TY - JOUR
T1 - Global symmetry is unnecessary for fast quantum search
AU - Janmark, Jonatan
AU - Meyer, David A.
AU - Wong, Thomas G.
PY - 2014/5/28
Y1 - 2014/5/28
N2 - Grover's quantum search algorithm can be formulated as a quantum particle randomly walking on the (highly symmetric) complete graph, with one vertex marked by a nonzero potential. From an initial equal superposition, the state evolves in a two-dimensional subspace. Strongly regular graphs have a local symmetry that ensures that the state evolves in a three-dimensional subspace but most have no global symmetry. Using degenerate perturbation theory, we show that quantum random walk search on known families of strongly regular graphs, nevertheless, achieves the full quantum speed-up of Θ(N), disproving the intuition that fast quantum search requires global symmetry.
AB - Grover's quantum search algorithm can be formulated as a quantum particle randomly walking on the (highly symmetric) complete graph, with one vertex marked by a nonzero potential. From an initial equal superposition, the state evolves in a two-dimensional subspace. Strongly regular graphs have a local symmetry that ensures that the state evolves in a three-dimensional subspace but most have no global symmetry. Using degenerate perturbation theory, we show that quantum random walk search on known families of strongly regular graphs, nevertheless, achieves the full quantum speed-up of Θ(N), disproving the intuition that fast quantum search requires global symmetry.
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U2 - 10.1103/PhysRevLett.112.210502
DO - 10.1103/PhysRevLett.112.210502
M3 - Article
AN - SCOPUS:84901675814
VL - 112
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 21
M1 - 210502
ER -