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Physical Review A

Robust and fast geometric quantum computation with multiqubit gates in cavity QED

Gongwei Lin, Xu‐Bo Zou, Xiu‐Min Lin, Guang‐Can Guo

Published Jun 9, 2009• 23 citations
Publisher

Abstract

A scheme is proposed for realizing geometric quantum computation with one-qubit unitary gates and $N$-qubit $(N\ensuremath{\ge}2)$ phase gates in cavity QED. In the scheme, the cavity field and excited states are virtually excited by controlling appropriately atom-field couplings and engineering adiabatic passage; thus the gate operations are insensitive to the cavity decay and the atomic spontaneous emission. Furthermore, the $N$-qubit $(N\ensuremath{\ge}2)$ geometric phase gates can be realized just by one step and the required time does not increase with the number of qubits, which can significantly reduce complexity of physical realization of practical quantum computation and quantum algorithms.

DOI
10.1103/physreva.79.064303

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A scheme is proposed for realizing geometric quantum computation with one-qubit unitary gates and NNN-qubit (N\ensuremath≥2)(N\ensuremath{\ge}2)(N\ensuremath≥2) phase gates in cavity QED. In the scheme, the cavity field and excited states are virtually excited by controlling appropriately atom-field couplings and engineering adiabatic passage; thus the gate operations are insensitive to the cavity decay and the atomic spontaneous emission. Furthermore, the NNN-qubit (N\ensuremath≥2)(N\ensuremath{\ge}2)(N\ensuremath≥2) geometric phase gates can be realized just by one step and the required time does not increase with the number of qubits, which can significantly reduce complexity of physical realization of practical quantum computation and quantum algorithms.
We propose a scheme for realizing two-qubit quantum phase gates via an unconventional geometric phase shift with atoms in a cavity. In the scheme the atoms interact simultaneously with a highly detuned cavity mode and a classical field. The atoms undergo no transitions during the gate operation, while the cavity mode is displaced along a circle in the phase space, aquiring a geometric phase conditional upon the atomic state. Under certain conditions, the atoms are disentangled with the cavity mode and thus the gate is insensitive to both the atomic spontaneous emission and the cavity decay.
We propose a one-step scheme to implement a multiqubit controlled phase gate with one qubit simultaneously controlling multiple qubits with three-level atoms at distant nodes in coupled cavity arrays. Selective qubit-qubit couplings are achieved by adiabatically eliminating the atomic excited states and photonic states, and the required phase shifts between the control qubit and any target qubit can be realized through suitable choices of the parameters of the external fields. Moreover, the effective model is robust against decoherence because neither the atoms nor the field modes are excited during the gate operation, leading to a useful step toward scalable quantum computing networks.
In this paper, we present a scheme for implementing the unconventional geometric two-qubit phase gate with nonzero dynamical phase based on two-channel Raman interaction of two atoms in a cavity. We show that the dynamical phase and the total phase for a cyclic evolution are proportional to the geometric phase in the same cyclic evolution; hence they possess the same geometric features as does the geometric phase. In our scheme, the atomic excited state is adiabatically eliminated, and the operation of the proposed logic gate involves only the metastable states of the atoms; thus the effect of the atomic spontaneous emission can be neglected. The influence of the cavity decay on our scheme is examined. It is found that the relations regarding the dynamical phase, the total phase, and the geometric phase in the ideal situation are still valid in the case of weak cavity decay. Feasibility and the effect of the phase fluctuations of the driving laser fields are also discussed.
We propose a way to realize a multiqubit controlled-phase gate with one qubit simultaneously controlling n target qubits using atoms in cavity QED. In this proposal, there is no need to use classical pulses during the entire gate operation. The gate operation time scales as |n\sqrt {n}n​| only and thus the gate can be performed faster when compared with sending atoms through the cavity one at a time. In addition, only three operational steps are required to realize this n-target-qubit controlled-phase gate. This proposal is quite general and can be applied to other physical systems, such as various superconducting qubits coupled to a resonator, NV centers coupled to a microsphere cavity, or quantum dots in cavity QED.
Using two cyclic three-level artificial atoms, we propose a scheme for realizing two-qubit quantum phase gates via an unconventional geometric phase shift in a cavity. In this scheme, the excited states of the two artificial atoms are adiabatically eliminated, and the logical gates' operation only involves their metastable states. Moreover, under certain conditions, the artificial atoms are disentangled with the cavity mode. Thus the gate is insensitive to both the cavity decay and the spontaneous emission of the artificial atoms.