Variational Methods for Computing Non-Local Quantum Strategies

• URL: http://arxiv.org/abs/2311.01363v2
• Date: Thu, 1 Feb 2024 20:53:11 GMT
• Title: Variational Methods for Computing Non-Local Quantum Strategies
• Authors: Jim Furches, Nathan Wiebe, Carlos Ortiz Marrero
• Abstract summary: 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. We show that our algorithm is capable of generating a short-depth circuit that implements an optimal quantum strategy for a graph coloring game.
• Score: 1.95414377613382
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 develop a variational algorithm for computing strategies of nonlocal games and show that it can yield optimal strategies for small examples of both convex and non-convex games. We show that our algorithm is capable of generating a short-depth circuit that implements an optimal quantum strategy for a graph coloring game. Moreover, we describe how this technique can be run on quantum computers and argue that such circuits will be useful for benchmarking because of their sensitivity to 2-qubit gate noise and application to self-testing. Finally, we demonstrate the use of these strategies experimentally on 11 IBM quantum computers.

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