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An Explicit Construction of Quantum Expanders · Around

2007

An Explicit Construction of Quantum Expanders

Ben-Aroya, Avraham, Schwartz, Oded, Ta-Shma, Amnon

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Understand

Quantum expanders are a natural generalization of classical expanders.

These objects were introduced and studied by Ben-Aroya and Ta-Shma and by Hastings.
In this note we show how to construct explicit, constant-degree quantum expanders.
The construction is essentially the classical Zig-Zag expander construction, applied to quantum expanders.

Built on

Entropy waves, the zig-zag graph product, and new constant-degree expanders
O. Reingold, S. Vadhan, and A. Wigderson · 2002
Earlier work this paper cites.
The Solovay-Kitaev algorithm
C. M. Dawson and M. A. Nielsen · 2006
Earlier work this paper cites.

Similar

Entropy and entanglement in quantum ground states
M. B. Hastings · 2007
Cited alongside, same era.
Quantum expanders and the quantum entropy difference problem
A. Ben-Aroya and A. Ta-Shma
Cited in the paper.

Then

Random unitaries give quantum expanders
Original
M. B. Hastings · 2007
Closest in time.

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