Differential Evolution VQE for Crypto-currency Arbitrage. Quantum
  Optimization with many local minima
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 three-currency scenario, the algorithm converged in 417 steps
over a 12-hour period on the "ibm_geneva" machine. These results suggest the
potential for achieving a quantum advantage in solving increasingly complex
problems.
Gines Carrascal Beatriz Roman Guillermo Botella Alberto del Barrio