2023/11/07 by Augustino, Brandon, Leng, Jiaqi, Nannicini, Giacomo +2 · 5 citations
#Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Optimization and Control (math.OC) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2311.03977
We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive linearizations of the perturbed KKT conditions, we perform a single simulation working directly with the nonlinear complementarity equations. This approach yields an algorithm for solving linear optimization problems involving m constraints and n variables to ε-optimality using O ( √(m + n) \fracR1ε) queries to an oracle that evaluates a potential function, where R1 is an ℓ1-norm upper bound on the size of the optimal solution. In the standard gate model (i.e., without access to quantum RAM) our algorithm can obtain highly-precise solutions to LO problems using at most O ( √(m + n) \textsfnnz (A) (R1)/(ε)) elementary gates, where \textsfnnz (A) is the total number of non-zero elements found in the constraint matrix.