Coupling-selective quantum optimal control in weak-coupling NV-$$^{13}$$C system
At a Glance
Section titled āAt a Glanceā| Metadata | Details |
|---|---|
| Publication Date | 2023-01-05 |
| Journal | AAPPS bulletin |
| Authors | Feihao Zhang, Jian Xing, Xiaoxiao Hu, Xinyu Pan, GuiāLu Long |
| Institutions | Tsinghua University, Institute of Physics |
| Citations | 14 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled āExecutive SummaryāThis analysis focuses on the implementation of Coupling-Selective Optimal Control Theory (COCT) to enhance gate fidelity and coherence in a weak-coupling Nitrogen-Vacancy (NV) center in diamond coupled to 13C nuclear spins.
- Core Innovation: Development of Coupling-Selective Optimal Control Theory (COCT), which combines Average Hamiltonian Theory (AHT) and standard OCT to selectively suppress unwanted weak-coupling noise from the 13C nuclear bath.
- Coherence Extension: The method successfully prolonged the operational lifetime of the NV electron spin, achieving a coherence time (Tcoh) of 1.02 ms under repetitive gate operations.
- Performance vs. Baseline: This achieved Tcoh is approximately five times longer than the native phase decoherence time (T2 = 203 Āµs) of the NV qubit.
- High-Fidelity Gate Implementation: The iSWAP+ gate was implemented in a control time (Tctrl) of 170.25 Āµs, a duration comparable to the native T2, demonstrating efficient control in the presence of noise.
- Robustness: The COCT method is inherently robust against quasi-static errors (like thermal noise and control amplitude errors) and is designed to handle the dynamic evolution of the 13C bath.
- Universality: The COCT method is presented as a universal technique applicable to other weak-coupling quantum systems operating in the Noisy Intermediate-Scale Quantum (NISQ) era.
Technical Specifications
Section titled āTechnical Specificationsā| Parameter | Value | Unit | Context |
|---|---|---|---|
| Qubit Platform | NV Center in Type IIa Diamond | N/A | Electron spin (ms = 0, -1) used as qubit |
| Native Phase Decoherence Time (T2) | 203 | Āµs | Baseline coherence of the NV electron spin |
| Inhomogeneous Broadening (Ī) | ~380 | kHz | Measured noise level in the 13C bath |
| Static Magnetic Field (B0) | 511 | G | Applied along the [1 1 1] crystallographic axis |
| iSWAP+ Gate Control Time (Tctrl) | 170.25 | Āµs | Implemented using 30 decoupled sub-sequences |
| Controlled Rotation (C-R) Gate Time | 1020 (Ā±80) | Āµs | 5 times the native T2 time |
| Electron Spin Coherence (Tcoh) | 1.02 (Ā±0.08) | ms | Achieved under repetitive C-R gate application |
| 13C Spin 1 Isotropic Coupling (Ī³z1) | 40 (Ā±3) | kHz | Hyperfine coupling strength to NV center |
| 13C Spin 2 Anisotropic Coupling (Ī³x2) | -35.6 (Ā±0.8) | kHz | Hyperfine coupling strength to NV center |
| Nuclear Ramsey Frequency (Ļ0) | 547.1 (Ā±0.7) | kHz | Measured precession frequency of nuclear spin |
Key Methodologies
Section titled āKey MethodologiesāThe experiment utilized Coupling-Selective Optimal Control Theory (COCT) to generate microwave pulse sequences that achieve high-fidelity gates while dynamically decoupling the system from the weak-coupling 13C bath.
- System Modeling: The system Hamiltonian was defined for a 3-qubit system: the NV electron spin and two detectable, weakly coupled 13C nuclear spins. The remaining 13C spins constitute the evolving bath.
- COCT Objective Function: The optimization task was defined as a multi-objective function:
- Maximization Term: Maximize the fidelity (FS) between the achieved propagator (US) and the target quantum gate (Uwant).
- Minimization Term: Minimize the norm of the first-order perturbation term (Qx/z) of the propagator, which represents the unwanted system-bath coupling evolution.
- Decoupling Constraint: A penalty parameter (Ī±k) was introduced to ensure the unwanted coupling term (Q) is minimized, forcing it into the form IS ā V, where V is an operator only in the bath space, thus achieving decoupling.
- Pulse Sequence Segmentation: The total control time (T) was divided into N equal-width sub-sequences (e.g., N=30 for iSWAP+). The optimization was performed iteratively across these sub-sequences to improve dynamic decoupling performance over the long control period.
- Optimization Algorithm: The objective function was optimized using the Gradient Ascent Pulse Engineering (GRAPE) method to generate the complex microwave pulse waveforms (Ī©x(t) and Ī©y(t)).
- Experimental Implementation: The optimized microwave pulse sequences were applied to the NV center in a Type IIa diamond sample under a 511 G static magnetic field to realize the iSWAP+ and Control-Rx gates.
- Coherence Measurement: The coherence protection capability was tested by repeatedly applying the Control-Rx gate and measuring the electron spin coherence (Tcoh) as a function of the number of gate repetitions.
Commercial Applications
Section titled āCommercial ApplicationsāThe robust, long-coherence quantum control demonstrated by COCT is critical for advancing solid-state quantum technologies, particularly in the following areas:
- NISQ Quantum Computing:
- Product: Solid-state quantum processors based on spin defects (like NV centers).
- Value: Enables the execution of deeper quantum circuits by extending the operational coherence time (Tcoh > 1 ms) and ensuring high-fidelity gate operations (iSWAP+, C-Rx) necessary for complex algorithms.
- Quantum Sensing and Metrology:
- Product: Nanoscale magnetic field sensors and gyroscopes.
- Value: The ability to suppress environmental noise (13C bath) over long integration times allows for ultra-weak magnetic field detection and high-resolution Nuclear Magnetic Resonance (NMR) spectroscopy.
- Quantum Error Correction (QEC):
- Product: Fault-tolerant quantum registers.
- Value: Robust control against dynamic noise is a fundamental requirement for implementing QEC protocols, moving NV systems closer to fault-tolerant quantum computation.
- Universal Quantum Control Software:
- Product: Optimization software packages (e.g., based on GRAPE/COCT).
- Value: COCT is a universal method that can be adapted to optimize control sequences for other weak-coupling platforms, including superconducting qubits and other solid-state defects.
- Diamond Material Engineering:
- Product: High-purity Type IIa diamond substrates.
- Value: Confirms the viability of high-purity diamond as the essential material foundation for robust, long-coherence solid-state quantum devices.
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=āhttp://www.w3.org/1998/Math/MathMLā> <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=āhttp://www.w3.org/1998/Math/MathMLā> <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=āhttp://www.w3.org/1998/Math/MathMLā> <mml:msup> <mml:mrow/> <mml:mo>ā </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=āhttp://www.w3.org/1998/Math/MathMLā> <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=āhttp://www.w3.org/1998/Math/MathMLā> <mml:mi>Ī¼</mml:mi> </mml:math> s, which is comparable to the phase decoherence time $$T_2$$ <mml:math xmlns:mml=āhttp://www.w3.org/1998/Math/MathMLā> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> = 203 $$\mu s$$ <mml:math xmlns:mml=āhttp://www.w3.org/1998/Math/MathMLā> <mml:mrow> <mml:mi>Ī¼</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=āhttp://www.w3.org/1998/Math/MathMLā> <mml:mi>Ī¼</mml:mi> </mml:math> s, which is five times of the phase decoherence time. These results could find important applications in the NISQ era.