Coupling-selective quantum optimal control in weak-coupling NV-$$^{13}$$C system
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2023-01-05 |
| Journal | AAPPS bulletin |
| Authors | Feihao Zhang, Jian Xing, Xiaoxiao Hu, Xinyu Pan, GuiâLu Long |
| Institutions | Chinese Academy of Sciences, Tsinghua University |
| Citations | 14 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Coupling-Selective Quantum Control in NV-13C Systems
Section titled âTechnical Documentation & Analysis: Coupling-Selective Quantum Control in NV-13C SystemsâThis document analyzes the research paper âCoupling-selective quantum optimal control in weak-coupling NV-13C systemâ (Zhang et al., 2023) to highlight the critical role of high-quality MPCVD diamond substrates and to position 6CCVDâs capabilities as the ideal solution for replicating and advancing this quantum control research.
Executive Summary
Section titled âExecutive SummaryâThis research successfully demonstrates a novel quantum control methodâCoupling-selective Optimal Control Theory (COCT)âapplied to the Nitrogen-Vacancy (NV) center in diamond, achieving significant extension of qubit coherence time.
- Core Achievement: Implementation of COCT to selectively suppress unwanted weak coupling interactions originating from the 13C nuclear spin bath.
- Coherence Extension: The electron spin coherence time ($T_{coh}$) was extended to 1.02(8) ms, representing a five-fold increase over the native phase decoherence time ($T_2 \approx 203$ ”s).
- Methodology: COCT combines Optimal Control Theory (OCT) with Average Hamiltonian Theory (AHT) to decouple the system (NV electron spin) from the evolving environment (13C bath).
- Gate Implementation: High-fidelity two-qubit gates (iSWAP+ and Control-RxÏ/2) were realized using optimized pulse sequences within the systemâs coherence window.
- Material Requirement: The experiment relied on high-purity Type IIa diamond, underscoring the necessity of ultra-low defect density Single Crystal Diamond (SCD) for Noise Intermediate-Scale Quantum (NISQ) applications.
- Relevance to 6CCVD: The success of this control method is fundamentally dependent on the high intrinsic quality and low noise floor provided by premium MPCVD SCD, a core offering of 6CCVD.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the experimental results:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Qubit System | 3 | Qubits | 1 NV electron spin + 2 weakly coupled 13C nuclear spins. |
| Static Magnetic Field ($B_0$) | 511 | G | Applied along the [1 1 1] axis. |
| Native Phase Decoherence Time ($T_2$) | 203 | ”s | Baseline coherence time of the NV qubit. |
| iSWAP+ Gate Control Time ($T_{ctrl}$) | 170.25 | ”s | Implemented using 30 decoupled sub-sequences. |
| Achieved Coherence Time ($T_{coh}$) | 1.02(8) | ms | Coherence achieved using repetitive Control-RxÏ/28 gates. |
| Coherence Improvement Factor | 5 | Times | $T_{coh}$ is 5 times longer than $T_2$. |
| Material Used | Type IIa | N/A | High-purity diamond substrate. |
| Nuclear Spin Coupling ($\gamma_{x/z}$) | 28.3 to 65 | kHz | Measured coupling strengths of the two 13C spins. |
Key Methodologies
Section titled âKey MethodologiesâThe experiment utilized a sophisticated combination of material science and quantum control theory to achieve robust gate operation and extended coherence.
- Material Foundation: The experiment utilized Type IIa diamond, characterized by extremely low nitrogen content, to minimize the intrinsic decoherence mechanisms of the NV electron spin.
- Hamiltonian Definition: The total Hamiltonian was defined, separating the system (NV electron spin), the target qubit nuclear spins ($i \in S$), and the environmental bath nuclear spins ($j \in B$).
- COCT Development: Coupling-selective Optimal Control Theory (COCT) was developed to address the challenge of weak-coupling systems where the required control time is comparable to the $T_2$ time.
- Optimization Objective: The objective function was designed as a multi-objective optimization:
- Maximize the fidelity of the target quantum gate (e.g., iSWAP+).
- Minimize the norm of the first-order perturbation term (Q), ensuring the system is decoupled from the bath evolution.
- Sub-sequence Decoupling: The total pulse sequence was divided into multiple equal-width sub-sequences (e.g., 30 for iSWAP+), allowing the decoupling optimization to be performed iteratively within each sub-sequence, significantly improving performance.
- Experimental Validation: The optimized pulse sequences were tested by implementing iSWAP+ and Control-Rx gates, demonstrating high selectivity against variations in coupling parameters ($\gamma_x, \gamma_z$).
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe successful implementation of COCT for coherence extension in NV systems relies entirely on the quality of the underlying diamond material. 6CCVD is uniquely positioned to supply the high-specification MPCVD diamond required for replicating and scaling this critical quantum research.
Applicable Materials
Section titled âApplicable MaterialsâTo replicate or extend this research, researchers require diamond with the highest possible purity and crystalline quality to ensure a long intrinsic $T_2$ time, minimizing the initial noise floor.
| Research Requirement | 6CCVD Material Recommendation | Technical Rationale |
|---|---|---|
| Ultra-High Purity Substrate | Optical Grade Single Crystal Diamond (SCD) | Guaranteed ultra-low nitrogen concentration (< 1 ppb) and minimal strain, essential for maximizing the native $T_2$ and minimizing inhomogeneous broadening ($\Delta \approx 380$ kHz in the paper). |
| Qubit Integration | SCD Plates (0.1 ”m to 500 ”m) | Precise thickness control allows for optimal NV creation (e.g., shallow implantation) and integration with surface control structures. |
| Future Scaling | Polycrystalline Diamond (PCD) Substrates | Available up to 125mm diameter, providing large-area platforms for scaling up multi-qubit registers or integrating complex control electronics. |
Customization Potential
Section titled âCustomization PotentialâThe complexity of quantum control experiments often necessitates custom material engineering beyond standard wafers. 6CCVDâs in-house capabilities directly address these needs:
- Custom Dimensions and Orientation: The experiment requires the magnetic field to be aligned with the [1 1 1] axis. 6CCVD supplies SCD substrates with precise [1 1 1] orientation and custom dimensions up to 125mm (PCD).
- Surface Preparation: The achieved coherence relies on minimal surface defects. 6CCVD offers SCD polishing down to Ra < 1nm and inch-size PCD polishing down to Ra < 5nm, ensuring an atomically smooth surface for optimal NV performance.
- Integrated Control Structures: The COCT method requires precise microwave control ($\Omega_{x/y}(t)$). 6CCVD offers in-house metalization services (Au, Pt, Pd, Ti, W, Cu) for fabricating high-frequency microwave striplines directly onto the diamond substrate, enabling robust implementation of the optimized pulse sequences.
Engineering Support
Section titled âEngineering SupportâThe development of advanced quantum control techniques like COCT requires deep collaboration between material scientists and quantum engineers.
6CCVDâs in-house PhD team specializes in the material science of quantum platforms. We offer expert consultation on:
- Material Selection: Guiding researchers in choosing the optimal SCD grade (e.g., specific NV concentration or isotopic purity) for similar Quantum Control and NISQ projects.
- Decoherence Mitigation: Assisting with material specifications to minimize strain and intrinsic defects that limit the baseline $T_2$ time, thereby maximizing the effectiveness of external control methods.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Abstract Quantum systems are under various unwanted interactions due to their coupling with the environment. Efficient control of quantum system is essential for quantum information processing. Weak-coupling interactions are ubiquitous, and it is very difficult to suppress them using optimal control method, because the control operation is at a time scale of the coherent life time of the system. Nitrogen-vacancy (NV) center of diamond is a promising platform for quantum information processing. The $$^{13}$$ <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ> <mml:msup> <mml:mrow/> <mml:mn>13</mml:mn> </mml:msup> </mml:math> C nuclear spins in the bath are weakly coupled to the NV, rendering the manipulation extremely difficulty. Here, we report a coupling selective optimal control method that selectively suppresses unwanted weak coupling interactions and at the same time greatly prolongs the life time of the wanted quantum system. We applied our theory to a 3 qubit system consisting of one NV electron spin and two $$^{13}$$ <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ> <mml:msup> <mml:mrow/> <mml:mn>13</mml:mn> </mml:msup> </mml:math> C nuclear spins through weak-coupling with the NV center. In the experiments, the iSWAP $$^{\dagger }$$ <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ> <mml:msup> <mml:mrow/> <mml:mo>â </mml:mo> </mml:msup> </mml:math> gate with selective optimal quantum control is implemented in a time-span of $$T_{ctrl}$$ <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>ctrl</mml:mi> </mml:mrow> </mml:msub> </mml:math> = 170.25 $$\mu$$ <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ> <mml:mi>ÎŒ</mml:mi> </mml:math> s, which is comparable to the phase decoherence time $$T_2$$ <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> = 203 $$\mu s$$ <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ> <mml:mrow> <mml:mi>ÎŒ</mml:mi> <mml:mi>s</mml:mi> </mml:mrow> </mml:math> . The two-qubit controlled rotation gate is also completed in a strikingly 1020(80) $$\mu$$ <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ> <mml:mi>ÎŒ</mml:mi> </mml:math> s, which is five times of the phase decoherence time. These results could find important applications in the NISQ era.