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arXiv:1411.7434 · Physical Review A

Shortcuts to adiabatic passage for multiqubit controlled-phase gate

Yan Liang, Qi‐Cheng Wu, Shi‐Lei Su, Xin Ji, Shou Zhang

Published Mar 11, 2015• 69 citations
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Abstract

We propose an alternative scheme of shortcuts to a quantum controlled phase gate in a much shorter time based on the approach of Lewis-Riesenfeld invariants in cavity quantum electrodynamics systems. This scheme can be used to perform a one-qubit phase gate, a two-qubit controlled phase gate, as well as a multiqubit controlled phase gate. The strict numerical simulations demonstrate that the total operation time for implementing controlled phase gates is much shorter than previous schemes and very robust against decoherence.

DOI
10.1103/physreva.91.032304

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We propose an alternative scheme of shortcuts to a quantum controlled phase gate in a much shorter time based on the approach of Lewis-Riesenfeld invariants in cavity quantum electrodynamics systems. This scheme can be used to perform a one-qubit phase gate, a two-qubit controlled phase gate, as well as a multiqubit controlled phase gate. The strict numerical simulations demonstrate that the total operation time for implementing controlled phase gates is much shorter than previous schemes and very robust against decoherence.
The ``Lewis-Riesenfeld phases'' which play a crucial role in constructing shortcuts to adiabaticity may be a resource for the implementation of quantum phase gates. By combining ``Lewis-Riesenfeld invariants'' with ``quantum Zeno dynamics,'' we propose an effective scheme of rapidly implementing $\ensuremath{\pi}$ phase gates via constructing shortcuts to adiabatic passage in a two-distant-atom-cavity system. The influence of various decoherence processes such as spontaneous emission and photon loss on the fidelity is discussed. It is noted that this scheme is insensitive to both error sources. Additionally, a creation of NNN-atom cluster states is put forward as a typical example of the applications of the fast and noise-resistant phase gates. The study results show that the shortcuts idea is not only applicable in other logic gates with different systems, but also propagable for many quantum information tasks.
Abstract Through combining ‘Lewis–Riesenfeld invariants’ and ‘transitionless quantum driving’ with ‘quantum zeno subspace’ and ‘second-order perturbation approximation’, respectively, we put forward two different methods to construct shortcuts via nonadiabatic processes to present robust quantum phase gates in a two-atom system. The influence of various decoherence processes such as spontaneous emission and photon loss on the fidelity is discussed. The result shows that this scheme is insensitive to both the two error sources. Moreover, the interaction time of the scheme is very short and precise control is not required. Additionally, this scheme is not only implemented without requiring extra complex conditions, but is also insensitive to variations of the parameters. Therefore, this scheme may provide a new perspective for quantum computation.
Based on the shortcuts to adiabatic passage, we propose a scheme for directly implementing a controlled-not (CNOT) gate in a cavity quantum electrodynamics system. Moreover, we generalize the scheme to realize a CNOT gate in two separate cavities connected by an optical fiber. The strictly numerical simulation shows that the schemes are fast and insensitive to the decoherence caused by atomic spontaneous emission and photon leakage. In addition, the schemes can provide a theoretical basis for the manipulation of the multiqubit quantum gates in distant nodes of a quantum network.
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.