Runtime of unstructured search with a faulty Hamiltonian oracle
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PhysRevA.90.022310.pdf
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86.45 KB
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Author(s)
Temme, Kristan
Date Issued
August 2014
Journal
Physical Review A
Publisher
American Physical Society
Citation
Temme, Kristan. “Runtime of Unstructured Search with a Faulty Hamiltonian Oracle.” Phys. Rev. A 90, no. 2 (August 2014). © 2014 American Physical Society.
Version
Final published version
Abstract
We show that it is impossible to obtain a quantum speedup for a faulty Hamiltonian oracle. The effect of dephasing noise to this continuous-time oracle model has first been investigated by Shenvi, Brown, and Whaley [Phys. Rev. A 68, 052313 (2003).]. The authors consider a faulty oracle described by a continuous-time master equation that acts as dephasing noise in the basis determined by the marked item. The analysis focuses on the implementation with a particular driving Hamiltonian. A universal lower bound for this oracle model, which rules out a better performance with a different driving Hamiltonian, has so far been lacking. Here, we derive an adversary-type lower bound which shows that the evolution time T has to be at least in the order of N, i.e., the size of the search space, when the error rate of the oracle is constant. This means that quadratic quantum speedup vanishes and the runtime assumes again the classical scaling. For the standard quantum oracle model this result was first proven by Regev and Schiff [in Automata, Languages and Programming, Lecture Notes in Computer Science Vol. 5125 (Springer, Berlin, 2008), pp. 773–781]. Here, we extend this result to the continuous-time setting.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.90.022310
