Dominic W. Berry, Yu Tong, Tanuj Khattar, Alec White, Tae In Kim, Sergio Boixo, Lin Lin, Seunghoon Lee, Garnet Kin-Lic Chan, Ryan Babbush, Nicholas C. Rubin
{"title":"Rapid initial state preparation for the quantum simulation of strongly correlated molecules","authors":"Dominic W. Berry, Yu Tong, Tanuj Khattar, Alec White, Tae In Kim, Sergio Boixo, Lin Lin, Seunghoon Lee, Garnet Kin-Lic Chan, Ryan Babbush, Nicholas C. Rubin","doi":"arxiv-2409.11748","DOIUrl":null,"url":null,"abstract":"Studies on quantum algorithms for ground state energy estimation often assume\nperfect ground state preparation; however, in reality the initial state will\nhave imperfect overlap with the true ground state. Here we address that problem\nin two ways: by faster preparation of matrix product state (MPS)\napproximations, and more efficient filtering of the prepared state to find the\nground state energy. We show how to achieve unitary synthesis with a Toffoli\ncomplexity about $7 \\times$ lower than that in prior work, and use that to\nderive a more efficient MPS preparation method. For filtering we present two\ndifferent approaches: sampling and binary search. For both we use the theory of\nwindow functions to avoid large phase errors and minimise the complexity. We\nfind that the binary search approach provides better scaling with the overlap\nat the cost of a larger constant factor, such that it will be preferred for\noverlaps less than about $0.003$. Finally, we estimate the total resources to\nperform ground state energy estimation of Fe-S cluster systems, including the\nFeMo cofactor by estimating the overlap of different MPS initial states with\npotential ground-states of the FeMo cofactor using an extrapolation procedure.\n{With a modest MPS bond dimension of 4000, our procedure produces an estimate\nof $\\sim 0.9$ overlap squared with a candidate ground-state of the FeMo\ncofactor, producing a total resource estimate of $7.3 \\times 10^{10}$ Toffoli\ngates; neglecting the search over candidates and assuming the accuracy of the\nextrapolation, this validates prior estimates that used perfect ground state\noverlap. This presents an example of a practical path to prepare states of high\noverlap in a challenging-to-compute chemical system.","PeriodicalId":501226,"journal":{"name":"arXiv - PHYS - Quantum Physics","volume":"20 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Quantum Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11748","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Studies on quantum algorithms for ground state energy estimation often assume
perfect ground state preparation; however, in reality the initial state will
have imperfect overlap with the true ground state. Here we address that problem
in two ways: by faster preparation of matrix product state (MPS)
approximations, and more efficient filtering of the prepared state to find the
ground state energy. We show how to achieve unitary synthesis with a Toffoli
complexity about $7 \times$ lower than that in prior work, and use that to
derive a more efficient MPS preparation method. For filtering we present two
different approaches: sampling and binary search. For both we use the theory of
window functions to avoid large phase errors and minimise the complexity. We
find that the binary search approach provides better scaling with the overlap
at the cost of a larger constant factor, such that it will be preferred for
overlaps less than about $0.003$. Finally, we estimate the total resources to
perform ground state energy estimation of Fe-S cluster systems, including the
FeMo cofactor by estimating the overlap of different MPS initial states with
potential ground-states of the FeMo cofactor using an extrapolation procedure.
{With a modest MPS bond dimension of 4000, our procedure produces an estimate
of $\sim 0.9$ overlap squared with a candidate ground-state of the FeMo
cofactor, producing a total resource estimate of $7.3 \times 10^{10}$ Toffoli
gates; neglecting the search over candidates and assuming the accuracy of the
extrapolation, this validates prior estimates that used perfect ground state
overlap. This presents an example of a practical path to prepare states of high
overlap in a challenging-to-compute chemical system.