2025/09/17 by Rafael S. Carmo, Carmo, Rafael S. do, R. Reis +7 · 2 citations
Computer Science · #Quantum Computing Algorithms and Architecture #Error Correcting Code Techniques #Quantum Information and Cryptography
paper · pdf · doi:10.48550/arxiv.2509.14414
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--64% of instances, versus 4--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.