Abstract
We solve the unstructured search problem in constant time by computing with a physically motivated nonlinearity of the Gross-Pitaevskii type. This speedup comes, however, at the novel expense of increasing the time-measurement precision. Jointly optimizing these resource requirements results in an overall scaling of N1/4. This is a significant, but not unreasonable, improvement over the N1/2 scaling of Grover's algorithm. Since the Gross-Pitaevskii equation approximates the multi-particle (linear) Schrödinger equation, for which Grover's algorithm is optimal, our result leads to a quantum information-theoretic lower bound on the number of particles needed for this approximation to hold, asymptotically.
| Original language | English (US) |
|---|---|
| Article number | 063014 |
| Journal | New Journal of Physics |
| Volume | 15 |
| DOIs | |
| State | Published - Jun 1 2013 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
Cite this
Nonlinear quantum search using the Gross-Pitaevskii equation. / Meyer, David A.; Wong, Thomas.
In: New Journal of Physics, Vol. 15, 063014, 01.06.2013.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Nonlinear quantum search using the Gross-Pitaevskii equation
AU - Meyer, David A.
AU - Wong, Thomas
PY - 2013/6/1
Y1 - 2013/6/1
N2 - We solve the unstructured search problem in constant time by computing with a physically motivated nonlinearity of the Gross-Pitaevskii type. This speedup comes, however, at the novel expense of increasing the time-measurement precision. Jointly optimizing these resource requirements results in an overall scaling of N1/4. This is a significant, but not unreasonable, improvement over the N1/2 scaling of Grover's algorithm. Since the Gross-Pitaevskii equation approximates the multi-particle (linear) Schrödinger equation, for which Grover's algorithm is optimal, our result leads to a quantum information-theoretic lower bound on the number of particles needed for this approximation to hold, asymptotically.
AB - We solve the unstructured search problem in constant time by computing with a physically motivated nonlinearity of the Gross-Pitaevskii type. This speedup comes, however, at the novel expense of increasing the time-measurement precision. Jointly optimizing these resource requirements results in an overall scaling of N1/4. This is a significant, but not unreasonable, improvement over the N1/2 scaling of Grover's algorithm. Since the Gross-Pitaevskii equation approximates the multi-particle (linear) Schrödinger equation, for which Grover's algorithm is optimal, our result leads to a quantum information-theoretic lower bound on the number of particles needed for this approximation to hold, asymptotically.
UR - http://www.scopus.com/inward/record.url?scp=84879340622&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84879340622&partnerID=8YFLogxK
U2 - 10.1088/1367-2630/15/6/063014
DO - 10.1088/1367-2630/15/6/063014
M3 - Article
AN - SCOPUS:84879340622
VL - 15
JO - New Journal of Physics
JF - New Journal of Physics
SN - 1367-2630
M1 - 063014
ER -