Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems
Abstract
We present a quantum eigenstate filtering algorithm based on quantum signal processing (QSP) and minimax polynomials. The algorithm allows us to efficiently prepare a target eigenstate of a given Hamiltonian, if we have access to an initial state with nontrivial overlap with the target eigenstate and have a reasonable lower bound for the spectral gap. We apply this algorithm to the quantum linear system problem (QLSP), and present two algorithms based on quantum adiabatic computing (AQC) and quantum Zeno effect respectively. Both algorithms prepare the final solution as a pure state, and achieves the near optimal $$\mathcal{\tilde{O}}$$(dκlog(1/ϵ)) query complexity for a
 Authors:

 Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Univ. of California, Berkeley, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC); US Air Force Office of Scientific Research (AFOSR)
 OSTI Identifier:
 1763676
 Grant/Contract Number:
 AC0205CH11231; SC0017867; FA95501810095
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Quantum
 Additional Journal Information:
 Journal Volume: 4; Journal ID: ISSN 2521327X
 Publisher:
 Quantum Science Open Community
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Lin, Lin, and Tong, Yu. Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems. United States: N. p., 2020.
Web. https://doi.org/10.22331/q20201111361.
Lin, Lin, & Tong, Yu. Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems. United States. https://doi.org/10.22331/q20201111361
Lin, Lin, and Tong, Yu. Wed .
"Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems". United States. https://doi.org/10.22331/q20201111361. https://www.osti.gov/servlets/purl/1763676.
@article{osti_1763676,
title = {Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems},
author = {Lin, Lin and Tong, Yu},
abstractNote = {We present a quantum eigenstate filtering algorithm based on quantum signal processing (QSP) and minimax polynomials. The algorithm allows us to efficiently prepare a target eigenstate of a given Hamiltonian, if we have access to an initial state with nontrivial overlap with the target eigenstate and have a reasonable lower bound for the spectral gap. We apply this algorithm to the quantum linear system problem (QLSP), and present two algorithms based on quantum adiabatic computing (AQC) and quantum Zeno effect respectively. Both algorithms prepare the final solution as a pure state, and achieves the near optimal $\mathcal{\tilde{O}}$(dκlog(1/ϵ)) query complexity for a dsparse matrix, where κ is the condition number, and ϵ is the desired precision. Neither algorithm uses phase estimation or amplitude amplification.},
doi = {10.22331/q20201111361},
journal = {Quantum},
number = ,
volume = 4,
place = {United States},
year = {2020},
month = {11}
}
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