Ming-Zhi Chung, Andreas Thomasen, Henry Liao, Ryosuke Imai
{"title":"Contrasting Statistical Phase Estimation with the Variational Quantum Eigensolver in the era of Early Fault Tolerant Quantum Computation","authors":"Ming-Zhi Chung, Andreas Thomasen, Henry Liao, Ryosuke Imai","doi":"arxiv-2409.07749","DOIUrl":null,"url":null,"abstract":"In this review, we give an overview of the proposed applications in the\nearly-FTQC (EFTQC) era. Starting from the error correction architecture for EFTQC device, we first\nreview the recently developed space-time efficient analogue rotation (STAR)\narchitecture \\cite{akahoshiPartiallyFaultTolerantQuantum2024}, which is a\npartially fault-tolerant error correction architecture. Then, we review the requirements of an EFTQC algorithm. In particular, the class of ground state energy estimation (GSEE) algorithm\nknown as the statistical phase estimation algorithm (SPE) is studied. We especially cast our attention on two SPE-type algorithms, the\nstep-function filter-based variant by Lin and Tong (LT22) \\cite{Lin:2021rwb}\nand Gaussian Filter \\cite{Wang:2022gxu}. Based on the latter, we introduce the Gaussian Fitting algorithm, which uses\nan alternative post-processing procedure compared to \\cite{Wang:2022gxu}. Finally, we systematically simulate the aforementioned algorithms and\nVariational Quantum Eigensolver (VQE) using the 1-uCJ ansatz with different\nshot counts. Most importantly, we perform noisy simulations based on the STAR\narchitecture. We find that for estimating the ground state energy of the 4-qubit $H_2$\nHamiltonian in the STO-3G basis, SPE becomes more advantageous over VQE when\nthe physical error rate is sufficiently low.","PeriodicalId":501226,"journal":{"name":"arXiv - PHYS - Quantum Physics","volume":"47 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","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-2409.07749","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
In this review, we give an overview of the proposed applications in the
early-FTQC (EFTQC) era. Starting from the error correction architecture for EFTQC device, we first
review the recently developed space-time efficient analogue rotation (STAR)
architecture \cite{akahoshiPartiallyFaultTolerantQuantum2024}, which is a
partially fault-tolerant error correction architecture. Then, we review the requirements of an EFTQC algorithm. In particular, the class of ground state energy estimation (GSEE) algorithm
known as the statistical phase estimation algorithm (SPE) is studied. We especially cast our attention on two SPE-type algorithms, the
step-function filter-based variant by Lin and Tong (LT22) \cite{Lin:2021rwb}
and Gaussian Filter \cite{Wang:2022gxu}. Based on the latter, we introduce the Gaussian Fitting algorithm, which uses
an alternative post-processing procedure compared to \cite{Wang:2022gxu}. Finally, we systematically simulate the aforementioned algorithms and
Variational Quantum Eigensolver (VQE) using the 1-uCJ ansatz with different
shot counts. Most importantly, we perform noisy simulations based on the STAR
architecture. We find that for estimating the ground state energy of the 4-qubit $H_2$
Hamiltonian in the STO-3G basis, SPE becomes more advantageous over VQE when
the physical error rate is sufficiently low.