice and Bob leverage entanglement in their strategies but also upon a suitably defined representation-theoretic intertwining operation.
Game theory is a well established branch of mathematics whose formalism has a vast range of applications from the social sciences, biology, to economics. Motivated by quantum information science, there has been a leap in the formulation of novel game strategies that lead to new (quantum Nash) equilibrium points whereby players in some classical games are always outperformed if sharing and processing joint information ruled by the laws of quantum physics is allowed. We show that, for a bipartite non zero-sum game, input local quantum correlations, and separable states in particular, suffice to achieve an advantage over any strategy that uses classical resources, thus dispensing with quantum nonlocality, entanglement, or even discord between the players' input states. This highlights the remarkable key role played by pure quantum coherence at powering some protocols. Finally, we propose an experiment that uses separable states and basic photon interferometry to demonstrate the locally-correlated quantum advantage.
The notions of entanglement and nonlocality are among the most striking ingredients found in quantum information theory. One tool to better understand these notions is the model of nonlocal games; a mathematical framework that abstractly models a physical system. The simplest instance of a nonlocal game involves two players, Alice and Bob, who are not allowed to communicate with each other once the game has started and who play cooperatively against an adversary referred to as the referee. The focus of this thesis is a class of games called extended nonlocal games, of which nonlocal games are a subset. In an extended nonlocal game, the players initially share a tripartite state with the referee. In such games, the winning conditions for Alice and Bob may depend on outcomes of measurements made by the referee, on its part of the shared quantum state, in addition to Alice and Bob's answers to the questions sent by the referee. We build up the framework for extended nonlocal games and study their properties and how they relate to nonlocal games.
This paper investigates the powers and limitations of quantum entanglement in the context of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement outperform all possible classical strategies. One implication of these examples is that entanglement can profoundly affect the soundness property of two-prover interactive proof systems. We then establish limits on the probability with which strategies making use of entanglement can win restricted types of nonlocal games. These upper bounds may be regarded as generalizations of Tsirelson-type inequalities, which place bounds on the extent to which quantum information can allow for the violation of Bell inequalities. We also investigate the amount of entanglement required by optimal and nearly optimal quantum strategies for some games.