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Title: Near-term quantum algorithms for linear systems of equations with regression loss functions
Authors: Huang, Hsin-Yuan
Bharti, Kishor
Rebentrost, Patrick 
Keywords: Linear systems
Near-term quantum algorithms
Quantum computing
Issue Date: 1-Nov-2021
Publisher: IOP Publishing Ltd
Citation: Huang, Hsin-Yuan, Bharti, Kishor, Rebentrost, Patrick (2021-11-01). Near-term quantum algorithms for linear systems of equations with regression loss functions. New Journal of Physics 23 (11) : 113021. ScholarBank@NUS Repository.
Rights: Attribution 4.0 International
Abstract: Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum resources are not immediately available on near-term quantum devices. In this work, we study near-term quantum algorithms for linear systems of equations, with a focus on the two-norm and Tikhonov regression settings. We investigate the use of variational algorithms and analyze their optimization landscapes. There exist types of linear systems for which variational algorithms designed to avoid barren plateaus, such as properly-initialized imaginary time evolution and adiabatic-inspired optimization, suffer from a different plateau problem. To circumvent this issue, we design near-term algorithms based on a core idea: the classical combination of variational quantum states (CQS). We exhibit several provable guarantees for these algorithms, supported by the representation of the linear system on a so-called ansatz tree. The CQS approach and the ansatz tree also admit the systematic application of heuristic approaches, including a gradient-based search. We have conducted numerical experiments solving linear systems as large as 2300 × 2300 by considering cases where we can simulate the quantum algorithm efficiently on a classical computer. Our methods may provide benefits for solving linear systems within the reach of near-term quantum devices. © 2021 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft
Source Title: New Journal of Physics
ISSN: 1367-2630
DOI: 10.1088/1367-2630/ac325f
Rights: Attribution 4.0 International
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