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Title: Grover Search and the No-Signaling Principle

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 117; Journal Issue: 12; Related Information: CHORUS Timestamp: 2016-09-14 18:09:40; Journal ID: ISSN 0031-9007
American Physical Society
Country of Publication:
United States

Citation Formats

Bao, Ning, Bouland, Adam, and Jordan, Stephen P. Grover Search and the No-Signaling Principle. United States: N. p., 2016. Web. doi:10.1103/PhysRevLett.117.120501.
Bao, Ning, Bouland, Adam, & Jordan, Stephen P. Grover Search and the No-Signaling Principle. United States. doi:10.1103/PhysRevLett.117.120501.
Bao, Ning, Bouland, Adam, and Jordan, Stephen P. 2016. "Grover Search and the No-Signaling Principle". United States. doi:10.1103/PhysRevLett.117.120501.
title = {Grover Search and the No-Signaling Principle},
author = {Bao, Ning and Bouland, Adam and Jordan, Stephen P.},
abstractNote = {},
doi = {10.1103/PhysRevLett.117.120501},
journal = {Physical Review Letters},
number = 12,
volume = 117,
place = {United States},
year = 2016,
month = 9

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevLett.117.120501

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  • In this Comment on Feng's paper [Phys. Rev. A 63, 052308 (2001)], we show that Grover's algorithm may be performed exactly using the gate set given, provided that small changes are made to the gate sequence. An analytic expression for the probability of success of Grover's algorithm for any unitary operator U instead of Hadamard gate is presented.
  • Following the proposal by [F. Yamaguchi et al. Phys. Rev. A 66, 010302(R) (2002)], we present an alternative way to implement the two-qubit Grover search algorithm in cavity QED. Compared with Yamaguchi et al.'s proposal, with a strong resonant classical field added, our method is insensitive to both the cavity decay and thermal field, and does not require that the cavity remain in the vacuum state throughout the procedure. Moreover, the qubit definitions are the same for both atoms, which makes the experiment easier. The strictly numerical simulation shows that our proposal is good enough to demonstrate a two-qubit Grover'smore » search with high fidelity.« less
  • Using resonant interaction of three Rydberg atoms with a single-mode microwave cavity, we consider a realization of the three-qubit Grover search algorithm in the presence of weak cavity decay, based on a previous idea for a three-qubit quantum gate [Chen et al., Phys. Rev. A 73, 064304 (2006)]. We simulate the searching process under the influence of the cavity decay and show that our scheme could be achieved efficiently to find a marked state with high fidelity. The required operations are very close to the capabilities of current cavity QED techniques.
  • We propose the physical implementation of a Grover-like search problem by means of Frenkel exciton trapping at a shallow isotopic impurity against a background of competing mechanisms. The search, culminating at the impurity molecule, designated the 'winner' site, is marked by its enhanced interaction with acoustic phonons at low temperatures. The quantum search proceeds with the assistance of an oracle-like exciton-phonon interaction that addresses only the impurity site via the Dyson propagator within the Green's function formalism. The optimum parameters of a graph lattice with long-range intersite interactions required to trap the exciton in the fastest time are determined, andmore » estimates of error rates for the naphthalene-doped organic system are evaluated. We extend the analysis of the quantum search to a fluctuating long-range interacting cycle (LRIC) graph-lattice system.« less
  • It is well-known that when searching one out of four, the original Grover's search algorithm is exact; that is, it succeeds with certainty. It is natural to ask the inverse question: If we are not searching one out of four, is Grover's algorithm definitely not exact? In this article we give a complete answer to this question through some rationality results of trigonometric functions.