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Rapid transform optimization strategy for decoherence-protected quantum register in diamond

Jiazhao Tian, Haibin Liu, Roberto Sailer, Liantuan Xiao, Fedor Jelezko, and Ressa S. Said
Phys. Rev. A 109, 022614 – Published 21 February 2024
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  • INTRODUCTION
  • DECOHERENCE-PROTECTED SPACE OF NUCLEAR…
  • OPTIMIZATION
  • EXPERIMENTAL FEASIBILITY
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Decoherence-protected spins associated with nitrogen-vacancy color centers in diamond possess remarkably long coherence time, which makes them one of the most promising and robust quantum registers. The current demand is to explore practical rapid control strategies for preparing and manipulating such registers. Our work provides all-microwave control strategies optimized using multiple optimization methods to significantly reduce the processing time by 80% with a set of smooth near-zero-end-point control fields that are shown to be experimentally realizable. Furthermore, we optimize and analyze the robustness of these strategies under frequency and amplitude imperfections of the control fields, during which process we use only 16 samples to give a fair estimation of the robustness map with 2500 pixels. Overall, we provide a ready-to-implement recipe to facilitate high-performance information processing via a decoherence-protected quantum register for future quantum technology applications.

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    • Received 11 October 2023
    • Accepted 10 January 2024

    DOI:https://doi.org/10.1103/PhysRevA.109.022614

    ©2024 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Quantum controlQuantum state transfer
    Quantum Information, Science & Technology

    Authors & Affiliations

    Jiazhao Tian1,*, Haibin Liu2, Roberto Sailer3, Liantuan Xiao1,†, Fedor Jelezko3, and Ressa S. Said3,‡

    • 1School of Physics, Taiyuan University of Technology, Taiyuan 430000, People's Republic of China
    • 2School of Physics, Hubei University, Wuhan 430062, People's Republic of China
    • 3Institute for Quantum Optics and Center for Integrated Quantum Science and Technology, Ulm University, 89081 Ulm, Germany

    • *tianjiazhao@tyut.edu.cn
    • †xiaoliantuan@tyut.edu.cn
    • ‡ressa.said@uni-ulm.de

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    Vol. 109, Iss. 2 — February 2024

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    Images

    • Figure 1
      Figure 1

      (a) Triparticle system comprising one NV− electron spin (S=1) and two proximal C13 nuclear spins (I=1/2). (b) Explicit formation of eigenstates (without normalization) of the Hamiltonian of the triparticle system shown in Eq. (2). For j=1,3,4, αj=(2d12−2Ej)(−d12−2Ej−2Bzγc)2Bx2γc2 and βj=−d12−2Ej−2Bzγc2Bxγc, with Ej the solution of the equation −2d123−4Bx2d12γc2+8Bz2d12γc2−(3d122+4Bx2γc2+4Bz2γc2)Ej+Ej3=0. The explicit values of E1, E3, and E4 under different magnetic fields are shown in Appendix pp1. (c) Schematic diagram of the transition process |ψ1〉→|ψ2〉 in the initialization step and |ψ2〉→|ψ3〉 in the spin-flip step.

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    • Figure 2
      Figure 2

      (a) Transition efficiency of the process |ψ1〉→|ψ2〉 given by STIRAP methods with a Gaussian-shaped control field following Eq. (10). The black line with dots shows the results with optimized parameters σ and td. The gray line with triangles shows the results with fixed parameters σ=T/8 and td=2σ. (b) and (c) Control field and population transition at T=4µs, with optimized parameters σ=1.95μs and td=2.15µs. (d) and (e) Control field and population transition at T=16µs, with optimized parameters σ=4.77µs and td=8.34µs. (f) and (g) Control field and population transition at T=28µs, with fixed parameters σ=T/8=3.5µs and td=2σ=4.95µs.

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    • Figure 3
      Figure 3

      (a) Optimization fidelity with different optimization methods for different evolution times. The inset shows the average number of functions evaluated by the PM and CRAB methods. Also shown is the population transition at T=4µs, given by the (b) GRAPE(G), (c) PM, and (d) CRAB methods.

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    • Figure 4
      Figure 4

      Comparison of the simulation pulse and the real pulse generated by the AWG (Tektronix AWG-70002A, connected with the software Qudi) and measured by the oscilloscope (LECROY-WAVEACE 234) after a rf amplifier (Model No. 60S1G4AM3, AR Germany with frequency bandwidth 0.7–4.2 GHz and gain power of 60 W) for the same gain level. The simulation pulses are given by different optimization methods: (a) and (d) GRAPE, (b) and (e) PM, and (c) and (f) CRAB. The amplitudes of the measured values of the real pulses are scaled to make a direct comparison visible (see the text for details).

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    • Figure 5
      Figure 5

      (a) Simulated fidelity of the transition process from |ψ1〉 to |ψ2〉 for different values of detuning and amplitude bias of the control field. The total evolution time is T=4µs and the control field is given by the PM method, shown in Figs. 4 and 4. (b) Estimation values of the fidelity using the Bayesian-based estimation method. The black circles represent the locations of the samples. We used 16 randomly chosen sample points; only those with locations within the range (δ/2π∈[−100,100]MHz,κ∈[−0.5,0.5]) are shown. (c) Simulated fidelity of the control field optimized by the BPM method. (d) Estimation values of the fidelity using the Bayesian-based estimation method with the optimized field given by the BPM method. The black circles represent the location of samples. We used 16 randomly chosen sample points; only those with locations within the range (δ/2π∈[−100,100]MHz,κ∈[−0.5,0.5]) are shown.

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    • Figure 6
      Figure 6

      (a) Explicit value of E3 for different Bx and Bz values. (b) Comparison between E1 and E3, evaluated by log10|E1/E3|. (c) Comparison between E4 and E3, evaluated by log10|E4/E3|.

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    • Figure 7
      Figure 7

      Calibration curve between the input voltage from the AWG and the measured Rabi frequency from a single NV experiment. The fit values are aΩ=40.4±1.2 MHz/V and bΩ=1.0±0.2 V.

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    • Figure 8
      Figure 8

      Calibration curve between the input voltage from the AWG and the measured voltage from the oscilloscope. The fit values are aosc-AWG=0.016±0.003 Vosci/VAWG and bosc-AWG=−0.0026±0.0006Vosci.

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    • Figure 9
      Figure 9

      Calibration curve for the relation between the frequency of the input signal and the measured voltage from the oscilloscope (with an input voltage of 230 mV). The parameters are aV−f=−0.0092±0.0028 V/GHz and bV−f=0.029±0.008 V.

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    • Figure 10
      Figure 10

      Comparison of the pulse shapes. For clarity, the scale is predetermined to simply compare the pulse shapes from the numerically obtained pulses and the measured ones. For the case of Ωs obtained via the CRAB method at time of 3µs, the amplitude goes up according to the pulse envelope of the electronic signal.

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