资源高效的锚定货币套利QUBO公式化
Resource-Efficient QUBO Formulation for Anchored Currency Arbitrage
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中文总结 AI 辅助
本文针对货币套利问题提出一种资源高效的QUBO公式化方案，引入现实约束，压缩系数范围，经基准测试其为唯一可恢复手续费调整后精确最优解的编码。
中文摘要 AI 辅助
货币套利（CA）涉及通过循环交易货币来利用市场估值的差异。二次无约束二元优化（QUBO）旨在最小化二元变量的二次代价（能量）函数。此前已有研究探索用QUBO解决CA问题，本文在这些工作的基础上，引入了从持有货币开始循环、计入每笔交易手续费等现实约束。研究表明，该公式化方案所需的逻辑变量（量子比特）数量少于文献中现有QUBO编码；推导了其约束项的可证充分惩罚权重；还引入了汇率的精确锚定尺度重加权，将QUBO系数范围从汇率尺度压缩至套利尺度，解决了退火硬件的有限模拟精度问题。在同一CPU上，使用经典模拟退火算法与精确Held-Karp基准对比验证了该公式化方案的有效性，其可有效找到盈利循环并计入交易手续费；在匹配采样器预算的情况下，对五种现有QUBO编码的忠实实现进行基准测试，结果显示本文提出的编码是唯一能恢复经手续费调整后的精确最优解的方案。
英文摘要
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.
发表机构
- University of Alabama（阿拉巴马大学）
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