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arXiv:0707.0334 · Physical Review A

Implementation of three-qubit Grover search in cavity quantum electrodynamics

Wan Li Yang, C. Y. Chen, Mang Feng

Published Nov 1, 2007• 37 citations
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Abstract

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.

DOI
10.1103/physreva.76.054301

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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 study the possibility of an implementation of N-qubit (N>3) Grover search in cavity QED, based on a fast operation of N-qubit controlled phase-flip with atoms in resonance with the cavity mode. We demonstrate both analytically and numerically that, our scheme could be achieved efficiently to find a marked state with high fidelity and high success probability. As cavity decay is involved in our quantum trajectory treatment, we could analytically understand the implementation of a Grover search subject to dissipation, which would be very helpful for relevant experiments.
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.
Abstract This work concerns a three-qubit processor implemented as three transmon-type superconducting qubits capacitively coupled to a superconducting resonator driven by a microwave field. Based on an effective Hamiltonian of this system, we propose a scheme to realize an X -rotation gate for three qubits requiring only a single-step operation. During the gate operation, the cavity photon-number is canceled due to the strong microwave field. It does not require the cavity to be initially in the vacuum state and the scheme is insensitive to cavity decay. We also present an effective scheme to implement Grover’s search algorithm based on this quantum gate and a phase oracle. Using numerical simulation and analysis, we show that the proposed schemes allow for efficiently finding the target state with a high fidelity. The potential application of these proposals with current QED circuit technology is also discussed.
We theoretically study the realization of a multi-qubit refined Deutsch-Jozsa (DJ) algorithm using resonant interaction of many Rydberg atoms with a single-mode microwave cavity, in which the multi-qubit controlled phase gates could be accomplished efficiently. We show how to achieve a multi-qubit refined DJ algorithm in high fidelity, even in the case of a weak cavity decay and some imperfection. We argue that the required operations in our scheme are almost within the present experimental possibilities.