Understanding the Nature of Depth-1 Equivariant Quantum Circuit
This work addresses scalability issues for quantum reinforcement learning researchers by providing an efficient benchmarking tool for larger TSP problems, though it is incremental as it builds on existing EQC methods.
The paper tackled the challenge of scaling Equivariant Quantum Circuits (EQCs) for the Travelling Salesman Problem (TSP) by proposing the Size-Invariant Grid Search (SIGS) training optimization, which reduced simulation times by 96.4% for 100-node TSP instances and enabled analysis up to 350 nodes while maintaining a mean optimality gap within 0.005.
The Equivariant Quantum Circuit (EQC) for the Travelling Salesman Problem (TSP) has been shown to achieve near-optimal performance in solving small TSP problems (up to 20 nodes) using only two parameters at depth 1. However, extending EQCs to larger TSP problem sizes remains challenging due to the exponential time and memory for quantum circuit simulation, as well as increasing noise and decoherence when running on actual quantum hardware. In this work, we propose the Size-Invariant Grid Search (SIGS), an efficient training optimization for Quantum Reinforcement Learning (QRL), and use it to simulate the outputs of a trained Depth-1 EQC up to 350-node TSP instances - well beyond previously tractable limits. At TSP with 100 nodes, we reduce total simulation times by 96.4%, when comparing to RL simulations with the analytical expression (151 minutes using RL to under 6 minutes using SIGS on TSP-100), while achieving a mean optimality gap within 0.005 of the RL trained model on the test set. SIGS provides a practical benchmarking tool for the QRL community, allowing us to efficiently analyze the performance of QRL algorithms on larger problem sizes. We provide a theoretical explanation for SIGS called the Size-Invariant Properties that goes beyond the concept of equivariance discussed in prior literature.