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arXiv · 2209.04655

Satisfiability Phase Transtion for Random Quantum 3XOR Games

Adam Bene Watts·J. William Helton·Zehong Zhao
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Abstract

Recent results showed it was possible to determine if a modest size 3XOR game has a perfect quantum strategy. We build on these and give an explicit polynomial time algorithm which constructs such a perfect strategy or refutes its existence. This new tool lets us numerically study the behavior of randomly generated 3XOR games with large numbers of questions. A key issue is: how common are pseudotelephathy games (games with perfect quantum strategies but no perfect classical strategies)? Our experiments strongly indicate that the probability of a randomly generated game being pseudotelpathic stays far from 1, indeed it is bounded below 0.15. We also find strong evidence that randomly generated 3XOR games undergo both a quantum and classical "phase transition", transitioning from almost certainly perfect to almost certainly imperfect as the ratio of number of clauses ($m$) to number of questions ($n$) increases. The locations of these two phase transitions appear to coincide at $m/n \approx 2.74$.

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Adam Bene Watts, J. William Helton, Zehong Zhao. 2022-09-10. Satisfiability Phase Transtion for Random Quantum 3XOR Games. https://arxiv.org/abs/2209.04655

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