Quantum expanders from any classical Cayley graph expander
2008 ◽
Vol 8
(8&9)
◽
pp. 715-721
◽
Keyword(s):
We give a simple recipe for translating walks on Cayley graphs of a group G into a quantum operation on any irrep of G. Most properties of the classical walk carry over to the quantum operation: degree becomes the number of Kraus operators, the spectral gap becomes the gap of the quantum operation (viewed as a linear map on density matrices), and the quantum operation is efficient whenever the classical walk and the quantum Fourier transform on G are efficient. This means that using classical constant-degree constant-gap families of Cayley expander graphs on e.g. the symmetric group, we can construct efficient families of quantum expanders.
2004 ◽
Vol 323
(1-2)
◽
pp. 48-56
◽
2005 ◽
Vol 03
(02)
◽
pp. 413-424
◽
2016 ◽
Vol 114
(2)
◽
pp. 20004
◽
2012 ◽
Vol 12
(2)
◽
pp. 793-803
◽
2015 ◽
Vol 13
(07)
◽
pp. 1550059
◽
2018 ◽
Vol 22
(12)
◽
pp. 2427-2430
◽
2007 ◽
Vol 103
(6)
◽
pp. 969-975
◽