2023/02/05 by Kyriakos Lotidis, Panayotis Mertikopoulos, Lotidis, Kyriakos +3 · 1 citation
Computer Science · Physics and Astronomy · #37N40 #68Q32 #81Q93 #91B80 #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Primary 91A81 #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #secondary 68T05
paper · pdf · doi:10.48550/arxiv.2302.02333
openalex publication_date 2023/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce a class of learning dynamics for general quantum games, that we call "follow the quantum regularized leader" (FTQL), in reference to the classical "follow the regularized leader" (FTRL) template for learning in finite games. We show that the induced quantum state dynamics decompose into (i) a classical, commutative component which governs the dynamics of the system's eigenvalues in a way analogous to the evolution of mixed strategies under FTRL; and (ii) a non-commutative component for the system's eigenvectors which has no classical counterpart. Despite the complications that this non-classical component entails, we find that the FTQL dynamics incur no more than constant regret in all quantum games. Moreover, adjusting classical notions of stability to account for the nonlinear geometry of the state space of quantum games, we show that only pure quantum equilibria can be stable and attracting under FTQL while, as a partial converse, pure equilibria that satisfy a certain "variational stability" condition are always attracting. Finally, we show that the FTQL dynamics are Poincaré recurrent in quantum min-max games, extending in this way a very recent result for the quantum replicator dynamics.