Nearly-frustration-free ground state preparation

Journal Article · Wed Aug 16 00:00:00 EDT 2023 · Quantum

DOI:https://doi.org/10.22331/q-2023-08-16-1084· OSTI ID:2279810

Thibodeau, Matthew ^[1]; Clark, Bryan K. ^[1]

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1. Department of Physics, University of Illinois at Urbana-Champaign, IL 61801, USA, IQUIST and Institute for Condensed Matter Theory and NCSA Center for Artificial Intelligence Innovation, University of Illinois at Urbana-Champaign, IL 61801, USA

Solving for quantum ground states is important for understanding the properties of quantum many-body systems, and quantum computers are potentially well-suited for solving for quantum ground states. Recent work [1] has presented a nearly optimal scheme that prepares ground states on a quantum computer for completely generic Hamiltonians, whose query complexity scales as ${\delta }^{-1}$ , i.e. inversely with their normalized gap. Here we consider instead the ground state preparation problem restricted to a special subset of Hamiltonians, which includes those which we term "nearly-frustration-free": the class of Hamiltonians for which the ground state energy of their block-encoded and hence normalized Hamiltonian ${\alpha }^{-1}H$ is within ${\delta }^y$ of -1, where $\delta$ is the spectral gap of ${\alpha }^{-1}H$ and $0\le y\le 1$ . For this subclass, we describe an algorithm whose dependence on the gap is asymptotically better, scaling as ${\delta }^{y/2-1}$ , and show that this new dependence is optimal up to factors of $\log \delta$ . In addition, we give examples of physically motivated Hamiltonians which live in this subclass. Finally, we describe an extension of this method which allows the preparation of excited states both for generic Hamiltonians as well as, at a similar speedup as the ground state case, for those which are nearly frustration-free.

• Sponsoring Organization: USDOE
• Grant/Contract Number: DESC0020165
• OSTI ID: 2279810
• Journal Information: Quantum, Journal Name: Quantum Vol. 7; ISSN 2521-327X
• Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
• Country of Publication: Austria
• Language: English