Reinforcement learning for Quantum Tiq-Taq-Toe

TL;DR

This paper explores applying reinforcement learning to Quantum Tiq-Taq-Toe, a complex quantum game, to serve as a testbed for integrating quantum computing and machine learning techniques.

Contribution

It introduces the first reinforcement learning approach to Quantum Tiq-Taq-Toe, addressing its unique challenges and complexity.

Findings

RL methods can be adapted to quantum games with partial observability

Quantum Tiq-Taq-Toe presents significant complexity for classical algorithms

The study provides insights into quantum state representation and strategy development

Abstract

Quantum Tiq-Taq-Toe is a well-known benchmark and playground for both quantum computing and machine learning. Despite its popularity, no reinforcement learning (RL) methods have been applied to Quantum Tiq-Taq-Toe. Although there has been some research on Quantum Chess this game is significantly more complex in terms of computation and analysis. Therefore, we study the combination of quantum computing and reinforcement learning in Quantum Tiq-Taq-Toe, which may serve as an accessible testbed for the integration of both fields. Quantum games are challenging to represent classically due to their inherent partial observability and the potential for exponential state complexity. In Quantum Tiq-Taq-Toe, states are observed through Measurement (a 3x3 matrix of state probabilities) and Move History (a 9x9 matrix of entanglement relations), making strategy complex as each move can collapse the quantum state.