Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems

Lin, Lin; Tong, Yu

doi:10.22331/q-2020-11-11-361

Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems

Journal Article · Wed Nov 11 00:00:00 EST 2020 · Quantum

DOI:https://doi.org/10.22331/q-2020-11-11-361· OSTI ID:1763676

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Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Univ. of California, Berkeley, CA (United States)

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 non-trivial 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 d -sparse matrix, where κ is the condition number, and ϵ is the desired precision. Neither algorithm uses phase estimation or amplitude amplification.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: US Air Force Office of Scientific Research (AFOSR); USDOE Office of Science (SC)

Grant/Contract Number:: AC02-05CH11231; SC0017867

OSTI ID:: 1763676

Journal Information:: Quantum, Journal Name: Quantum Vol. 4; ISSN 2521-327X

Publisher:: Quantum Science Open CommunityCopyright Statement

Country of Publication:: United States

Language:: English

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