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Communications in Theoretical Physics

Protected two-qubit entangling gate with mechanical driven continuous dynamical decoupling

Xue-jian Sun, Wenxiao Liu, Hao Chen, Chengyuan Wang, Hui-Zhong Ma, Hongrong Li

Published Apr 25, 2022• 2 citations
Publisher

Abstract

Abstract In this work, we propose a high-fidelity phonon-mediated entangling gate in a hybrid mechanical system based on two silicon-vacancy color centers in diamond. In order to suppress the influence of the spin decoherence on the entangling gate, we use a continuous dynamical decoupling approach to create new dressed spin states, which are less sensitive to environmental fluctuations and exhibit an extended T 2 * spin dephasing time. The effective spin–spin Hamiltonian modified by the mechanical driving field and the corresponding master equation are derived in the dispersive regime. We show that in the presence of the mechanical driving field, the effective spin–spin coupling can be highly controlled. By calculating the entangling gate fidelity in the dressed basis, we find that once the mechanical field is turned on, the gate fidelity can be significantly improved. In particular, under an optimized spin-phonon detuning and a stronger Rabi frequency of the mechanical driving field, the two-qubit gate is capable of reaching fidelity exceeding 0.99. Moreover, by employing appropriate driving modulation, we show that a high-fidelity full quantum gate can be also realized, in which the initial and final spin states are on a bare basis. Our work provides a promising scheme for realizing high-fidelity quantum information processing.

DOI
10.1088/1572-9494/ac69c5

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Abstract In this work, we propose a high-fidelity phonon-mediated entangling gate in a hybrid mechanical system based on two silicon-vacancy color centers in diamond. In order to suppress the influence of the spin decoherence on the entangling gate, we use a continuous dynamical decoupling approach to create new dressed spin states, which are less sensitive to environmental fluctuations and exhibit an extended T 2 * spin dephasing time. The effective spin–spin Hamiltonian modified by the mechanical driving field and the corresponding master equation are derived in the dispersive regime. We show that in the presence of the mechanical driving field, the effective spin–spin coupling can be highly controlled. By calculating the entangling gate fidelity in the dressed basis, we find that once the mechanical field is turned on, the gate fidelity can be significantly improved. In particular, under an optimized spin-phonon detuning and a stronger Rabi frequency of the mechanical driving field, the two-qubit gate is capable of reaching fidelity exceeding 0.99. Moreover, by employing appropriate driving modulation, we show that a high-fidelity full quantum gate can be also realized, in which the initial and final spin states are on a bare basis. Our work provides a promising scheme for realizing high-fidelity quantum information processing.
We analyze the implementation of high-fidelity, phonon-mediated gate operations and quantum simulation schemes for spin qubits associated with silicon vacancy centers in diamond. Specifically, we show how the application of continuous dynamical decoupling techniques can substantially boost the coherence of the qubit states while increasing at the same time the variety of effective spin models that can be implemented in this way. Based on realistic models and detailed numerical simulations, we demonstrate that this decoupling technique can suppress gate errors by more than two orders of magnitude and enable gate infidelities below $\ensuremath{\sim}{10}^{\ensuremath{-}4}$ for experimentally relevant noise parameters. Therefore, when generalized to phononic lattices with arrays of implanted defect centers, this approach offers a realistic path toward moderate- and large-scale quantum devices with spins and phonons at a level of control that is competitive with other leading quantum-technology platforms.
Hybrid systems consisting of different types of qubits are promising for building quantum computers if they combine useful properties of their constituent qubits. However, they also pose additional challenges if one type of qubits is more susceptible to environmental noise than the others. Dynamical decoupling can help to protect such systems by reducing the decoherence due to the environmental noise, but the protection must be designed such that it does not interfere with the control fields driving the logical operations. Here, we test such a protection scheme on a quantum register consisting of the electronic and nuclear spins of a nitrogen-vacancy center in diamond. The results show that processing is compatible with protection: The dephasing time was extended almost to the limit given by the longitudinal relaxation time of the electron spin.
Exchange-based two-qubit gates in semiconductor spin qubits are sensitive to low-frequency detuning noise and control errors. Here, we extend concatenated continuous driving (CCD), implemented by phase modulation of a global microwave drive, to exchange-based SWAP and SWAP\sqrt{\mathrm{SWAP}}SWAP​ operations between double-dressed spin qubits and investigate its effectiveness for protecting two-qubit gates. We find that CCD retains strong protection against quasistatic common-mode detuning errors while substantially improving robustness against Rabi-frequency errors and qubit-to-qubit Rabi-frequency mismatch compared with conventional continuous dressing. By contrast, the gate fidelity is impacted by differential detuning errors. By modeling partially correlated quasistatic detuning noise, we further show that the noise-averaged gate fidelity depends strongly on the spatial correlation of the qubit-frequency fluctuations, with positive correlations enhancing CCD protection by suppressing the differential-noise component. These results identify the symmetry and spatial correlation of qubit-frequency noise as key factors governing continuous-drive protection in coupled spin-qubit systems.
The recent realization of a coherent interface between a single electron in a silicon quantum dot and a single photon trapped in a superconducting cavity opens the way for implementing photon-mediated two-qubit entangling gates. In order to couple a spin to the cavity electric field, some type of spin-charge hybridization is needed, which impacts spin control and coherence. In this work we propose a cavity-mediated two-qubit gate and calculate cavity-mediated entangling gate fidelities in the dispersive regime, accounting for errors due to the spin-charge hybridization, as well as photon- and phonon-induced decays. By optimizing the degree of spin-charge hybridization, we show that two-qubit gates mediated by cavity photons are capable of reaching fidelities exceeding 9090%90 in present-day device architectures. High iswap gate fidelities are achievable even in the presence of charge noise at the level of $2\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{eV}$.
A practical implementation of a quantum computer requires robust qubits that are protected against their noisy environment. Dynamical decoupling techniques have been successfully used in the past to offer protected high-fidelity gate operations in negatively charged nitrogen-vacancy (${\mathrm{NV}}^{\ensuremath{-}}$) centers in diamond, albeit under specific conditions with the intrinsic nitrogen nuclear spin initialized. In this work, we show how the sinusoidally modulated, always rotating, and tailored (SMART) protocol, an extension of the dressed-qubit concept, can be implemented for continuous protection to offer Clifford gate fidelities compatible with fault-tolerant schemes, whilst prolonging the coherence time of a single ${\mathrm{NV}}^{\ensuremath{-}}$ qubit at room temperature. We show an improvement in the average Clifford gate fidelity from $0.940\ifmmode\pm\else\textpm\fi{}0.005$ for the bare qubit to $0.993\ifmmode\pm\else\textpm\fi{}0.002$ for the SMART qubit, with the nitrogen nuclear spin in a random orientation. We further show a $\ensuremath{\gtrsim}30$ times improvement in the qubit T2∗{T}_{2}^{*}T2∗​ coherence times compared to the bare qubit.
A field configuration utilizing local static fields and a few continuous-wave driving fields is constructed to achieve universal (but low-order) protection of two-qubit states. That is, two-qubit states can be protected against arbitrary system-environment coupling with control fields if their frequencies are sufficiently large as compared with the cutoff frequency of the environment. Equally important, we show that it is possible to construct driving fields to protect two-qubit entangling gates against decoherence, without assuming any particular form of system-environment coupling. Using a non-Markovian master equation, we further demonstrate the effectiveness of our continuous dynamical decoupling fields in protecting entanglement and the excellent performance of protected two-qubit gates in generating entanglement. The results are complementary to current studies of entanglement protection using universal dynamical decoupling pulse sequences.