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arXiv:0707.3054 · Physical Review Letters

Adiabatic Quantum Search Scheme With Atoms In a Cavity Driven by Lasers

D. Daems, S. Guérin

Published Oct 25, 2007• 26 citations
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Abstract

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.

DOI
10.1103/physrevlett.99.170503

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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.
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.
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.
We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover's problem [L. K. Grover, Phys. Rev. Lett. 79, 325 (1997)] of finding a marked item inside of an unsorted database. We show that the energy gap between the ground and excited states depends on the relaxation parameters and is not exponentially small. This allows a significant reduction of the searching time, which is proportional to the number of qubits. We discuss the relations between the probabilities of finding the ground state and the survival of a quantum computer in a dissipative environment, and we discuss alternate ways to solve NPNPNP-complete problems.
We propose a robust and decoherence insensitive scheme to generate controllable entangled states of two three-level atoms interacting with an optical cavity and a laser beam. Losses due to atomic spontaneous transitions and to cavity decay are efficiently suppressed by employing fractional adiabatic passage and appropriately designed atom-field couplings. In this scheme the two atoms traverse the cavity-mode and the laser beam in opposite directions and become entangled in the free space outside the cavity. We also show that the coherence of a traveling atom can be transferred to the other one without populating the cavity mode.
We present a method for realizing efficiently Grover's search algorithm in an array of coupled cavities doped with three-level atoms. We show that by encoding information in the lowest two ground states of the dopants and through the application of appropriately tuned global laser fields, the reflection operator needed for the quantum search algorithm can be realized in a single physical operation. Thus, the time steps in which Grover's search can be implemented become equal to the mathematical steps , where N is the size of the register. We study the robustness of the implementation against errors due to photon loss and fluctuations in the cavity frequencies and atom-photon coupling constants.