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2010

Quantum Expanders: Motivation and Construction

9 years 4 months ago
Quantum Expanders: Motivation and Construction
: We define quantum expanders in a natural way and give two constructions of quantum expanders, both based on classical expander constructions. The first construction is algebraic, and is based on the construction of Cayley Ramanujan graphs over the group PGL(2,q) given by Lubotzky, Phillips, and Sarnak (1988). The second construction is combinatorial, and is based on a quantum variant of the Zig-Zag product introduced by Reingold, Vadhan, and Wigderson (2000). Both constructions are of constant degree, and the second one is explicit. Using another construction of quantum expanders by Ambainis and Smith (2004), we characterize the complexity of comparing and estimating quantum entropies. Specifically, we consider the following task: given two mixed states, each given by a quantum circuit generating it, decide which mixed state has more entropy. We show that this problem is QSZK
Avraham Ben-Aroya, Oded Schwartz, Amnon Ta-Shma
Added 22 May 2011
Updated 22 May 2011
Type Journal
Year 2010
Where TOC
Authors Avraham Ben-Aroya, Oded Schwartz, Amnon Ta-Shma
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