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Recent advances in quantum machine learning and quantum state embedding are integrated, providing a resource efficient framework for solutions of linear systems on Noisy Intermediate Scale Quantum (NISQ) machines. A divide and conquer algorithm is used to embed the indexing vector after which the Coherent Variational Quantum Linear Solver (CVQLS) algorithm is used to invert the problem matrix. This integrated procedure has an improved complexity scaling in the quantum resources needed to execute and produces solutions which agree with what is found classically.
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Sean T. Crowe, Ramiro Rodriguez, Daniel Gunlycke, Fernando Escobar, Joanna N. Ptasinski, "Efficient embedding to solve the quantum linear systems problem in near-term quantum processors," Proc. SPIE 12238, Quantum Communications and Quantum Imaging XX, 122380A (4 October 2022); https://doi.org/10.1117/12.2632069