Efficient circuit implementation for coined quantum walks on binary trees and application to reinforcement learning

Thomas Mullor (1) , David Vigouroux (1) , Louis Bethune (2)

1 IRT Saint Exupéry - Institut de Recherche Technologique
2 Université Paul Sabatier, IRIT

Quantum walks on binary trees are used in many quantum algorithms to achieve important speedup over classical algorithms. The formulation of this kind of algorithms as quantum circuit presents the advantage of being easily readable, executable on circuit based quantum computers and simulators and optimal on the usage of resources. We propose a strategy to compose quantum circuit that performs quantum walk on binary trees following universal gate model quantum computation principles. We give a particular attention to NAND formula evaluation algorithm as it could have many applications in game theory and reinforcement learning. We therefore propose an application of this algorithm and show how it can be used to train a quantum reinforcement learning agent in a two player game environment.

Keywords: Quantum circuits; Reinforcement Learning; Quantum walks

Domains: Quantum Physics [quant-ph]; Emerging Technologies [cs.ET]

Thomas Mullor, David Vigouroux, Louis Bethune. Efficient circuit implementation for coined quantum walks on binary trees and application to reinforcement learning. ACM/IEEE International Workshop on Quantum Computing, Dec 2022, Seattle, United States. ⟨hal-03812297v1⟩