Problem
Research questions and friction points this paper is trying to address.
Currency Arbitrage
QUBO
Resource Efficiency
Trading Fees
Analog Precision
Resource-Efficient QUBO Formulation for Anchored Currency Arbitrage
🤖 AI Summary
This study addresses the limitations of existing QUBO currency arbitrage models, which often lack realistic constraints and incur high resource overhead. We propose a resource-efficient QUBO formulation that incorporates starting currency and transaction fee constraints while employing an anchor-based reweighting strategy to compress the dynamic range of coefficients. This approach significantly reduces qubit requirements, thereby aligning with the precision limits of quantum annealing hardware. Experimental results demonstrate that our method not only drastically decreases variable counts but also uniquely recovers exact fee-adjusted optimal solutions and effectively identifies profitable cycles. Consequently, this work achieves simultaneous improvements in both modeling accuracy under real-world constraints and computational efficiency for quantum-enabled arbitrage optimization.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
QUBO formulation
Currency arbitrage
Anchor-gauge reweighting
Resource-efficient
Trading fees
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