AI 中文总结
研究针对泡利相关编码（PCE）测量开销大的问题，引入高效可模拟PCE，利用自由费米子演化由匹配门及IQP电路实现，在多个基准测试中不同规模问题上产生高质量解，为评估量子PCE实现提供去量化基线。
AI 中文摘要
泡利相关编码（PCE）是一种用于二元优化的启发式框架，它将经典变量编码到多体泡利可观测量中。虽然PCE比其他方法需要的量子比特更少，但它依赖于估计大量泡利期望值，其符号决定变量的值，这可能会带来大量测量开销。在此，我们引入高效可模拟的PCE，这是一类去量化的PCE实现，其中所需的所有期望值都可以在经典计算机上高效计算。我们使用由匹配门电路和瞬时量子多项式（IQP）电路实现的自由费米子演化来实例化这一想法。在最大割、最大独立集、多维背包和最大三元可满足性基准测试中，这些方法在从几十到数千个变量的问题规模上都能产生高质量的解决方案。我们的结果表明，PCE自然可被理解为一个基于相关性的优化框架，具有量子和经典可模拟的实现。这为评估未来的量子PCE实现提供了一个去量化的基线。
英文摘要
Pauli Correlation Encoding (PCE) is a heuristic framework for binary optimisation that encodes classical variables into many-body Pauli observables. While PCE requires fewer qubits than other approaches, it relies on estimating a large number of Pauli expectation values whose signs determine the variables' values, which can incur substantial measurement overhead. Here, we introduce efficiently simulable PCE, a class of dequantised PCE realisations where all expectation values needed can be computed efficiently classically. We instantiate this idea using free-fermionic evolutions, realised by matchgate circuits, and Instantaneous Quantum Polynomial (IQP) circuits. On MaxCut, Maximum Independent Set, Multi-Dimensional Knapsack, and Max3SAT benchmarks, these methods produce high-quality solutions across problem sizes ranging from tens to thousands of variables. Our results show that PCE is naturally understood as a correlation-based optimisation framework with both quantum and classically simulable realisations. This yields a dequantised baseline for evaluating future quantum PCE implementations.
Comments24 pages, 8 figures
