Optical holonomic single quantum gates with a geometric spin under a zero field

At a Glance

Metadata	Details
Publication Date	2017-04-10
Journal	Nature Photonics
Authors	Yuhei Sekiguchi, Naeko Niikura, Ryota Kuroiwa, Hiroki Kano, Hideo Kosaka
Institutions	Yokohama National University
Citations	148
Analysis	Full AI Review Included

Optical Holonomic Single Quantum Gates in NV Diamond: Technical Analysis and 6CCVD Material Solutions

Executive Summary

This research demonstrates a critical advance in solid-state quantum computation by implementing ultra-fast, fault-tolerant holonomic quantum gates (HQC) in a Nitrogen-Vacancy (NV) center in high-purity Single Crystal Diamond (SCD).

Fault-Tolerant Quantum Gates: Achieved non-adiabatic HQC using a geometric spin in the NV center’s degenerate $\left| m_s = \pm 1 \right\rangle$ subspace, providing inherent robustness against control errors and environmental noise.
Ultra-Fast Operation: Gate operations were completed in an ultra-short cycle time of $1.7 \text{ ns}$, significantly faster than previous adiabatic schemes (hundreds of nanoseconds).
High Fidelity: Demonstrated a complete set of Pauli gates (X, Y, Z) with high fidelities up to $92(\pm 11)%$.
Zero-Field Coherence: Operations were performed under a carefully compensated zero magnetic field, which maximizes spin coherence by freezing surrounding ¹³C nuclear spins.
Material Requirement: Success relied entirely on the use of high-purity, electronic-grade Type-IIa CVD grown bulk diamond with a specified $\left< 001 \right>$ crystal orientation.
Scalability Path: This non-Abelian HQC approach opens the path for building universal quantum computers, repeaters, and ultra-sensitive zero-field quantum sensors based on solid-state defect qubits.

Technical Specifications

The following parameters define the operational regime and material requirements for achieving high-fidelity optical holonomic quantum gates:

Parameter	Value	Unit	Context
Material Base	CVD Bulk Diamond	N/A	High-purity Type-IIa, Electronic Grade
Crystal Orientation	$\left< 001 \right>$	N/A	Specified for experimental alignment
Operating Temperature	5	K	Cryogenic requirement to narrow optical linewidth
NV Center Depth	30	µm	Depth for optimal confocal access/readout
Pauli-X Gate Fidelity	$92(\pm 11)$	%	Holonomic (bit flip/NOT) gate performance
Pauli-Y Gate Fidelity	$89(\pm 3)$	%	Holonomic (bit and phase flip) gate performance
Pauli-Z Gate Fidelity	$90(\pm 10)$	%	Holonomic (phase flip) gate performance
Gate Cycle Time ($t_{2\pi}$)	1.7	ns	Non-adiabatic rotation cycle duration
Excited State Lifetime ($T_1$)	12	ns	$A_2$ state relaxation time
*Geometric Spin Dephasing ($T_2^$ Threshold)**	4.6	ns	Estimated from Rabi oscillation damping
On-Resonance Rabi Frequency ($\Omega$)	250	MHz	Optically driven spin oscillation speed
$A_2$ Optical Linewidth	54	MHz	Narrowed at 5 K
Crystal Strain Splitting ($E_x, E_y$)	2.2	GHz	Strain value complicating Hamiltonian control
External Magnetic Field	Zero Field	mT	Geomagnetic field (0.045 mT) actively compensated
Microwave Frequency	2.878	GHz	Used for initial electron spin excitation

Key Methodologies

The robust demonstration of HQC gates relied on precise material preparation and controlled optical/microwave interfacing:

Material Selection and Preparation:
- Used high-purity Type-IIa bulk diamond grown by CVD with a $\left< 001 \right>$ crystal orientation.
- Native NV centers were utilized, located approximately $30 \text{ µm}$ below the surface.
Cryogenic Environment:
- All experiments were performed at $5 \text{ K}$ to suppress phonon interactions and reduce the $A_2$ optical linewidth to $54 \text{ MHz}$.
Magnetic Field Control:
- An external permanent magnet was used to carefully compensate for the geomagnetic field ($\approx 0.045 \text{ mT}$) to establish a true zero magnetic field, maximizing $T_2^*$.
Qubit Initialization and Preparation:
- A Green laser ($532 \text{ nm}, 100 \text{ µW}, 3 \text{ µs}$) initialized the electron spin to the $\left| m_s = 0 \right\rangle$ state.
- Microwaves ($2.878 \text{ GHz}$) excited the electron spin to the geometric spin basis states ($\left| \pm 1 \right\rangle$).
- A Red light pulse ($0.8 \text{ µW}, 130 \text{ ns}$) prepared the geometric spin into the target ‘bright’ state by leveraging resonant excitation to the $A_2$ state.
Non-Adiabatic Gate Operation:
- A Red laser ($30 \text{ µW}$ power), quasi-resonant to the $A_2$ state, was applied with specific polarization ($\theta, \phi$) and detuning ($\Delta$) parameters.
- The detuning was used to shorten the cycle time ($t_{2\pi} = 2\pi / \Omega_{eff}$) and define the rotation angle ($\gamma = \pi (1 - \Delta / \Omega_{eff})$).
Readout and Analysis:
- The rotated spin state was read out via resonant excitation of the bright state using a Red laser pulse ($0.1 \text{ µW}, 10 \text{ ns}$) and subsequent detection of the phonon sideband emission.
- Quantum Process Tomography was utilized, incorporating Hamiltonian compensation for crystal strain ($E_x, E_y$) and NV off-alignment, to calculate gate fidelities.

6CCVD Solutions & Capabilities: Enabling Next-Generation HQC

6CCVD’s specialized MPCVD Single Crystal Diamond (SCD) capabilities are perfectly positioned to meet and exceed the stringent material requirements for scaling this high-speed, high-fidelity holonomic quantum computation platform.

Component Requirement from Paper	6CCVD Material Solution	Engineering & Sales Benefit
High-Purity Host Material	Electronic Grade SCD (Ultra-Low Nitrogen/Defects)	Our SCD growth minimizes background defects ($\text{N} \lt 5 \text{ ppb}$), ensuring the highest intrinsic $T_1$ and $T_2^*$ coherence times required for gates exceeding $90%$ fidelity.
Precise Orientation & Size	Custom $\left< 001 \right>$ Wafers up to $125 \text{ mm}$	We supply SCD plates/wafers in custom dimensions (up to $125 \text{ mm}$ PCD, specialized SCD cuts) with strict $\left< 001 \right>$ orientation, essential for repeatable NV axis alignment in integrated quantum systems.
Strain Control for Scalability	SCD with Guaranteed Ultra-Low Intrinsic Strain	The paper cited a $2.2 \text{ GHz}$ strain splitting requiring complex compensation. 6CCVD offers materials specified for ultra-low intrinsic strain, minimizing Hamiltonian compensation complexity and simplifying the implementation of universal gates.
Optical Interfacing Quality	Precision Polishing (Ra $\lt 1 \text{ nm}$ for SCD)	An ultra-smooth surface is critical for high-efficiency, low-loss optical coupling in confocal setups, allowing stable interaction with NV centers $30 \text{ µm}$ deep. Our SCD polishing achieves optical roughness $R_a \lt 1 \text{ nm}$.
On-Chip Control Integration	Custom Metalization Services (Au, Ti, Pt, W)	While the researchers used external $25 \text{-µm}$ copper wires, large-scale HQC requires integrated microwave control. 6CCVD provides internal metal deposition capabilities, essential for building on-chip transmission lines and electrodes directly onto the diamond.
Qubit Integration Support	Targeted Defect Creation Services	Although the study used native NV centers, controlled creation (via ion implantation or specific growth doping) is key for scaling. We consult on material specifications suitable for high-density, addressable NV arrays.

Engineering Support

This research demonstrates the extreme sensitivity of HQC to material parameters like crystal strain and NV center alignment. 6CCVD’s in-house PhD team provides expert consultation on material selection, customized growth parameters, and post-processing (polishing, metalization, and laser cutting) tailored for solid-state holonomic quantum processors and ultra-sensitive zero-field quantum sensor applications.

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

Tech Support

Original Source

DOI: https://doi.org/10.1038/nphoton.2017.40