Quantum Speedups for Zero-Sum Games via Improved Dynamic Gibbs Sampling

Abstract

We give a quantum algorithm for computing an $\epsilon$-approximate Nash equilibrium of a zero-sum game in a $m\times n$ payoff matrix with bounded entries. Given a standard quantum oracle for accessing the payoff matrix our algorithm runs in time $\tilde{O}(\sqrt{m+n}\cdot {\epsilon }^{-2.5}+{\epsilon }^{-3})$ and outputs a classical representation of the $\epsilon$-approximate Nash equilibrium. This improves upon the best prior quantum runtime of $\tilde{O}(\sqrt{m+n}\cdot {\epsilon }^{-3})$ obtained by [vAG19] and the classic $\tilde{O}((m+n)\cdot {\epsilon }^{-2})$ runtime due to [GK95] whenever $\epsilon =\Omega ((m+n{)}^{-1})$. We obtain this result by designing new quantum data structures for efficiently sampling from a slowly-changing Gibbs distribution.

Cited by in corpus (1)

• Quantum computing for finance