TY - JOUR
T1 - Nonlinear quantum search using the Gross-Pitaevskii equation
AU - Meyer, David A.
AU - Wong, Thomas G.
PY - 2013/6
Y1 - 2013/6
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.
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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 -