Abstract
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.
| Original language | English (US) |
|---|---|
| Article number | 210502 |
| Journal | Physical Review Letters |
| Volume | 112 |
| Issue number | 21 |
| DOIs | |
| State | Published - May 28 2014 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
Cite this
Global symmetry is unnecessary for fast quantum search. / Janmark, Jonatan; Meyer, David A.; Wong, Thomas.
In: Physical Review Letters, Vol. 112, No. 21, 210502, 28.05.2014.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Global symmetry is unnecessary for fast quantum search
AU - Janmark, Jonatan
AU - Meyer, David A.
AU - Wong, Thomas
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
VL - 112
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 21
M1 - 210502
ER -