Quantum algorithm for large-scale market equilibrium computation

2024-05-22

Neural Information Processing Systems

AI Summary

To address the scalability bottleneck in computing large-scale market equilibria for internet applications—such as online auctions, recommendation systems, and fair allocation—this paper introduces the first sublinear quantum algorithm, breaking the classical O(mn) time complexity barrier. Our method integrates quantum amplitude estimation, sparse Hamiltonian simulation, and quantum encoding of market utility functions to construct an end-to-end quantum solver. It preserves the optimization objective accuracy of proportional-response dynamics while achieving a theoretical complexity of O(√(mn)). Numerical simulations demonstrate significant speedup over classical algorithms on 16,384 × 16,384 instances, with relative error bounded within 10⁻³. This work provides the first rigorously proven quantum complexity advantage for large-scale economic mechanism design, establishing a feasible pathway toward quantum-accelerated equilibrium computation.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Machine Learning: Quantum Machine Learning

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Quantum algorithm for market equilibrium
• Scalability issues in classical algorithms
• Polynomial runtime speedup in computation

Innovation

• Quantum algorithm
• Sub-linear performance
• Polynomial runtime speedup