Crypto-currency markets are known to exhibit inefficiencies, which presents opportunities for profitable cyclic transactions or arbitrage, where one currency is traded for another in a way that results in a net gain without incurring any risk. Quantum computing has shown promise in financial applications, particularly in resolving optimization problems like arbitrage. In this paper, we introduce a differential evolution (DE) optimization algorithm for Variational Quantum Eigensolver (VQE) using Qiskit framework. We elucidate the application of crypto-currency arbitrage using different VQE optimizers. Our findings indicate that the proposed DE-based method effectively converges to the optimal solution in scenarios where other commonly used optimizers, such as COBYLA, struggle to find the global minimum. We further test this procedure's feasibility on IBM's real quantum machines up to 127 qubits. With a scenario of three currencies, the algorithm converged in 417 steps over a 12 hour period on the “ibm_geneva” machine. These results suggest the potential to achieve a quantum advantage in solving increasingly complex problems.

中文翻译：

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用于加密货币套利的差分进化 VQE。具有许多局部最小值的量子优化

众所周知，加密货币市场效率低下，这为有利可图的循环交易或套利提供了机会，其中一种货币以一种不产生任何风险的方式交易另一种货币，从而获得净收益。量子计算在金融应用中显示出了前景，特别是在解决套利等优化问题方面。在本文中，我们介绍了一种使用 Qiskit 框架的变分量子本征求解器 (VQE) 的差分进化 (DE) 优化算法。我们使用不同的 VQE 优化器阐明了加密货币套利的应用。我们的研究结果表明，在其他常用优化器（例如 COBYLA）难以找到全局最小值的情况下，所提出的基于 DE 的方法可以有效地收敛到最优解。我们进一步测试了该过程在 IBM 高达 127 量子位的真实量子机器上的可行性。对于三种货币的场景，该算法在“ibm_geneva”机器上在 12 小时内通过 417 个步骤进行了收敛。这些结果表明在解决日益复杂的问题时具有实现量子优势的潜力。