Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers

Lacroix, Denis; Ruiz Guzman, Edgar Andres; Siwach, Pooja

doi:10.1140/epja/s10050-022-00911-7

Title: Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers

Journal Article · Tue Jan 10 00:00:00 EST 2023 · European Physical Journal. A, Hadrons and Nuclei (Online)

DOI:https://doi.org/10.1140/epja/s10050-022-00911-7· OSTI ID:1908376

Lacroix, Denis ^[1]; Ruiz Guzman, Edgar Andres ^[1]; Siwach, Pooja ^[2]

Univ. Paris-Saclay (France); Centre National de la Recherche Scientifique (CNRS), Paris (France). Inst. National de Physique Nucleaire et de Physique des Particules (IN2P3)
Univ. of Wisconsin, Madison, WI (United States)

In this article, we discuss some aspects related to the symmetries of a quantum many-body problem when trying to treat it on a quantum computer. Several features related to symmetry conservation, symmetry breaking, and possible symmetry restoration are reviewed. After briefly discussing some of the standard symmetries relevant for many-particle systems, we discuss the advantage of encoding some symmetries directly in quantum ansätze, especially to reduce the quantum register size. It is, however, well-known that the use of symmetry-breaking states can also be a unique way to incorporate specific internal correlations when a spontaneous symmetry breaking occurs. These aspects are discussed in the quantum computing context. Ultimately, an accurate description of quantum systems can be achieved only when the initially broken symmetries are properly restored. We review several methods explored previously to perform symmetry restoration on a quantum computer, for instance, the ones based on symmetry filtering by quantum phase estimation and by an iterative independent set of Hadamard tests. We propose novel methods that pave the new directions to perform symmetry restoration, like those based on the purification of the state employing the linear combination of unitaries (LCU) approach.

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Research Organization:: Univ. of Wisconsin, Madison, WI (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0019465

OSTI ID:: 1908376

Journal Information:: European Physical Journal. A, Hadrons and Nuclei (Online), Vol. 59, Issue 1; ISSN 1434-601X

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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