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International Journal of Geometric Methods in Modern Physics

Realization of the quantum Toffoli gate based on a six-level atomic system

A. Chouikh, Taoufik Said, M. Hammani, Mohamed Bennai

Published Jan 12, 2022• 3 citations
Publisher

Abstract

In this paper, we propose a scheme for implementing a Toffoli gate in a system with an atom that has six levels in a lambda configuration, interacting with a high-Q cavity containing four modes. Here, we reduce a six-level system into an effective three-level behavior by applying the adiabatic elimination method. Next, we calculate the probabilities of the states of the interest as well as the fidelity. We also study the effects of photonic and atomic decay rates on the evolution of the system which is reasonably less sensitive to decoherence.

DOI
10.1142/s0219887822500414

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In this paper, we propose a scheme for implementing a Toffoli gate in a system with an atom that has six levels in a lambda configuration, interacting with a high-Q cavity containing four modes. Here, we reduce a six-level system into an effective three-level behavior by applying the adiabatic elimination method. Next, we calculate the probabilities of the states of the interest as well as the fidelity. We also study the effects of photonic and atomic decay rates on the evolution of the system which is reasonably less sensitive to decoherence.
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 discuss how to implement quantum logic gates by considering a two-level-atom driven by a strong microwave field and successively interacting with m+1 cavity modes. The scheme is insensitive to the initial state of the atom, and the operation time is independent of the number of cavity modes involved in the system operations. This scheme is used to realize two quantum logic gates (m-target-qubit controlled-global-phase gate and Multi-qubit phase shift gate) in a time much shorter than the photonic lifetime. We also studied the influence of decoherence on the fidelity. In general, our system is reasonably less sensitive to the photonic and atomic decay rates and therefore it can be experimentally realized.
Single-step implementations of multiqubit gates are generally believed to provide a simpler design, a faster operation, and a lower decoherence. For three coupled qubits interacting with a photon field, a realizable scheme for a single-step Toffoli gate is investigated. We find that the three-qubit system can be described by four effective modified Jaynes-Cummings models in the states of two control qubits. Within the rotating-wave approximation, the modified Jaynes-Cummings models are shown to be reduced to the conventional Jaynes-Cummings models with renormalized couplings between qubits and photon fields. A single-step Toffoli gate is shown to be realizable with tuning of the four characteristic oscillation periods that satisfy a commensurate condition. Possible values of the system parameters are estimated for a single-step Toffoli gate. Further, we discuss our single-step Toffoli-gate operation errors due to imperfections in the system parameters; numerical calculations show that a Toffoli gate with high fidelity can be obtained by adjusting pairs of the photon-qubit and qubit-qubit coupling strengths. In addition, a decoherence effect on the Toffoli-gate operation due to a thermal reservoir is discussed.
We propose a distributed quantum architecture (three atoms trapped in three coupled cavities) to construct an asymmetric spin 1/2 Heisenberg XY model. The effective atom–atom coupling is obtained with the cavity modes and the atomic excited states being virtually populated. We then demonstrate that the model can be used for implementing a three-qubit Toffoli gate with high fidelity. The feasibility and effectiveness of our scheme as well as the influences of decoherence effects (the atomic spontaneous emission and the cavity decay) on the gate fidelity are finally discussed. The scheme can be generalized for distributed quantum computation with the Heisenberg XY model.
The Toffoli gate is an essential logic element, which permits implementation of a reversible processor. It is of relevance both for classical as well as quantum logics. We propose and theoretically study all-optical implementations of three-bit and four-bit Toffoli gates by application of adiabatic population transfer techniques. For a three-bit Toffoli gate we use variants of stimulated Raman adiabatic passage (STIRAP) processes in a ΛΛΛ-type level scheme, driven by two laser pulses at sufficiently large detunings. For the implementation of a four-bit Toffoli gate, we apply reversible adiabatic population transfer in five-level quantum systems, interacting with three laser pulses. We demonstrate correct all-optical implementation of the truth table of three-bit and four-bit Toffoli gates. Moreover, we derive conditions for adiabatic evolution of the population dynamics and robust operation of the gates.