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Journal of Physics B Atomic Molecular and Optical Physics

Fault tolerant analogue search algorithm within a quantum network

Jie Song, Xiudong Sun, Yan Xia, He‐Shan Song

Published May 19, 2011• 0 citations
Publisher

Abstract

We investigate how to implement an analogue search algorithm by adiabatic passage in distant cavities. Any atom with a mark can be found by adjusting the classical fields according to the search condition. The decoherence due to the spontaneous emission of excited states and the decay of fibre modes is efficiently suppressed. In the presence of cavity decay, the fidelity for performing the search algorithm is improved by quantum feedback control.

DOI
10.1088/0953-4075/44/11/115503

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We investigate how to implement an analogue search algorithm by adiabatic passage in distant cavities. Any atom with a mark can be found by adjusting the classical fields according to the search condition. The decoherence due to the spontaneous emission of excited states and the decay of fibre modes is efficiently suppressed. In the presence of cavity decay, the fidelity for performing the search algorithm is improved by quantum feedback control.
This paper proposes a scheme for implementing the adiabatic quantum search algorithm of different marked items in an unsorted list of N items with atoms in a cavity driven by lasers. N identical three-level atoms are trapped in a single-mode cavity. Each atom is driven by a set of three pulsed laser fields. In each atom, the same level represents a database entry. Two of the atoms are marked differently. The marked atom has an energy gap between its two ground states. The two different marked states can be sought out respectively starting from an initial entangled state by controlling the ratio of three pulse amplitudes. Moreover, the mechanism, based on adiabatic passage, constitutes a decoherence-free method in the sense that spontaneous emission and cavity damping are avoided since the dynamics follows the dark state. Furthermore, this paper extends the algorithm with m (m > 2) atoms marked in an ideal situation. Any different marked state can be sought out.
We propose an implementation of the quantum search algorithm of a marked item in an unsorted list of N items by adiabatic passage in a cavity-laser-atom system. We use an ensemble of N identical three-level atoms trapped in a single-mode cavity and driven by two lasers. In each atom, the same level represents a database entry. One of the atoms is marked by having an energy gap between its two ground states. Appropriate time delays between the two laser pulses allow one to populate the marked state starting from an initial entangled state within a decoherence-free adiabatic subspace. The time to achieve such a process is shown to exhibit the square root N Grover speedup.
A physical implementation of the adiabatic Grover search is theoretically investigated in a system of NNN identical three-level atoms trapped in a single-mode cavity. Some of the atoms are marked through the presence of an energy gap between their two ground states. The search is controlled by two partially delayed lasers which allow a deterministic adiabatic transfer from an initially entangled state to the marked states. Pulse schemes are proposed to satisfy the Grover speedup either exactly or approximately, and the success rate of the search is calculated.
A scheme is presented to realize transfer of a three-dimensional quantum state between two atoms trapped in distant cavities connected by an optical fiber, whose mode is resonant with the polarization cavity modes. Performing an adiabatic passage along dark states, the fiber mode remains in the vacuum state and the population of the cavities being excited can be negligible under certain conditions. In addition, atomic transitions in our scheme are largely detuned from cavity modes. As a consequence, the atomic spontaneous emission and the fiber decay can be effectively eliminated. Furthermore, we give some discussions about the fidelity of our scheme.
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.