提出更省资源的币种套利量子编码，能精准算手续费并节省量子比特。
Resource-Efficient QUBO Formulation for Anchored Currency Arbitrage
- 基于真实交易约束设计新QUBO编码，减少所需逻辑变量数。
- 在相同硬件预算下，唯一找到精确含手续费最优套利路径。
- 通过汇率重加权压缩系数范围，适配量子退火机精度限制。
货币套利（CA）指通过货币循环交易利用市场估值差异获利。二次无约束二元优化（QUBO）旨在最小化二元变量的二次代价函数。现有研究已尝试用QUBO求解CA问题，但未考虑实际约束。本文引入关键约束：套利必须从持有货币开始，并计入每笔交易的手续费。所提编码比文献中其他QUBO方案所需逻辑变量更少。我们推导出保证约束成立的充分惩罚权重，并引入精确的锚点-规范重加权方法，将交换率系数范围从原始汇率尺度压缩至套利尺度，缓解退火硬件有限模拟精度的问题。使用经典模拟退火在相同CPU上与精确的Held-Karp基线对比，验证了该方法可有效发现盈利路径并处理手续费。最终，在相同采样预算下对五种已有编码进行基准测试，结果表明仅本方法能恢复精确的含手续费最优解。
原文摘要 · Abstract (English)
Currency arbitrage (CA) involves trading currencies in cycles to exploit discrepancies in market valuations. Quadratic unconstrained binary optimization (QUBO) involves minimizing a quadratic cost (energy) function of binary variables. Previous works have explored the use of QUBO to solve CA problems. We build on these previous works by introducing realistic constraints such as beginning cycles from a held currency and accounting for per-transaction trading fees. We show that this formulation requires fewer logical variables (qubits) than previous QUBO encodings in the literature. We derive provably sufficient penalty weights for its constraint terms. We also introduce an exact anchor-gauge reweighting of the exchange rates that compresses the QUBO coefficient range from the rate scale to the arbitrage scale, addressing the finite analog precision of annealing hardware. We demonstrate the efficacy of this formulation using classical simulated annealing against an exact Held-Karp baseline on the same CPU and show that it can effectively find profitable cycles and account for trading fees. Finally, we benchmark faithful implementations of five prior QUBO encodings at matched sampler budgets and show that the proposed encoding is the only one to recover the exact fee-adjusted optimum.
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