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Results in Physics

Quantum Toffoli gate in hybrid optomechanical system

Lei Peng, Yang Zhang, Jiong Cheng, Wen-Zhao Zhang

Published Feb 22, 2022• 7 citations
Publisher

Abstract

An quantum Toffoli gate based on optomechanical system is proposed. By exploring the hybrid optomechanical system, we show that there are equivalence third order Kerr nonlinear effects between optical and mechanical modes. Through parameter analysis, we find that the nonlinear coefficient can be much stronger than the one under natural conditions. By taking advantage of this nonlinear effect, we can achieve high fidelity photon–phonon Toffoli gate. In the presence of dissipation and noise, we calculate the implementation time and fidelity of Toffoli gate. In addition, the application of this protocol in universal fault-tolerant quantum computation is also analyzed. Our study provides an effective platform for hybrid quantum computation.

DOI
10.1016/j.rinp.2022.105338

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An quantum Toffoli gate based on optomechanical system is proposed. By exploring the hybrid optomechanical system, we show that there are equivalence third order Kerr nonlinear effects between optical and mechanical modes. Through parameter analysis, we find that the nonlinear coefficient can be much stronger than the one under natural conditions. By taking advantage of this nonlinear effect, we can achieve high fidelity photon–phonon Toffoli gate. In the presence of dissipation and noise, we calculate the implementation time and fidelity of Toffoli gate. In addition, the application of this protocol in universal fault-tolerant quantum computation is also analyzed. Our study provides an effective platform for hybrid quantum computation.
Abstract A high‐dimensional quantum gate not only enables the processing of more information through parallel quantum channels but also enhances fault tolerance in a higher Hilbert space. In this paper, a protocol is presented for implementing a three‐qudit ‐Dimensional (D) Toffoli gate for a hybrid system, where the first control qudit, the second control qudit, and the target qudit of four dimension are encoded in the spatial‐polarization state of a flying photon, the electron‐spin state of the first two quantum dots (QDs), and the one of the remaining two QDs, respectively. Besides, the high‐dimensional Toffoli gate does not require any assistance. Moreover, the gate operates deterministically in principle, as the photon is easy to manipulate feasibly using simple optical elements, and four QDs have a long electron‐spin coherent time used for storage and manipulation. Furthermore, the success probability and fidelity of the high‐dimensional Toffoli gate, in alignment with current technological capabilities, demonstrate satisfactory results. This indicates that it is feasible in experimental settings and promises a quantum computing paradigm that excels in speed, error resilience, and scalability for intricate quantum operations.
Based on photon-phonon nonlinear interaction, a scheme of controllable photon-phonon converters is proposed at single-quantum level in a composed quadratically coupled optomechanical system. With the assistance of the mechanical oscillator, the Kerr nonlinear effect between photon and phonon is enhanced so that the single-photon state can be converted into the phonon state with high fidelity even under the current experimental condition that the single-photon coupling rate is much smaller than mechanical frequency (g ≪ ωm). The state transfer protocols and their transfer fidelity are discussed analytically and numerically. A multi-path photon-phonon converter is designed by combining the optomechanical system with low frequency resonators, which can be controlled by experimentally adjustable parameters. This work provides us a potential platform for quantum state transfer and quantum information.
High-fidelity quantum logic gates are essential in quantum computation, and both photons and electron spins in quantum dots (QDs) have their own unique advantages in implementing quantum computation. It is of critical significance to achieve high-fidelity quantum gates for photon-QD hybrid systems. Here, we propose two schemes for implementing high-fidelity universal quantum gates including Toffoli gate and Fredkin gate for photon-QD hybrid systems, utilizing the practical scattering of a single photon off a QD-cavity system. The computation errors from the imperfections involved in the practical scattering are detected and prevented from arising in the final results of the two gates. Accordingly, the unity fidelity of each quantum gate is obtained in the nearly realistic condition, and the requirement for experimental realization is relaxed. Furthermore, the quantum circuits for the two gates are compact and no auxiliary qubits are required, which would also be the advantages regarding their experimental feasibility. These features indicate that our schemes may be useful in the practical quantum computation tasks.
We propose a scheme for an optomechanical control phase-flip gate(CPFG) based on optomechanical equivalence Kerr nonlinearity. Analytical conditions for realization of CPFG is provided. By numerically solving the master equation of the system, we show that the fidelity of the two-qubit CPFG periodically achieves its maximum values under the condition of the appropriate rate of the coupling strengths. This scheme can break the limit of the Kerr effect at the single-photon level compared with the nature Kerr medium.
The Toffoli gate is an especially important case of the quantum gates. In this paper, we show how to construct Toffoli gates using several additional (ancilla) photons, linear optical instruments and cross-Kerr nonlinearities. Then they are expanded to implement Extended Toffoli gates (ETOF). Our work shows only one n-IPC (n-input parity check) gate plus at most 2m CNOT or NCNOT gates can implement arbitrary ETOF (n, m), indicating the feasibility and advantage of modularizing quantum gates with photons.
Abstract Photon statistics in a weakly driven optomechanical cavity, with Kerr-type nonlinearity, are analyzed both analytically and numerically. The single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function g (2) (0). The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. A systematic study on the parameter regime for observing photon blockade in the weak coupling regime is reported. The parameter regime where the photon blockade is not realizable due to the combined effect of nonlinearities owing to the optomechanical coupling and the Kerr-effect is demonstrated. The experimental feasibility with state-of-the-art device parameters is discussed and it is observed that photon blockade could be generated at the telecommunication wavelength. An elaborate analysis of the thermal effects on photon antibunching is presented. The system is found to be robust against pure dephasing-induced decoherences and thermal phonon number fluctuations.