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

At a Glance

Metadata	Details
Publication Date	2024-02-21
Journal	Physical review. A/Physical review, A
Authors	Jiazhao Tian, Haibin Liu, Roberto Sailer, Liantuan Xiao, Fedor Jelezko
Institutions	Center for Integrated Quantum Science and Technology, Taiyuan University of Technology
Citations	1
Analysis	Full AI Review Included

Technical Documentation & Analysis: Rapid Transform Optimization for Diamond Quantum Registers

6CCVD Reference Document: QREG-NV-2402 Source Paper: Tian et al., Rapid transform optimization strategy for decoherence-protected quantum register in diamond (arXiv:2310.04371v2)

Executive Summary

This research demonstrates a significant advancement in controlling solid-state quantum registers by achieving rapid, high-fidelity manipulation of nuclear spins within the Nitrogen-Vacancy (NV) center decoherence-free subspace (DFS) in diamond.

Core Achievement: Successful implementation of all-microwave control strategies to manipulate nuclear spins in the NV-diamond DFS, reducing processing time by 80% compared to conventional adiabatic methods (STIRAP).
High Fidelity at Speed: Achieved transition fidelity (F) exceeding 0.8 for ultra-short evolution times (T) down to 4 µs.
Optimization Methods: Compared and validated three optimal control methods: Gradient Ascent Pulse Engineering (GRAPE), Chopped Random Basis (CRAB), and Phase Modulation (PM).
Experimental Feasibility: Optimized control fields feature smooth shapes and near-zero endpoints, confirmed to be experimentally realizable using standard Arbitrary Wave Generator (AWG) and RF amplifier setups.
Robustness Engineering: Introduced the Bayesian-Estimation Phase-Modulated (B-PM) method, enabling fast and accurate optimization of pulse robustness against inevitable frequency and amplitude biases using only 16 samples.
Material Requirement: The work relies fundamentally on high-quality, isotopically controlled Single Crystal Diamond (SCD) to host the NV center and proximal ${}^{13}$C nuclear spins, ensuring long coherence times ($T_{2n}$ up to 700 µs).

Technical Specifications

The following hard data points were extracted from the research paper, detailing the physical constraints and performance metrics of the quantum register system and control apparatus.

Parameter	Value	Unit	Context
Zero-Field Splitting (D)	2π x 2.87	GHz	NV Electron Spin
Isotropic Hyperfine Coupling ($A_{zz}^{(1)}$)	12.45	MHz	Proximal ${}^{13}$C Nuclear Spin 1
Maximum Control Field Amplitude ($\Omega_{max}$)	$\pi$	MHz	Constraint for optimized pulses
Target Fidelity (F)	$\ge 0.8$	Dimensionless	Achieved transition effectiveness
Minimum Evolution Time (T)	4	µs	Time required to achieve F $\ge 0.8$
Electron Spin Coherence Time ($T_{2e}^*$)	7	µs	Transverse relaxation time
Nuclear Spin Coherence Time ($T_{2n}$)	500, 700	µs	Transverse relaxation times
AWG Bandwidth	14	GHz	Experimental apparatus capability (Tektronix AWG-70002A)
AWG Amplitude Resolution	10	bits	Experimental apparatus capability
Fidelity Map Pixels	50 x 50	Pixels	Robustness map resolution
B-PM Sample Count	16	Samples	Required for accurate robustness estimation

Key Methodologies

The experiment focused on constructing and manipulating a decoherence-protected quantum register using optimized microwave control fields.

System Construction: The quantum register is a tri-partite system comprising one NV electron spin (S=1) and two proximal ${}^{13}$C nuclear spins (I=1/2), leveraging the decoherence-free subspace (DFS) defined by states $\vert\psi_2\rangle$ and $\vert\psi_3\rangle$.
Control Strategy: Indirect control via microwave fields driving transitions through the $m_s = 1$ states ($\vert\psi_{5,6,7,8}\rangle$) was used to achieve rapid transitions, circumventing the slow dynamics associated with direct radio frequency (RF) driving of nuclear spins.
Pulse Optimization: Three optimal control methods were compared for maximizing fidelity (F) under short evolution times (T):
- GRAPE (Gradient Ascent Pulse Engineering): Exploitative, locally converging method.
- CRAB (Chopped Random Basis): Explorative, global search method using truncated expansion with randomized frequencies.
- PM (Phase Modulation): Explorative method featuring phase modulation for optimization efficiency.
Boundary Constraints: A boundary function $\lambda(t)$ was applied to all optimized control fields to ensure smooth pulse shapes with near-zero values at the beginning and end, crucial for minimizing distortion by experimental amplifiers.
Robustness Analysis: The Bayesian-Estimation Phase-Modulated (B-PM) method was employed to rapidly estimate and optimize the control field robustness against frequency detuning ($\delta$) and amplitude bias ($\kappa$), significantly reducing the required calculation time from 2500 to 16 samples.
Experimental Validation: Optimized pulse sequences were generated using a high-bandwidth (14 GHz) Arbitrary Wave Generator (AWG) and measured via an oscilloscope, confirming the consistency between simulated and real pulse shapes.

6CCVD Solutions & Capabilities

This research highlights the critical need for high-quality, engineered diamond substrates to realize robust, high-speed quantum registers. 6CCVD is uniquely positioned to supply the foundational materials and customization services required to replicate and advance this work.

Applicable Materials for Quantum Registers

The success of this decoherence-protected register relies on maximizing nuclear spin coherence time ($T_{2n}$ up to 700 µs), which mandates extremely low concentrations of background spin impurities.

Material Requirement	6CCVD Solution	Technical Advantage
High Purity Substrate	Optical Grade Single Crystal Diamond (SCD)	Ultra-low nitrogen content (< 1 ppb) minimizes background ${}^{14}$N noise, essential for long $T_{2e}^*$ and $T_{2n}$.
Isotopic Control	High Purity ${}^{12}$C SCD	Reduces the concentration of native ${}^{13}$C (I=1/2) spins, allowing for precise, controlled introduction of specific proximal ${}^{13}$C spins necessary for the DFS register structure.
Doping/Sensing	Boron-Doped Diamond (BDD) (Optional)	While not used in this specific NV register, BDD is available for related quantum sensing applications requiring conductive diamond electrodes.

Customization Potential & Integration Services

The experimental setup requires precise integration of the diamond substrate with high-frequency microwave delivery structures. 6CCVD offers end-to-end customization to facilitate this integration.

Custom Dimensions and Geometry:
- 6CCVD provides Custom SCD Plates/Wafers up to 125mm in diameter (PCD) and SCD thicknesses from 0.1 µm to 500 µm.
- We offer Precision Laser Cutting to create specific geometries (e.g., micro-disks, cantilevers, or integration features) required for mounting in microwave cavities or near strip lines.
Microwave Circuit Integration (Metalization):
- The use of all-microwave control fields necessitates high-quality on-chip transmission lines.
- 6CCVD offers Internal Metalization Capabilities (Au, Pt, Pd, Ti, W, Cu) for depositing high-conductivity layers directly onto the diamond surface, enabling the fabrication of optimized microwave strip lines or coplanar waveguides (CPWs) for efficient pulse delivery.
Surface Preparation:
- High-fidelity quantum control requires minimal surface defects.
- 6CCVD guarantees Ultra-Low Roughness Polishing (Ra < 1 nm for SCD), critical for minimizing surface noise and ensuring optimal interface quality for metalization and NV creation.

Engineering Support

The complexity of optimal control methods (GRAPE, B-PM) and the strict material requirements for DFS quantum registers demand expert consultation.

PhD-Level Consultation: 6CCVD’s in-house PhD team specializes in MPCVD growth and material science for quantum applications. We can assist researchers in selecting the optimal diamond orientation, isotopic purity, and surface termination necessary to maximize $T_{2n}$ and $T_{2e}^*$ for similar Decoherence-Protected Quantum Register projects.
Recipe Optimization: We provide technical guidance on how material parameters (e.g., residual nitrogen, surface termination) influence the experimental feasibility of optimized pulse sequences, ensuring the material meets the stringent requirements for high-speed, robust control.

Call to Action: For custom specifications or material consultation tailored to high-fidelity quantum control and NV center research, visit 6ccvd.com or contact our engineering team directly. We ship globally (DDU default, DDP available).

View Original Abstract

Decoherence-protected spins associated with nitrogen-vacancy color centers in\ndiamond possess remarkable long coherence time, which make them one of the most\npromising and robust quantum registers. The current demand is to explore\npractical rapid control strategies for preparing and manipulating the such\nregister. Our work provides all-microwave control strategies optimized using\nmultiple optimization methods to significantly reduce the processing time by\n$80\%$ with a set of smooth near-zero-endpoints control fields that are shown\nto be experimentally realizable. Furthermore, we optimize and analyze the\nrobustness of these strategies under frequency and amplitude imperfections of\nthe control fields, during which process we use only $16$ samples to give a\nfair estimation of the robustness map with $2500$ pixels. Overall, we provide a\nready-to-implement recipe to facilitate high-performance information processing\nvia decoherence-protected quantum register for future quantum technology\napplications.\n

Tech Support

Original Source

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