Abstract
A randomly walking quantum particle searches in Grover’s (formula presented) iterations for a marked vertex on the complete graph of N vertices by repeatedly querying an oracle that flips the amplitude at the marked vertex, scattering by a “coin” flip, and hopping. Physically, however, potential energy barriers can hinder the hop and cause the search to fail, even when the amplitude of not hopping decreases with N. We correct for these errors by interpreting the quantum walk search as an amplitude amplification algorithm and modifying the phases applied by the coin flip and oracle such that the amplification recovers the (formula presented) runtime.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1365-1372 |
| Number of pages | 8 |
| Journal | Quantum Information and Computation |
| Volume | 15 |
| Issue number | 15-16 |
| State | Published - Jan 1 2015 |
| Externally published | Yes |
Fingerprint
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Computational Theory and Mathematics
Cite this
Correcting for potential barriers in quantum walk search. / Ambainis, Andris; Wong, Thomas.
In: Quantum Information and Computation, Vol. 15, No. 15-16, 01.01.2015, p. 1365-1372.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Correcting for potential barriers in quantum walk search
AU - Ambainis, Andris
AU - Wong, Thomas
PY - 2015/1/1
Y1 - 2015/1/1
N2 - A randomly walking quantum particle searches in Grover’s (formula presented) iterations for a marked vertex on the complete graph of N vertices by repeatedly querying an oracle that flips the amplitude at the marked vertex, scattering by a “coin” flip, and hopping. Physically, however, potential energy barriers can hinder the hop and cause the search to fail, even when the amplitude of not hopping decreases with N. We correct for these errors by interpreting the quantum walk search as an amplitude amplification algorithm and modifying the phases applied by the coin flip and oracle such that the amplification recovers the (formula presented) runtime.
AB - A randomly walking quantum particle searches in Grover’s (formula presented) iterations for a marked vertex on the complete graph of N vertices by repeatedly querying an oracle that flips the amplitude at the marked vertex, scattering by a “coin” flip, and hopping. Physically, however, potential energy barriers can hinder the hop and cause the search to fail, even when the amplitude of not hopping decreases with N. We correct for these errors by interpreting the quantum walk search as an amplitude amplification algorithm and modifying the phases applied by the coin flip and oracle such that the amplification recovers the (formula presented) runtime.
UR - http://www.scopus.com/inward/record.url?scp=84942066511&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84942066511&partnerID=8YFLogxK
M3 - Article
VL - 15
SP - 1365
EP - 1372
JO - Quantum Information and Computation
JF - Quantum Information and Computation
SN - 1533-7146
IS - 15-16
ER -