All-microwave holonomic control of an electron-nuclear two-qubit register in diamond

At a Glance

Metadata	Details
Publication Date	2020-04-20
Journal	Physical review. B./Physical review. B
Authors	V. O. Shkolnikov, Roman Mauch, Guido Burkard
Institutions	University of Konstanz
Citations	11
Analysis	Full AI Review Included

Technical Documentation & Analysis: All-Microwave Holonomic Control in Diamond

This document analyzes the research detailing the universal holonomic control of a two-qubit register (NV electron spin and nearby ¹³C nuclear spin) in diamond using only microwave pulses. This application requires ultra-high-purity Single Crystal Diamond (SCD) with precise isotopic control, a core capability of 6CCVD.

Executive Summary

The research demonstrates a robust, all-microwave scheme for universal quantum gates on a diamond NV center two-qubit register.

Qubit Register: Utilizes the electron spin of the Nitrogen-Vacancy (NV^-) center coupled to the spin of a nearest-neighbor ¹³C nuclear atom.
Control Mechanism: Achieves universal holonomic (geometric) gates using only microwave pulses, eliminating the need for slower radio frequency (RF) control.
Speed and Fidelity: Simulated gate operation times are fast (~285 ns), limited by the 36 MHz resonance splitting, achieving high fidelity (up to 0.995) under realistic detuning noise.
Key Innovation: Applying a precise axial magnetic field ($B_z = D_{gs}/\gamma_e$) mixes the electronic states $|-1\rangle$ and $|0\rangle$, allowing microwave fields to efficiently drive transitions previously forbidden by nuclear spin selection rules.
Material Requirement: Requires high-quality Single Crystal Diamond (SCD) with controlled ¹³C isotopic concentration to ensure strong, addressable hyperfine coupling.
Initialization: Coherent Population Trapping (CPT) protocol achieves 98% initialization fidelity in 100 µs.

Technical Specifications

The following hard data points are extracted from the analysis of the NV ground state and the proposed operating regime.

Parameter	Value	Unit	Context
NV Ground State Zero-Field Splitting ($D_{gs}$)	2.88	GHz	Fundamental NV property
Electronic Gyromagnetic Ratio ($\gamma_e$)	2.8	MHz/G	Used in Hamiltonian $H_e$
Nuclear Gyromagnetic Ratio ($\gamma_n$)	0.001	MHz/G	¹³C nuclear spin
Closest ¹³C Hyperfine Axial Coupling ($A_{zz}$)	201	MHz	Nearest neighbor ¹³C atom
Required Axial Magnetic Field ($B_z$)	$D_{gs}/\gamma_e$	G	Approx. 1028 G; sets $
Transverse Magnetic Field ($B_\perp$)	500	G	Used in initialization simulation
Closest Resonance Frequency Difference	36	MHz	Sets the limit for gate speed
Gate Operation Time ($\tau$)	~285	ns	Time required for CNOT gate
Initialization Fidelity	98	%	Achieved in 100 µs using CPT protocol
Simulated Average Gate Fidelity (Detuning Error)	0.995	N/A	CNOT gate on electron spin
Simulated Average Gate Fidelity (Energy Fluctuation Error)	0.985	N/A	CNOT gate on electron spin

Key Methodologies

The experiment relies on precise material engineering and complex electromagnetic control protocols.

Material Selection: Use of high-purity diamond hosting NV centers, specifically requiring the presence of ¹³C nuclear spins (either natural abundance or isotopically enriched) to form the two-qubit register via strong hyperfine interaction.
Magnetic Field Tuning: Application of a strong axial magnetic field ($B_z$) tuned precisely to the zero-field splitting ratio ($D_{gs}/\gamma_e$) to achieve degeneracy between the $|-1\rangle$ and $|0\rangle$ electronic states.
State Mixing: Application of a nonparallel magnetic field ($B_\perp$) to mix the electronic states, creating new eigenstates $|+\rangle$ and $|-\rangle$ separated by $|\Omega|$.
Microwave Control: Implementation of eight distinct microwave pulse protocols ($P_1$ through $P_8$) tuned to the specific hyperfine resonance frequencies (separated by $\ge 36$ MHz) to achieve universal holonomic control.
Initialization Protocol: Coherent Population Trapping (CPT) using simultaneous optical fields (resonant with the 1.945 eV Zero Phonon Line) and microwave tones to rapidly pump the system into the lowest hyperfine ground state with 98% fidelity.

6CCVD Solutions & Capabilities

6CCVD is uniquely positioned to supply the foundational diamond materials and custom engineering required to replicate and advance this high-fidelity quantum control research.

Applicable Materials

The success of this research hinges on the quality and isotopic purity of the diamond substrate. 6CCVD recommends the following:

Optical Grade Single Crystal Diamond (SCD): Required for high-fidelity optical initialization and readout (1.945 eV ZPL). Our SCD features extremely low nitrogen content (< 1 ppb) to minimize background noise and maximize NV coherence time ($T_2$).
Controlled Isotopic Purity: The two-qubit register relies on the ¹³C nuclear spin. 6CCVD offers:
- Natural Abundance ¹³C SCD: For projects utilizing randomly distributed nearest-neighbor ¹³C atoms.
- Isotopically Enriched ¹²C SCD: For applications requiring long $T_2$ coherence times, where ¹³C is intentionally minimized.
- Custom ¹³C Doping: For targeted research requiring specific, higher concentrations of ¹³C to increase the probability of finding strongly coupled nuclear spins.

Customization Potential

The implementation of all-microwave control often requires integrated on-chip structures for efficient microwave delivery.

Research Requirement	6CCVD Custom Capability	Benefit to Researcher
High-Quality Optical Access	Polishing: SCD surfaces polished to Ra < 1 nm.	Maximizes photon collection efficiency and minimizes scattering losses during optical initialization.
Microwave Pulse Delivery	Custom Metalization: Internal capability for deposition of Au, Pt, Ti, Cu, etc.	Allows researchers to fabricate on-chip microwave structures (e.g., coplanar waveguides) directly onto the diamond surface for precise field control.
Large-Scale Integration	Custom Dimensions: Plates/wafers up to 125 mm (PCD) and large SCD substrates (up to 10 mm thickness).	Supports scaling up the quantum register or integrating multiple NV devices on a single platform.
Device Fabrication	Laser Cutting/Shaping: Precision cutting services for unique geometries or mesa structures.	Enables integration into complex cryogenic or magnetic field setups.

Engineering Support

The theoretical scheme relies on complex perturbation theory and precise magnetic field tuning to achieve the required state mixing and resonance conditions ($B_z = D_{gs}/\gamma_e$).

6CCVD’s in-house PhD team specializes in the material science of NV centers and diamond growth parameters. We offer consultation on:

Material Selection: Optimizing nitrogen and ¹³C concentration to balance high coherence ($T_2$) with strong, addressable hyperfine coupling ($A_{ij}$).
Surface Termination: Ensuring optimal surface quality to maintain the NV^- charge state stability critical for long-term qubit operation.
Substrate Preparation: Providing substrates with specific crystallographic orientations necessary for alignment with external magnetic fields.

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

View Original Abstract

We present a theoretical scheme that allows to perform a universal set of\nholonomic gates on a two qubit register, formed by a $^{13}$C nuclear spin\ncoupled to the electron spin of a nitrogen-vacancy center in diamond. Strong\nhyperfine interaction between the electron spin and the spins of the first\nthree shells of $^{13}$C atoms allows to operate the state of the register on\nthe submicrosecond timescale using microwave pulses only. We describe the\nsystem and the operating regime analytically and numerically, as well as\nsimulate the initialization protocols.\n

Tech Support

Original Source

DOI: https://doi.org/10.1103/physrevb.101.155306