Understanding the Nature of Depth-1 Equivariant Quantum Circuit

Fuente: arXiv
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Hauptverfasser: Teo, Jonathan, Wei, Lee Xin, Lau, Hoong Chuin
Format: Preprint
Veröffentlicht: 2025
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author Teo, Jonathan
Wei, Lee Xin
Lau, Hoong Chuin
author_facet Teo, Jonathan
Wei, Lee Xin
Lau, Hoong Chuin
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_10756
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Understanding the Nature of Depth-1 Equivariant Quantum Circuit
Teo, Jonathan
Wei, Lee Xin
Lau, Hoong Chuin
Quantum Physics
Artificial Intelligence
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.
title Understanding the Nature of Depth-1 Equivariant Quantum Circuit
topic Quantum Physics
Artificial Intelligence
url https://arxiv.org/abs/2511.10756