Warm-Starting PCE for Traveling Salesman Problem

Fuente: arXiv
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Main Authors: Carmo, Rafael S. do, Reis, Renato Gomes dos, Silva, Samuel Fernando F, Arruda, Luiz Gustavo E., Fanchini, Felipe F.
Format: Preprint
Published: 2025
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author Carmo, Rafael S. do
Reis, Renato Gomes dos
Silva, Samuel Fernando F
Arruda, Luiz Gustavo E.
Fanchini, Felipe F.
author_facet Carmo, Rafael S. do
Reis, Renato Gomes dos
Silva, Samuel Fernando F
Arruda, Luiz Gustavo E.
Fanchini, Felipe F.
contents Variational quantum algorithms are promising for combinatorial optimization, but their scalability is often limited by qubit-intensive encoding schemes. To overcome this bottleneck, Pauli Correlation Encoding (PCE) has emerged as one of the most promising algorithms in this scenario. The method offers not only a polynomial reduction in qubit count and a suppression of barren plateaus but also demonstrates competitive performance with state-of-the-art methods on Maxcut. In this work, we propose a warm-start PCE, an extension that incorporates a classical bias from the Goemans-Williamson (GW) randomized rounding algorithm into the loss function to guide the optimization toward improved approximation ratios. We evaluated this method on the Traveling Salesman Problem (TSP) using a QUBO-to-MaxCut transformation for up to $5$ layers. Our results show that Warm-PCE consistently outperforms standard PCE, achieving the optimum solution in $28\text{--}64\%$ of instances, versus $4\text{--}26\%$ for PCE, and attaining higher mean approximation ratios that improve with circuit depth. These findings highlight the practical value of this warm-start strategy for enhancing PCE-based solvers on near-term hardware.
format Preprint
id arxiv_https___arxiv_org_abs_2509_14414
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Warm-Starting PCE for Traveling Salesman Problem
Carmo, Rafael S. do
Reis, Renato Gomes dos
Silva, Samuel Fernando F
Arruda, Luiz Gustavo E.
Fanchini, Felipe F.
Quantum Physics
Variational quantum algorithms are promising for combinatorial optimization, but their scalability is often limited by qubit-intensive encoding schemes. To overcome this bottleneck, Pauli Correlation Encoding (PCE) has emerged as one of the most promising algorithms in this scenario. The method offers not only a polynomial reduction in qubit count and a suppression of barren plateaus but also demonstrates competitive performance with state-of-the-art methods on Maxcut. In this work, we propose a warm-start PCE, an extension that incorporates a classical bias from the Goemans-Williamson (GW) randomized rounding algorithm into the loss function to guide the optimization toward improved approximation ratios. We evaluated this method on the Traveling Salesman Problem (TSP) using a QUBO-to-MaxCut transformation for up to $5$ layers. Our results show that Warm-PCE consistently outperforms standard PCE, achieving the optimum solution in $28\text{--}64\%$ of instances, versus $4\text{--}26\%$ for PCE, and attaining higher mean approximation ratios that improve with circuit depth. These findings highlight the practical value of this warm-start strategy for enhancing PCE-based solvers on near-term hardware.
title Warm-Starting PCE for Traveling Salesman Problem
topic Quantum Physics
url https://arxiv.org/abs/2509.14414