N. Cerf, L. Grover, and C. Williams. Nested quantum search and NP-complete problems. Los Alamos Physics preprint archive, http://xxx.lanl.gov/abs/quantph /9806078, 1998. Home/Search Document Not in Database Summary Related Articles Check |
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Finding Solutions to NP Problems: Philosophical Differences.. - Greenwood (2001) (2 citations) (Correct)
...., then the probability of measuring a solution is jP jtij = r=2 . For small r this probability is quite small. Hence, in practice quantum search algorithms try to exploit quantum interference to amplify the amplitude of the desirable solutions and attenuate all other amplitudes. Cerf, et al. [16] provide a good description of exactly how this is done. Their approach relies on an oracle function c(x) that equals one for the optimal input x (and zero elsewhere) The goal is for the quantum system to evolve from an initial state jsi to the target state jti in minimum time. Note that c(x) ....
....average to guarantee success. However, it is possible to reduce this to the order of jhtjU jsij which can be a considerable savings with an appropriate quantum search algorithm. The algorithm begins in a superposition of states and any measurement is postponed until the end. Cerf, et al. [16] defined a specific unitary operator Q = Ue U where P s = jsihsj and P t = jtihtj are projection operators on jsi and jti. These exponential operators simple flip the phase on a state. For example, the phase of state jxi is flipped by iff x = s. Since the objective is search for state ....
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N. Cerf, L. Grover, and C. Williams. Nested quantum search and NP-complete problems. Los Alamos Physics preprint archive, http://xxx.lanl.gov/abs/quantph /9806078, 1998.
The search for a practical 'Ultimate Laptop': A Comparison of.. - Daley (1999) (Correct)
....solution to the problem and then using the search algorithm to find the correct one. The known complexity of Grover s search algorithm is p n, where n is the size of the solution space. This can in fact be improved to p n ff ; ff 1 if we take advantage of the problem s structure. See [12] for details. Since each node of the graph can only be visited once in a Hamiltonian path, the worst case scenario with a fully interconnected graph will have a solution space of size 7 , which results in a time complexity of p 7 71. It should thus take approximately 71 iterations of ....
N. J. Cerf et. al. Nested quantum search and NP-complete problems. Available http://xxx.lanl.gov/quant-ph/9806078, 1998.
Quantum Computation: Theory and Implementation - Boyden, III (1999) (Correct)
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Cerf, N., Grover, L., Williams, C., "Nested quantum search and NP-complete problems." quant-ph/9806078. 23 Jun 1998.
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