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Realization of Toffoli Gate Based on Superconducting QuantumInterference Devices in Cavity Quantum Electrodynamics

彭俊 PENG Jun, 邬云文 WU Yunwen, 李小娟 LI Xiaojuan

Published Jan 1, 2011• 1 citation

Abstract

A theory scheme was proposed for implementing a Toffoli gate with three-level structure superconducting quantum-interference devices(SQUID),based on the cavity quantum electrodynamics(CQED).In this proposal,quantum information was encoded into the two lower levels of a SQUID while a higher level serves as the gate manipulation.Applying the coupling of the cavity field with a SQUID,which was driven by a classical microwave pulse to control the evolution of quantum state,the scheme could be extended to achieve N-qubit Toffoli gate.And,the experimental feasibility of Toffoli gate was disscussed,and the total operation time of four-qubit Toffoli gate was computed only 30 nanometers,which was much shorter than the decay time of the cavity mode or the energy relaxation time of the higher level.And the increasing rate of the gate response time became slow with the increase of the qubit number.

DOI: 10.3788/gzxb20114003.0466

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A theory scheme was proposed for implementing a Toffoli gate with three-level structure superconducting quantum-interference devices(SQUID),based on the cavity quantum electrodynamics(CQED).In this proposal,quantum information was encoded into the two lower levels of a SQUID while a higher level serves as the gate manipulation.Applying the coupling of the cavity field with a SQUID,which was driven by a classical microwave pulse to control the evolution of quantum state,the scheme could be extended to achieve N-qubit Toffoli gate.And,the experimental feasibility of Toffoli gate was disscussed,and the total operation time of four-qubit Toffoli gate was computed only 30 nanometers,which was much shorter than the decay time of the cavity mode or the energy relaxation time of the higher level.And the increasing rate of the gate response time became slow with the increase of the qubit number.

An alternative approach is proposed to realize an n -qubit Toffoli gate with superconducting quantum-interference devices (SQUIDs) in cavity quantum electrodynamics (QED). In the proposal, we represent two logical gates of a qubit with the two lowest levels of a SQUID while a higher-energy intermediate level of each SQUID is utilized for the gate manipulation. During the operating process, because the cavity field is always in vacuum state, the requirement on the cavity is greatly loosened and there is no transfer of quantum information between the cavity and SQUIDs.

This paper proposes a scheme for realization of a three-qubit Toffoli gate operation using three four-level atoms by a selective atom-field interaction in a cavity quantum electrodynamics system. In the proposed protocol, the quantum information is encoded on the stable ground states of atoms, and atomic spontaneous emission is negligible as the large atom-cavity detuning effectively suppresses the spontaneous decay of the atoms. The influence of the dissipation on fidelity and success probability of the three-qubit Toffoli gate is also discussed. The scheme can also be applied to realize an N -qubit Toffoli gate and the interaction time required does not rise with increasing the number of qubits.

We propose an approach to realize an

n

-qubit controlled-

U

gate with superconducting quantum interference devices (SQUIDs) in cavity QED. In this approach, the two lowest levels of a SQUID represent the two logical states of a qubit while a higher-energy intermediate level serves the gate manipulation. Our method operates essentially by creating a single photon through one of the control SQUIDs and then performing an arbitrary unitary transformation on the target SQUID with the assistance of the cavity photon. In addition, we show that the method can be applied to implement an

n

-qubit controlled-

U

gate with atomic qubits in cavity QED.

In the system with superconducting quantum interference devices (SQUID) in cavity, a scheme for constructing two-qubit quantum phase gate via a conventional geometric phase-shift is proposed by using a quantized cavity field and classical microwave pulses. In this scheme, the gate operation is realized in the subspace spanned by the two lower flux states of the SQUID system and the population operator of the excited state has no effect on it. Thus the effect of decoherence caused from the levels of the SQUID system is possible to minimize. Under cavity decay, our strictly numerical simulation shows that it is also possible to realize the unconventional geometric phase gate. The experimental feasibility is discussed in detail.

In the system with superconducting quantum interference devices (SQUID) in cavity,a scheme for con- structing two-qubit quantum phase gate via a conventional geometric phase-shift is proposed by using a quantized cavity field and classical microwave pulses.In this scheme,the gate operation is realized in the subspace spanned by the two lower flux states of the SQUID system and the population operator of the excited state has no effect on it.Thus the effect of decoherence caused from the levels of the SQUID system is possible to minimize.Under cavity decay,our strictly numerical simulation shows that it is also possible to realize the unconventional geometric phase gate.The experimental feasibility is discussed in detail.