Scholarlink

<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(28\text {--}64\%\)</EquationSource> </InlineEquation> of instances, versus <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(4\text {--}26\%\)</EquationSource> </InlineEquation> 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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Warm-Starting PCE for Traveling Salesman Problem

  • 期刊论文

  • 发表日期：

    2025年12月16日

查看全文
  • Rafael Simões do Carmo,
  • Renato Gomes dos Reis,
  • Samuel Fernando F Silva,
  • Luiz Gustavo E. Arruda,
  • Felipe F. Fanchini

摘要

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.