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Physical Review A

Multiqubit controlled unitary gate by adiabatic passage with an optical cavity

Hayato Goto, Kouichi Ichimura

Published Jul 9, 2004• 97 citations
Publisher

Abstract

A new implementation of quantum gates by adiabatic passage with an optical cavity is proposed. This implementation allows one to perform not only elementary gates, such as one-qubit gates and a controlled-NOT gate, but also multiqubit controlled unitary gates. Some quantum gates are numerically simulated. From the simulation results, it is concluded that this implementation of the three-qubit controlled gates is more efficient than decomposing into the elementary gates.

DOI
10.1103/physreva.70.012305

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A new implementation of quantum gates by adiabatic passage with an optical cavity is proposed. This implementation allows one to perform not only elementary gates, such as one-qubit gates and a controlled-NOT gate, but also multiqubit controlled unitary gates. Some quantum gates are numerically simulated. From the simulation results, it is concluded that this implementation of the three-qubit controlled gates is more efficient than decomposing into the elementary gates.
We propose a fast scheme involving atoms fixed in an optical cavity to directly implement the universal controlled-unitary gate. The present technique based on adiabatic passage uses dark states well suited for the controlled-rotation operation. We show that these dark states allow the robust implementation of a gate that is a generalization of the controlled-unitary gate to the case where the control qubit can be selected to be an arbitrary state. This gate has potential applications to the rapid implementation of quantum algorithms such as the projective measurement algorithm. This process is decoherence-free since excited atomic states and cavity modes are not populated during the dynamics.
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.
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.
A scheme is proposed for realizing geometric quantum computation with one-qubit unitary gates and NNN-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 NNN-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.
Fundamental quantum gates can be implemented effectively using adiabatic quantum computation or circuit model. Recently, Hen combined the two approaches to introduce a new model called controlled adiabatic evolutions [I. Hen, Phys. Rev. A, 91(2) (2015) 022309]. This model was specifically designed to implement one and two-qubit controlled gates. Later, Santos extended Hen’s work to implement [Formula: see text]-qubit controlled gates [A. C. Santos and M. S. Sarandy, Sci. Rep., 5 (2015) 15775]. In this paper, we discuss the implementation of each of the usual quantum gates, as well as demonstrate the possibility of preparing Bell’s states using the controlled adiabatic evolutions approach. We conclude by presenting the fidelity results of implementing single quantum gates and Bell’s states in open systems.
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.