Quantum Expanders: Motivation and Constructions

: 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 [29]. The second construction is combinatorial, and is based on a quantum variant of the Zig-Zag product introduced by Reingold, Vadhan and Wigderson [37]. Both constructions are of constant degree, and the second one is explicit. Using another construction of quantum expanders by Ambainis and Smith [6], 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

• Type: Conference
• Year: 2008
• Where: COCO
• Authors: Avraham Ben-Aroya, Oded Schwartz, Amnon Ta-Shma
• Keywords: Algorithms, COCO 2008, Israel BSF Grant, Quantum Expanders, USA Israel BSF