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

TL;DR

This paper presents an efficient quantum circuit design for implementing quantum walks on binary trees, with a focus on NAND formula evaluation, and demonstrates its application in training quantum reinforcement learning agents.

Contribution

It introduces a universal gate-based quantum circuit for binary tree quantum walks and applies it to reinforcement learning, bridging quantum algorithms with practical AI tasks.

Findings

Quantum walk circuits on binary trees can be efficiently implemented.

The NAND formula evaluation algorithm can be integrated into quantum reinforcement learning.

Quantum circuits can be used to train agents in game environments.

Abstract

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.