Experimental Hamiltonian Learning of an 11-Qubit Solid-State Quantum Spin Register*

At a Glance

Metadata	Details
Publication Date	2019-10-01
Journal	Chinese Physics Letters
Authors	Pan‐Yu Hou, Lingfeng He, F. Wang, Xianzhi Huang, Wen-Yi Zhang
Institutions	Tsinghua University
Citations	15
Analysis	Full AI Review Included

Technical Documentation & Analysis: 11-Qubit Quantum Spin Register in CVD Diamond

Executive Summary

This technical analysis reviews the experimental demonstration of an 11-qubit solid-state quantum spin register based on a single Nitrogen-Vacancy (NV) center in synthetic CVD diamond. The system employs a highly precise Hamiltonian learning approach, crucial for developing high-fidelity quantum gates in complex solid-state platforms.

Application: Creation of a scalable, multi-qubit single node for quantum networking and information processing based on the NV center’s electron spin coupled to ten neighboring ¹³C nuclear spins.
Material Foundation: The experiment utilized a high-quality Type-IIa CVD synthetic diamond substrate with natural ¹³C abundance (~1.1%) as the host material.
Core Achievement: Successful characterization of the effective many-body coupling Hamiltonian through a combined approach of Dynamical Decoupling Spectroscopy and Adaptive Quantum Phase Estimation (AQPE).
Gate Fidelity: Optimized universal quantum gates achieved high fidelities, with single-qubit nuclear spin rotations (e.g., R^X_π/2) demonstrating performance approaching 99.8%.
Advanced Fabrication: Integration required surface engineering, including the fabrication of a Solid-Immersion Lens (SIL) using Focused Ion Beam (FIB) for enhanced fluorescence collection and 200nm thick gold striplines for microwave delivery.
6CCVD Value: Replicating or extending this work necessitates ultra-pure, precisely polished Single Crystal Diamond (SCD) substrates with custom metalization capabilities, which are core offerings of 6CCVD.

Technical Specifications

Hard data extracted from the experimental results and setup:

Parameter	Value	Unit	Context
NV Host Material	Type-IIa CVD Synthetic Diamond	N/A	Natural ¹³C abundance (~1.1%)
Total Qubits	11	Qubits	1 electron spin + 10 ¹³C nuclear spins
Operating Temperature	~8	K	Cryogenic high-vacuum ambient
External Magnetic Field (B_z)	495	Gauss	Aligned along the NV symmetry axis
Electron Spin Initialization Fidelity	>99	%	Achieved via intersystem crossing
Electron Spin Readout Fidelity (Average)	90	%	Single shot
Zero-Field Splitting (∆)	2.8776	GHz	NV electron spin resonance
Nuclear Larmor Frequency (wn/2π)	~530.6	kHz	Range: 530.177(4) to 530.672(4) kHz
Hyperfine Parameter (A_zx/kHz, Spin 1)	208(1)	kHz	Measured via AQPE
Hyperfine Parameter (A_zz/kHz, Spin 1)	566.0(3)	kHz	Measured via AQPE
Single-Qubit Gate Fidelity (Maximum)	>99.5	%	For R^X_π/2 on nuclear spin 1
Gold Stripline Thickness	200	nm	Fabricated on the diamond surface
Fluorescence Enhancement	7	Times	Achieved using the fabricated SIL

Key Methodologies

The experiment combined advanced materials preparation, quantum control sequences, and adaptive estimation algorithms to characterize the NV-¹³C spin Hamiltonian.

Step	Methodology & Sequence	Key Parameters/Components
1. Substrate Preparation	Electronic Grade SCD material processing.	(100) crystal orientation; natural ¹³C content.
2. Surface Nano-Structuring	Solid-Immersion Lens (SIL) fabrication targeting individual NV centers.	FIB (Focused Ion Beam) used; optimal radius D/1.4.
3. Electrical & MW Integration	Fabrication of microwave signal delivery lines.	200nm thick gold (Au) striplines; wire bonded to CPW.
4. Rough Hamiltonian Estimation	Dynamical Decoupling Spectroscopy (DDS) applied to the electron spin.	CPMG-32 pulse sequence (32 π-pulses); interval τ scan (0 < τ < 50µs).
5. Precise Hyperfine Measurement	Adaptive Quantum Phase Estimation (AQPE) based on Ramsey Interferometry.	Optimized precession time t_n; high-confidence estimation of binary digits of frequency f.
6. Gate Optimization	Numerical simulation to design pulse sequences and minimize crosstalk.	Optimized dynamic decoupling sequences for R^X,Y,Z_θ and controlled R^c-X_π/2 gates.

6CCVD Solutions & Capabilities

This research relies on an ultra-high-quality diamond platform amenable to complex nanoscale fabrication and high-fidelity quantum control. 6CCVD provides the necessary material specifications and advanced customization required to replicate and scale this 11-qubit register.

Research Requirement	6CCVD Solution & Applicable Materials	Customization Potential & Value Proposition
Host Material Purity	The work requires a Type-IIa (high purity) SCD substrate for maximal spin coherence.	6CCVD offers Optical Grade Single Crystal Diamond (SCD) with extremely low nitrogen content (< 1 ppb) to minimize intrinsic background noise (spin bath).
Isotopic Control (Future Scaling)	Achieving scalable quantum registers requires precise control over qubit (¹³C) placement and density, demanding isotopically pure materials.	We supply Isotopically Controlled ¹²C SCD (>99.999% purity) to maximize T₂ coherence, or custom substrates with controlled ¹³C doping for engineered qubit placement.
Substrate Dimensions	Experiments in cryogenic/high-vacuum setups require robust, custom-sized substrates.	6CCVD provides custom SCD thicknesses from 0.1µm up to 500µm, and robust substrates up to 10mm thick for stable mounting in cryostats. Custom diameters up to 125mm (PCD) are available.
Surface Finish for SIL Fabrication	Successful FIB fabrication of the Solid-Immersion Lens (SIL) depends on an exceptionally smooth, defect-free surface.	Our standard Super-Polished SCD achieves R_a < 1 nm surface roughness, minimizing scatter and defects critical for lithography and high-efficiency optical interfaces.
Microwave Delivery Lines	The setup uses 200nm thick gold striplines for high-speed MW signal routing.	6CCVD offers extensive Custom Metalization Services including precise deposition of Ti/Pt/Au, W, Cu, or Pd stacks. We ensure reliable ohmic contacts and low-loss microwave transmission tailored to the customer’s CPW design.
Engineering Consultation	Optimization of dynamical decoupling sequences and selection of ideal materials for high-fidelity gates (up to 99.8%) requires expert material knowledge.	6CCVD’s in-house PhD team provides specialized Engineering Support for selecting materials (e.g., specific SCD thickness/orientation) and integrating fabrication steps for similar solid-state quantum computing projects.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Learning the Hamiltonian of a quantum system is indispensable for prediction of the system dynamics and realization of high fidelity quantum gates. However, it is a significant challenge to efficiently characterize the Hamiltonian which has a Hilbert space dimension exponentially growing with the system size. Here, we develop and implement an adaptive method to learn the effective Hamiltonian of an 11-qubit quantum system consisting of one electron spin and ten nuclear spins associated with a single nitrogen-vacancy center in a diamond. We validate the estimated Hamiltonian by designing universal quantum gates based on the learnt Hamiltonian and implementing these gates in the experiment. Our experimental result demonstrates a well-characterized 11-qubit quantum spin register with the ability to test quantum algorithms, and shows our Hamiltonian learning method as a useful tool for characterizing the Hamiltonian of the nodes in a quantum network with solid-state spin qubits.

Tech Support

Original Source

DOI: https://doi.org/10.1088/0256-307x/36/10/100303