Quantum expanders: Motivation and constructions

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

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations


We define quantum expanders in a natural way. We 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, Philips and Sarnak [27]. The second construction is combinatorial, and is based on a quantum variant of the Zig-Zag product introduced by Reingold, Vadhan and Wigderson [35]. Both constructions are of constant degree, and the second one is explicit. Using quantum expanders, we characterize the complexity of comparing and estimating quantum entropies. Specifically, we consider the following task: given two mixed stales, each given by a quantum circuit generating it, decide which mixed state has more entropy. We show that this problem is QSZK-complele (where QSZK is the class of languages having a zero-knowledge quantum interactive protocol). This problem is very well motivated from a physical point of view. Our proof resembles the classical proof that the entropy difference problem is SZK-complete, but crucially depends on the use of quantum expanders.

Original languageAmerican English
Title of host publicationProceedings - 23rd Annual IEEE Conference on Computational Complexity, CCC 2008
Number of pages12
StatePublished - 2008
Externally publishedYes
Event23rd Annual IEEE Conference on Computational Complexity, CCC 2008 - College Park, MD, United States
Duration: 23 Jun 200826 Jun 2008

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159


Conference23rd Annual IEEE Conference on Computational Complexity, CCC 2008
Country/TerritoryUnited States
CityCollege Park, MD


Dive into the research topics of 'Quantum expanders: Motivation and constructions'. Together they form a unique fingerprint.

Cite this