Distributed Variational Quantum Linear Solver
This addresses the problem of scaling quantum linear solvers for large systems, though it is incremental as it builds on existing variational methods with distributed optimization.
The paper tackles solving large-scale linear equations by developing a distributed variational quantum algorithm that partitions the matrix across multiple noisy intermediate-scale quantum (NISQ) computers, enabling solutions not limited by single-computer capacity.
This paper develops a distributed variational quantum algorithm for solving large-scale linear equations. For a linear system of the form $Ax=b$, the large square matrix $A$ is partitioned into smaller square block submatrices, each of which is known only to a single noisy intermediate-scale quantum (NISQ) computer. Each NISQ computer communicates with certain other quantum computers in the same row and column of the block partition, where the communication patterns are described by the row- and column-neighbor graphs, both of which are connected. The proposed algorithm integrates a variant of the variational quantum linear solver at each computer with distributed classical optimization techniques. The derivation of the quantum cost function provides insight into the design of the distributed algorithm. Numerical quantum simulations demonstrate that the proposed distributed quantum algorithm can solve linear systems whose size scales with the number of computers and is therefore not limited by the capacity of a single quantum computer.