An optimal quantum sampling regression algorithm for variational eigensolving in the low qubit number regime

ORAL

Abstract

The VQE algorithm, with all its merits, has turned out to be quite expensive to run given the way we currently access quantum processors (i.e. over the cloud). In order to alleviate this issue, in this paper we introduce an alternative hybrid quantum-classical algorithm, and analyze some of its use cases based on time complexity in the low qubit number regime. In exchange for some extra classical resources, this novel strategy is proved to be optimal in terms of the number of samples it requires from the quantum processor. We develop a simple ---yet general--- analytical model to evaluate when this algorithm is more efficient than VQE, and, from the same theoretical considerations, establish a threshold above which quantum advantage can occur. Finally, we demonstrate the efficacy of our algorithm for a benchmark problem.

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Authors

  • Pedro Rivero

    Illinois Institute of Technology, Argonne National Laboratory, Illinois Institute of Technology

  • Dmitri Sergatskov

    J.R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, KS 66506 USA, Department of Physics, Augustana University, Sioux Falls, SD 57197 USA, Northwestern University, Fermilab, University of Cambridge, Stanford University, Missouri State University - Dept. of Physics, Astronomy, and Materials Science, University of Alabama, Purdue University, Princeton, Illinois Institute of Technology, Argonne National Laboratory, Rutgers University, Stockholm University, University of Wisconsin, University of lowa, Oregon State University, Fermi National Accelerator Laboratory, New York University, University of Nevada, Reno, Retired

  • Dmitri Sergatskov

    J.R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, KS 66506 USA, Department of Physics, Augustana University, Sioux Falls, SD 57197 USA, Northwestern University, Fermilab, University of Cambridge, Stanford University, Missouri State University - Dept. of Physics, Astronomy, and Materials Science, University of Alabama, Purdue University, Princeton, Illinois Institute of Technology, Argonne National Laboratory, Rutgers University, Stockholm University, University of Wisconsin, University of lowa, Oregon State University, Fermi National Accelerator Laboratory, New York University, University of Nevada, Reno, Retired