Exponential Qubit Reduction in Optimization for Financial Transaction Settlement

TL;DR

This paper introduces an improved qubit-efficient encoding and variational circuit approach for quantum optimization in financial transaction settlement, achieving exponential qubit reduction and better performance on real hardware.

Contribution

It extends previous qubit-efficient encoding methods with symmetry incorporation and variance reduction techniques, enabling larger problem instances on NISQ hardware.

Findings

Achieved exponential qubit reduction in financial optimization problems.

Demonstrated successful handling of 128 transactions on real quantum hardware.

Outperformed previous bounds, enabling larger problem sizes on NISQ devices.

Abstract

We extend the qubit-efficient encoding presented in [Tan et al., Quantum 5, 454 (2021)] and apply it to instances of the financial transaction settlement problem constructed from data provided by a regulated financial exchange. Our methods are directly applicable to any QUBO problem with linear inequality constraints. Our extension of previously proposed methods consists of a simplification in varying the number of qubits used to encode correlations as well as a new class of variational circuits which incorporate symmetries, thereby reducing sampling overhead, improving numerical stability and recovering the expression of the cost objective as a Hermitian observable. We also propose optimality-preserving methods to reduce variance in real-world data and substitute continuous slack variables. We benchmark our methods against standard QAOA for problems consisting of 16 transactions and obtain competitive results. Our newly proposed variational ansatz performs best overall. We demonstrate tackling problems with 128 transactions on real quantum hardware, exceeding previous results bounded by NISQ hardware by almost two orders of magnitude.