Fetching the paper…

Reading the bibliography…

2021

A theory of quantum subspace diagonalization

Epperly, Ethan N., Lin, Lin, Nakatsukasa, Yuji

Original
PDF
Post on X

Understand

Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large\rev{-}scale eigenvalue problems using quantum computers.

Unfortunately, these methods require the solution of an ill-conditioned generalized eigenvalue problem, with a matrix pair corrupted by a non-negligible amount of noise that is far above the machine precision.
Despite pessimistic predictions from classical \rev{worst-case} perturbation theories, these methods can perform reliably well if the generalized eigenvalue problem is solved using a standard truncation strategy.
By leveraging and advancing classical results in matrix perturbation theory, we provide a theoretical analysis of this surprising phenomenon, proving that under certain natural conditions, a quantum subspace diagonalization algorithm can accurately compute the smallest eigenvalue of a large Hermitian matrix.

A theory of quantum subspace diagonalization · Around

Built on

R. M. Parrish and P. L. McMahon
Original
1909
Earlier work this paper cites.
P.-O. Löwdin
1967
Earlier work this paper cites.
C. Davis and W. M. Kahan
1970
Earlier work this paper cites.
G. Fix and R. Heiberger
1972
Earlier work this paper cites.
G. W. Stewart
1979
Earlier work this paper cites.
J. H. Wilkinson
1979
Earlier work this paper cites.
A. Emami-Naeini and P. Van Dooren
1982
Earlier work this paper cites.
L. A. Gribov and B. K. Novosadov
1986
Earlier work this paper cites.
J. W. Negele and H. Orland
1988
Earlier work this paper cites.
G. W. Stewart and J.-G. Sun
1990
Earlier work this paper cites.
M. Jungen and K. Kaufmann
1992
Earlier work this paper cites.
M. R. Wall and D. Neuhauser
1995
Earlier work this paper cites.
R. Bhatia
1997
Earlier work this paper cites.

Similar

V. A. Mandelshtam and H. S. Taylor
1997
Cited alongside, same era.
B. N. Parlett
1998
Cited alongside, same era.
M. A. Nielsen and I. Chuang
2000
Cited alongside, same era.
R. Mathias and C.-K. Li
2004
Cited alongside, same era.
Y. Cai, Z. Bai, J. E. Pask, and N. Sukumar
2013
Cited alongside, same era.
G. H. Golub and C. F. Van Loan
2013
Cited alongside, same era.
Å. Björck
2015
Cited alongside, same era.
J. A. Tropp
2015

Then

P. Weinberg and M. Bukov
2019
Later among the works it cites.
W. J. Huggins, J. Lee, U. Baek, B. O’Gorman, and K. B. Whaley
2020
Later among the works it cites.
M. Lotz and V. Noferini
2020
Later among the works it cites.
M. Motta, C. Sun, A. T. K. Tan, M. J. O’Rourke, E. Ye, A. J. Minnich, F. G. S. L. Brandão, and G. K.-L. Chan
2020
Later among the works it cites.
G. Nannicini
2020
Later among the works it cites.
I. Sabzevari, A. Mahajan, and S. Sharma
2020
Later among the works it cites.
N. H. Stair, R. Huang, and F. A. Evangelista
2020
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Cited alongside, same era.

J. R. McClean, M. E. Kimchi-Schwartz, J. Carter, and W. A. de Jong

2017

Cited alongside, same era.

P. Weinberg and M. Bukov

2017

Cited alongside, same era.

J. I. Colless, V. V. Ramasesh, D. Dahlen, M. S. Blok, M. E. Kimchi-Schwartz, J. R. McClean, J. Carter, W. A. de Jong, and I. Siddiqi

2018

Cited alongside, same era.

J. Preskill

2018

Cited alongside, same era.

A. M. Childs, Y. Su, M. C. Tran, N. Wiebe, and S. Zhu

2021

Closest in time.

C. L. Cortes and S. K. Gray

2021

Closest in time.

K. Klymko, C. Mejuto-Zaera, S. J. Cotton, F. Wudarski, M. Urbanek, D. Hait, M. Head-Gordon, K. B. Whaley, J. Moussa, N. Wiebe, W. A. de Jong, and N. M. Tubman

2021

Closest in time.

2021

Closest in time.

K. Seki and S. Yunoki

2021

Closest in time.