Random Unitaries Give Quantum Expanders

T. Eguchi and H. Kawai, Phys. Rev. Lett. 48

1982

Earlier work this paper cites.

R. M. Tanner, SIAM J. Algebraic Discrete Methods 5(3)

1984

Earlier work this paper cites.

N. Alon and V. D. Milman, J. Comb. Theory B 38

1985

Earlier work this paper cites.

M. Pinsker, 7th Internat. Teletraffic Confere

1987

Earlier work this paper cites.

G. A. Margulis, Problemy Peredaci Informacii, 9(4)

1988

Earlier work this paper cites.

N. Alon, Combinatorica 6

1991

Cited alongside, same era.

M. Fannes, B. Nachtergaele, and R. F. Werner, Commun. Math. Phys. 144

1992

Cited alongside, same era.

M. Sipser and D. Spielman, IEEE Trans. on Inf. Theory, 42(6)

1996

Cited alongside, same era.

J. Friedman, Conf. Proc. of the Annual ACM Symposium on Theory of Computing, 720 (2003); J. Friedman, preprint cs/0405020

2003

Cited alongside, same era.

M. B. Hastings, Phys. Rev. Lett. 93

2004

Cited alongside, same era.

M. B. Hastings, preprint cond-mat/0701055, Phys. Rev. B, in press

Cited in the paper.

A. Ben-Aroya and A. Ta-Shma, preprint quant-ph/0702129

Cited in the paper.

An appropriate formal definition may be to define a ( D , | λ 2 | , N , S ) (D,|\lambda_{2}|,N,S) expander, where S S is the entropy of the eigenvector with eigenvalue unity

Cited in the paper.

An example where the series has an infinite number of non-vanishing coefficients is the average of tr ⁡ ( U ​ U ​ V ​ V ) ​ tr ​ ( V † ​ V † ​ U † ​ U † ) {\rm tr}(UUVV){\rm tr}(V^{\dagger}V^{\dagger}U^{\dagger}U^{\dagger}) over all unitary matrices U , V U,V . A single application of Eq. ( 20

Cited in the paper.

We refer to these as “rung cancellations” because in certain diagrammatic expansions they correspond to a single rung of a ladder diagram from field theory

Cited in the paper.

M. B. Hastings, Phys. Rev. B 69

2004

Later among the works it cites.

S. Hoory, N. Linial, and A. Wigderson, Bulletin of the AMS 43(4)

2006

Later among the works it cites.

I. Dinur, Proc. of the Annual ACM Symposium on the Theory of Computing, 241 (2006)

2006

Later among the works it cites.

M. B. Hastings, arxiv:0705.2024

Original

2024

Closest in time.