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arXiv:2208.14671 · Physical Review A

High-fidelity control of a nitrogen-vacancy-center spin qubit at room temperature using the sinusoidally modulated, always rotating, and tailored protocol

Hyma Harish Vallabhapurapu, Ingvild Hansen, Chris Adambukulam, Rainer Stöhr, Andrej Denisenko, Chih Hwan Yang, Arne Laucht

Published Aug 9, 2023• 16 citations
arXivHTMLPDF

Abstract

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 ${T}_{2}^{*}$ coherence times compared to the bare qubit.

DOI
10.1103/physreva.108.022606

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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 (NV\ensuremath−{\mathrm{NV}}^{\ensuremath{-}}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 NV\ensuremath−{\mathrm{NV}}^{\ensuremath{-}}NV\ensuremath− qubit at room temperature. We show an improvement in the average Clifford gate fidelity from 0.940\ifmmode±\else\textpm\fi0.0050.940\ifmmode\pm\else\textpm\fi{}0.0050.940\ifmmode±\else\textpm\fi0.005 for the bare qubit to 0.993\ifmmode±\else\textpm\fi0.0020.993\ifmmode\pm\else\textpm\fi{}0.0020.993\ifmmode±\else\textpm\fi0.002 for the SMART qubit, with the nitrogen nuclear spin in a random orientation. We further show a \ensuremath≳30\ensuremath{\gtrsim}30\ensuremath≳30 times improvement in the qubit T2∗{T}_{2}^{*}T2∗​ coherence times compared to the bare qubit.
Quantum computing based on solid state spins allows for densely packed arrays of quantum bits. However, the operation of large-scale quantum processors requires a shift in paradigm toward global control solutions. Here, we report a proof-of-principle demonstration of the SMART (sinusoidally modulated, always rotating, and tailored) qubit protocol. We resonantly drive a two-level system and add a tailored modulation to the dressing field to increase robustness to frequency detuning noise and microwave amplitude fluctuations. We measure a coherence time of 2 ms, corresponding to two orders of magnitude improvement compared to a bare spin, and an average Clifford gate fidelity exceeding 99%, despite the relatively long qubit gate times. We stress that the potential of this work lies in the scalability of the protocol and the relaxation of the engineering constraints for a large-scale quantum processor. This work shows that future scalable spin qubit arrays could be operated using global microwave control and local gate addressability, while increasing robustness to relevant experimental inhomogeneities.
Realistic quantum computing is subject to noise. Therefore, an important frontier in quantum computing is to implement noise-resilient quantum control over qubits. At the same time, dynamical decoupling can protect the coherence of qubits. Here we demonstrate non-trivial quantum evolution steered by dynamical decoupling control, which simultaneously suppresses noise effects. We design and implement a self-protected controlled-NOT gate on the electron spin of a nitrogen-vacancy centre and a nearby carbon-13 nuclear spin in diamond at room temperature, by employing an engineered dynamical decoupling control on the electron spin. Final state fidelity of 0.91(1) is observed in preparation of a Bell state using the gate. At the same time, the qubit coherence time is elongated at least 30 fold. The design scheme does not require the dynamical decoupling control to commute with the qubit interaction and therefore works for general qubit systems. This work marks a step towards implementing realistic quantum computing systems. Realistic quantum computers require a high degree of qubit control and must also be resilient to noise. Using dynamical decoupling control techniques, Liuet al.implement a self-protected controlled-NOT gate for electron and nuclear spins that retains a high final state fidelity.
Nitrogen-vacancy (NV) centers in diamond provide room-temperature electron-nuclear spin registers for quantum sensing and quantum information processing, with surrounding 13C nuclear spins serving as long-lived quantum memories. However, coherent control of large nuclear-spin registers is limited by finite electron-spin coherence and spectral addressability. Existing approaches follow two complementary strategies: dynamical-decoupling (DD) gates exploit filter-function resonances to realize selective conditional evolution but permit only discrete rotation angles, whereas dynamical-decoupling radio-frequency (DDrf) control restores continuous tunability at the cost of stringent hyperfine-geometry and RF-power requirements. Here, we introduce hybrid dynamical-decoupling and radio-frequency (H-DDrf) control, which preserves the DD-induced conditional evolution and employs a geometrically phase-matched RF drive to complete the target operation. This approach reduces both RF power and gate duration while maintaining high-fidelity control, thereby expanding the accessible 13C nuclear-spin register for room-temperature NV-based quantum memories and quantum processors.
Abstract A nitrogen-vacancy (NV) center in a diamond enables the access to an electron spin, which is expected to present highly sensitive quantum sensors. Although exploiting a nitrogen nuclear spin improves the sensitivity, manipulating it using a resonant pulse requires a long gate time owing to its small gyromagnetic ratio. Another technique to control nuclear spins is a conditional rotation gate based on dynamical decoupling, which is faster but unavailable for nitrogen spins owing to the lack of transverse hyperfine coupling with the electron spin. In this study, we generated effective transverse coupling by applying a weak off-axis magnetic field. An effective coupling depends on the off-axis field; the conditional rotation gate on the nitrogen-14 spins of an NV center was demonstrated within 4.2 μs under an 1.8% off-axis field and a longitudinal field of approximately 280 mT. We estimated that a population transfer from the electron to nitrogen spins can be implemented with 8.7 μs. Our method is applicable to an ensemble of NV centers, in addition to a single NV center.
A negatively-charged nitrogen-vacancy (NV) center in diamond is a promising system for quantum computation and quantum information. It has the diamond structure with a substitutional nitrogen atom and a neighboring vacancy. An electron spin in the NV center has an exceptionally long coherence time at room temperature. Thus the NV center has a potential to realize a room-temperature quantum computer which is more efficient than a classical computer. In this dissertation, we focus on the nitrogen nuclear spin as well as the electron spin in the NV center. Every NV center has the nitrogen nuclear spin. Because of the long coherence time of the nitrogen nuclear spin, it is a good candidate for a quantum memory. Thus it is important to prepare the nitrogen nuclear spin qubit in a given pure state for quantum computation. We provide a theoretical understanding of the popular nuclear spin initialization technique. Furthermore, we propose an optimal condition for the initialization of the nitrogen nuclear spin by including the local strain in the NV center. We expect that this optimal condition can improve the purity of the nuclear spin initialization. We also propose an efficient quantum measurement protocol for the hyperfine interaction between the electron spin and the ¹⁵N nuclear spin in the NV center. A precise knowledge of the hyperfine interaction is important to reduce an error in a coherent control of the ¹⁵N nuclear spin. In this protocol, a sequence of quantum operations with successively increasing duration is utilized to estimate the hyperfine interaction with successively higher precision approaching the quantum metrology limit. Unlike common quantum metrological methods, this protocol does not need the preparation of the nuclear spin in a pure state. In the presence of realistic operation errors and electron spin decoherence, we show the overall precision of our protocol still surpasses the standard quantum limit
Abstract Color centers in solids, such as the nitrogen-vacancy center in diamond, offer well-protected and well-controlled localized electron spins that can be employed in various quantum technologies. Moreover, the long coherence time of the surrounding spinful nuclei can enable a robust quantum register controlled through the color center. We design pulse sequence protocols that drive the electron spin to generate robust entangling gates with these nuclear memory qubits. We find that compared to using Carr-Purcell-Meiboom-Gill (CPMG) alone, Uhrig decoupling sequence and hybrid protocols composed of CPMG and Uhrig sequences improve these entangling gates in terms of fidelity, spin control range, and spin selectivity. We provide analytical expressions for the sequence protocols and also show numerically the efficacy of our method on nitrogen-vacancy centers in diamond. Our results are broadly applicable to color centers weakly coupled to a small number of nuclear spin qubits.