Quantum Algorithms and Memory Games

Previous work has shown that injecting quantum principles into game theory, as in the PQ penny flip game, introduces strategies with a quantum advantage over classical strategies [PRL 82, 1052 (1999)]. I consider the single-player game of Memory, where the player identifies matching pairs of face-down cards, and investigate how quantum algorithms provide an improved solution. I focus on Simon's and Grover's Algorithms and search for the best-fitting versions of Memory that may display a quantum advantage. I then compare these quantum strategies to the classical ones and identify the circumstances for which each strategy is optimal.