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Article Dans Une Revue Eur.Phys.J.A Année : 2023

Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers: A quantum many-body perspective

Résumé

We discuss here some aspects related to 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 a brief discussion of some of the standard symmetries relevant for many-particle systems, we discuss the advantage to encode directly some symmetries in quantum ansatze, especially with the aim 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. Precise description of quantum systems can however be achieved only when the symmetries that are initially broken are properly restored. Several methods are introduced to perform symmetry restoration on a quantum computer, for instance, purification of the state by means of the Grover algorithm, use of the combination of Hadamard test and oracle concepts, symmetry filtering by quantum phase estimation and by an iterative independent set of Hadamard tests.

Dates et versions

hal-03772715 , version 1 (08-09-2022)

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Citer

Denis Lacroix, Edgar Andres Ruiz Guzman, Pooja Siwach. Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers: A quantum many-body perspective. Eur.Phys.J.A, 2023, 59 (1), pp.3. ⟨10.1140/epja/s10050-022-00911-7⟩. ⟨hal-03772715⟩
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