Simulations of frustrated Ising Hamiltonians using quantum approximate optimization

Lotshaw, Phillip C.; Xu, Hanjing; Khalid, Bilal; Buchs, Gilles; Humble, Travis S.; Banerjee, Arnab

doi:10.1098/rsta.2021.0414

Simulations of frustrated Ising Hamiltonians using quantum approximate optimization

Journal Article · Mon Dec 05 00:00:00 EST 2022 · Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences

DOI:https://doi.org/10.1098/rsta.2021.0414· OSTI ID:1905415

^[1]; Xu, Hanjing ^[2]; Khalid, Bilal ^[3]; ^[1]; ^[1]; Banerjee, Arnab ^[3]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Purdue Univ., West Lafayette, IN (United States)
Purdue Univ., West Lafayette, IN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Novel magnetic materials are important for future technological advances. Theoretical and numerical calculations of ground-state properties are essential in understanding these materials, however, computational complexity limits conventional methods for studying these states. Here we investigate an alternative approach to preparing materials ground states using the quantum approximate optimization algorithm (QAOA) on near-term quantum computers. We study classical Ising spin models on unit cells of square, Shastry-Sutherland and triangular lattices, with varying field amplitudes and couplings in the material Hamiltonian. We find relationships between the theoretical QAOA success probability and the structure of the ground state, indicating that only a modest number of measurements (≲100) are needed to find the ground state of our nine-spin Hamiltonians, even for parameters leading to frustrated magnetism. We further demonstrate the approach in calculations on a trapped-ion quantum computer and succeed in recovering each ground state of the Shastry-Sutherland unit cell with probabilities close to ideal theoretical values. The results demonstrate the viability of QAOA for materials ground state preparation in the frustrated Ising limit, giving important first steps towards larger sizes and more complex Hamiltonians where quantum computational advantage may prove essential in developing a systematic understanding of novel materials.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1905415

Journal Information:: Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences, Journal Name: Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences Journal Issue: 2241 Vol. 381; ISSN 1364-503X

Publisher:: The Royal Society PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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Supplementary material from "Simulations of frustrated Ising Hamiltonians using quantum approximate optimization" Lotshaw, Phillip C.; Xu, Hanjing; Khalid, Bilal The Royal Society https://doi.org/10.6084/m9.figshare.c.6260131	collection	January 2022

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Supplementary file for 'Simulations of Frustrated Ising Hamiltonians using Quantum Approximate Optimization' Lotshaw, Phillip C.; Xu, Hanjing; Khalid, Bilal https://doi.org/10.6084/m9.figshare.21377893.v1 The current record is supplemented by this text	text	January 2022
Supplementary material from "Simulations of frustrated Ising Hamiltonians using quantum approximate optimization" Lotshaw, Phillip C.; Xu, Hanjing; Khalid, Bilal https://doi.org/10.6084/m9.figshare.c.6260131 The current record is supplemented by this collection	collection	January 2022

Simulations of frustrated Ising Hamiltonians using quantum approximate optimization

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