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：经典的市场均衡计算算法（如比例响应动态）尽管在买家和商品数量的乘积上具有近乎线性的运行时间，但在面对基于互联网的应用（如拍卖、推荐系统和公平分配）时仍面临可扩展性问题。本研究首次提出了一种具有次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，即该量子算法提供了显著的加速效果。