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.

翻译：尽管比例响应动力学等经典市场均衡计算算法在运行时间上几乎与买家和商品数量的乘积呈线性关系，但在拍卖、推荐系统和公平分配等互联网应用中仍面临可扩展性问题。本研究首次提出了一种具有亚线性性能的市场均衡计算量子算法。该算法在买家和商品数量的乘积上实现了多项式级的运行时间加速，同时达到了与经典算法相同的优化目标值。对包含16384个买家和商品的系统进行的数值模拟支持了我们的理论结果，表明该量子算法提供了显著的加速效果。