aiqbench analysis
This research presents a resource-efficient Quadratic Unconstrained Binary Optimization (QUBO) formulation specifically designed for currency arbitrage, addressing critical hardware constraints like qubit count and analog precision in annealers. By compressing coefficient ranges through anchor-gauge reweighting and deriving sufficient penalty weights, the method achieves exact fee-adjusted optima that prior encodings missed under matched sampler budgets. The work advances practical quantum algorithm design by demonstrating how realistic financial constraints can be mapped to binary optimization problems without sacrificing solution accuracy on current hardware architectures.
Resource-Efficient QUBO Formulation for Anchored Currency Arbitrage
arXiv:2608.15889v1 Announce Type: cross Abstract: 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.
Abstract: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.
Quantum Physics (quant-ph); Machine Learning (cs.LG)
arXiv:2608.15889 [quant-ph]
(or arXiv:2608.15889v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.15889 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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