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This paper introduces a distributed variational quantum linear solver (DVQLS) for solving large linear systems $Ax=b$ on multiple NISQ computers. The matrix $A$ is partitioned into blocks, each processed by a separate quantum computer that communicates with row and column neighbors. By integrating a VQLS variant with distributed classical optimization, the DVQLS overcomes single-quantum-computer capacity limitations, enabling the solution of larger linear systems.
Quantum computers can now tackle linear systems larger than their individual capacities, thanks to a distributed algorithm that cleverly partitions the problem across multiple machines.
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.
