Quantum algorithm for large-scale market equilibrium computation

TL;DR

This paper introduces the first quantum algorithm for large-scale market equilibrium computation, achieving a polynomial speedup over classical methods while maintaining the same optimization quality, supported by numerical simulations.

Contribution

It presents a novel quantum algorithm that significantly improves the scalability of market equilibrium computation compared to classical algorithms.

Findings

Quantum algorithm achieves sub-linear runtime performance.

Numerical simulations confirm significant speedup with large datasets.

Maintains the same optimization objective as classical algorithms.

Abstract

Classical algorithms for market equilibrium computation such as proportional response dynamics face scalability issues with Internet-based applications such as auctions, recommender systems, and fair division, despite having an almost linear runtime in terms of the product of buyers and goods. In this work, we provide the first quantum algorithm for market equilibrium computation with sub-linear performance. Our algorithm provides a polynomial runtime speedup in terms of the product of the number of buyers and goods while reaching the same optimization objective value as the classical algorithm. Numerical simulations of a system with 16384 buyers and goods support our theoretical results that our quantum algorithm provides a significant speedup.