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arXiv:quant-ph/0203146 · Physical Review A

Quantum search with two-atom collisions in cavity QED

Fumiko Yamaguchi, P. Milman, M. Brune, J. M. Raimond, S. Haroche

Published Jul 24, 2002• 82 citations
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Abstract

We propose a scheme to implement the two-qubit Grover's quantum search algorithm using cavity quantum electrodynamics. In this scheme long-lived electronic states in circular Rydberg atoms are used as quantum bits (qubits). The atoms interact with the electromagnetic field of a nonresonant cavity. The quantum gate dynamics is provided by a cavity-assisted collision. We present the detailed procedure and analyze the experimental feasibility.

DOI
10.1103/physreva.66.010302

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We propose a scheme to implement the two-qubit Grover's quantum search algorithm using cavity quantum electrodynamics. In this scheme long-lived electronic states in circular Rydberg atoms are used as quantum bits (qubits). The atoms interact with the electromagnetic field of a nonresonant cavity. The quantum gate dynamics is provided by a cavity-assisted collision. We present the detailed procedure and analyze the experimental feasibility.
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.
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's search with high fidelity.
We explore the possibility of an N -qubit ( N > 3) Grover search in cavity QED, based on a fast operation of an N -qubit controlled phase-flip with atoms in resonance with the cavity mode. We demonstrate both analytically and numerically that our scheme can be achieved efficiently to find a marked state with high fidelity and high success probability. As an example, a ten-qubit Grover search is simulated specifically under the discussion of experimental feasibility and challenge. We argue that our scheme is applicable to the case involving an arbitrary number of qubits. As cavity decay is involved in our quantum trajectory treatment, we can analytically understand the implementation of a Grover search subject to dissipation, which will be very helpful for relevant experiments.
We present a simple protocol and quantum circuit for efficient implementation of the N-bit discrete quantum Fourier transform by using two-qubit controlled-NOT gate and SWCZ gate that is a combination of -SWAP and controlled-Z gates in cavity quantum electrodynamics. In this protocol long-lived electronic states in circular Rydberg atoms are used as quantum bits and the one-bit and two-bit quantum gate operations required for implementing the discrete quantum Fourier transform in the quantum circuit can be easily achieved with atom–microwave resonant interaction and atom–cavity interaction occurring only between two nearest-neighbour atoms. We present the detailed experimental procedure and analyse the experimental feasibility.