Quantum simulation of quantum phase transitions using the convex geometry of reduced density matrices

Warren, Samuel; Sager-Smith, LeeAnn M.; Mazziotti, David A.

doi:10.1103/physreva.106.012434

Title: Quantum simulation of quantum phase transitions using the convex geometry of reduced density matrices

Journal Article · 25 July 2022 · Physical Review A

DOI: https://doi.org/10.1103/physreva.106.012434 · OSTI ID:1979623

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University of Chicago, IL (United States); OSTI
University of Chicago, IL (United States)

Transitions of many-particle quantum systems between distinct phases at absolute-zero temperature, known as quantum phase transitions, require an exacting treatment of particle correlations. Here in this work, we present a general quantum-computing approach to quantum phase transitions that exploits the geometric structure of reduced density matrices. While typical approaches to quantum phase transitions examine discontinuities in the order parameters, the origin of phase transitions—their order parameters and symmetry breaking—can be understood geometrically in terms of the set of two-particle reduced density matrices (2-RDMs). The convex set of 2-RDMs provides a comprehensive map of the quantum system including its distinct phases as well as the transitions connecting these phases. Because 2-RDMs can potentially be computed on quantum computers at nonexponential cost, even when the quantum system is strongly correlated, they are ideally suited for a quantum-computing approach to quantum phase transitions. We compute the convex set of 2-RDMs for a Lipkin-Meshkov-Glick spin model on IBM superconducting-qubit quantum processors. Even though computations are limited to few-particle models due to device noise, comparisons with a classically solvable 1000-particle model reveal that the finite-particle quantum solutions capture the key features of the phase transitions including the strong correlation and the symmetry breaking.

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Research Organization:: Purdue University, West Lafayette, IN (United States); University of Chicago, IL (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0019215

OSTI ID:: 1979623

Journal Information:: Physical Review A, Journal Name: Physical Review A Journal Issue: 1 Vol. 106; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Title: Quantum simulation of quantum phase transitions using the convex geometry of reduced density matrices

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