Efficient Quantum Gates for Individual Nuclear Spin Qubits by Indirect Control

At a Glance

Metadata	Details
Publication Date	2020-06-02
Journal	Physical Review Letters
Authors	Swathi S. Hegde, Jingfu Zhang, Dieter Suter
Institutions	TU Dortmund University
Citations	45
Analysis	Full AI Review Included

Technical Documentation: Efficient Quantum Gates in NV Center Diamond

This document analyzes the research paper “Efficient quantum gates for individual nuclear spin qubits by indirect control” and outlines how 6CCVD’s advanced MPCVD diamond materials and fabrication services can support and extend this critical work in scalable quantum computing.

Executive Summary

The research successfully demonstrates highly efficient, universal quantum gates (Hadamard and CNOT) on a ${}^{13}\text{C}$ nuclear spin qubit within a Nitrogen Vacancy (NV) center in diamond using an Indirect Control (IC) scheme.

Core Achievement: Implementation of universal quantum gates on a nuclear spin qubit using minimal control overhead (2-3 short Microwave (MW) pulses) applied only to the electron spin.
Efficiency: Gate durations are short ($< 30\ \mu\text{s}$ for simulated 6-qubit systems), remaining well within the electron spin coherence time ($T_2^* \approx 20\ \mu\text{s}$).
Fidelity: High theoretical gate fidelities were achieved ($> 96%$ for Hadamard and CNOT), validating the numerical optimization protocol.
Material Requirement: The experiment relied on ultra-high purity diamond with 99.995% ${}^{12}\text{C}$ enrichment to minimize background nuclear spin decoherence.
Scalability: The IC scheme is shown via simulation to be scalable up to 6 qubits, requiring a minimum electron spin $T_2^*$ of $\approx 30\ \mu\text{s}$ for robust operation.
6CCVD Value Proposition: 6CCVD provides the necessary high-purity Single Crystal Diamond (SCD) substrates, custom dimensions, and integrated metalization required to replicate and scale these quantum registers.

Technical Specifications

The following hard data points were extracted from the experimental results and theoretical simulations:

Parameter	Value	Unit	Context
Diamond Purity	99.995	% ${}^{12}\text{C}$ Enrichment	Used to minimize decoherence from background nuclear spins.
Operating Environment	Room Temperature	°C	Experimental condition.
External Magnetic Field ($B_0$)	14.8	mT	Used to lift electronic state degeneracy.
Experimental Electron $T_2^*$	$\approx 20$	µs	Coherence time of the sample used in the experiment.
Required $T_2^*$ (6-Qubit System)	$\approx 30$	µs	Minimum required coherence time for scalable controlled-controlled rotations.
MW Rabi Frequency ($\omega_1/2\pi$)	0.5	MHz	Used for selective subspace control.
Theoretical Hadamard Fidelity ($U_H$)	> 96	%	Achieved via numerical optimization.
Theoretical CNOT Fidelity ($U_{CNOT}$)	> 97	%	Achieved via numerical optimization.
Maximum Gate Duration (6-Qubit)	22 - 28	µs	Total duration for controlled-controlled rotations.
Electron-${}^{13}\text{C}$ Distance ($r$)	0.8924	nm	Calculated spatial distance based on hyperfine coupling.

Key Methodologies

The experimental implementation of efficient quantum gates relied on the following key steps and parameters:

Material Preparation: Use of a high-purity diamond sample (99.995% ${}^{12}\text{C}$ enriched) containing isolated NV centers coupled to a single ${}^{13}\text{C}$ nuclear spin.
Initialization: Electron spin initialized to the $|0\rangle$ state using a 532 nm laser pulse (5 µs duration). The ${}^{13}\text{C}$ nuclear spin was initialized using an Indirect Control (IC) method.
Subspace Selection: The magnetic field ($B_0 = 14.8\ \text{mT}$) and MW pulse frequency were chosen to focus operations exclusively on the system subspace where the electron spin is $m_s = {0, -1}$ and the ${}^{14}\text{N}$ spin is $m_N = 1$.
Indirect Control (IC) Implementation: Quantum gates ($U_H$, $U_{CNOT}$) were realized using a sequence of 2-3 short MW pulses applied only to the electron spin, interspersed with free evolution periods governed by the electron-${}^{13}\text{C}$ hyperfine coupling.
Pulse Sequence Optimization: Pulse parameters (delays $\tau_i$, durations $t_i$, phases $\phi_i$) were numerically optimized using a genetic algorithm (MATLAB® subroutine) to maximize the gate fidelity ($F$) and ensure robustness against MW amplitude fluctuations ($\omega_1/2\pi = [0.48, 0.52]\ \text{MHz}$).
Readout: Final state determination was performed using a 400 ns laser pulse to measure the electron population ($m_s = 0$), followed by Free Precession Signals (FIDs) and Fourier transformation to determine ${}^{13}\text{C}$ coherence.

6CCVD Solutions & Capabilities

This research demonstrates the critical role of high-quality diamond in achieving scalable quantum registers. 6CCVD is uniquely positioned to supply the specialized materials and fabrication services required to advance this work from 3-qubit demonstration to multi-qubit systems.

Applicable Materials

To replicate and extend the high-fidelity results achieved in this paper, researchers require diamond substrates optimized for quantum coherence.

Research Requirement	6CCVD Material Solution	Key Specification
Ultra-High Purity	Optical Grade Single Crystal Diamond (SCD)	Ultra-low nitrogen concentration (< 1 ppb) to minimize background electron spins.
Isotopic Control	High ${}^{12}\text{C}$ Enriched SCD	Enrichment > 99.995% to maximize $T_2$ and $T_2^*$ coherence times for the target ${}^{13}\text{C}$ qubits.
Scalability	Polycrystalline Diamond (PCD) Wafers	Custom plates/wafers up to 125mm for high-density device fabrication and integration.
Qubit Control	Boron-Doped Diamond (BDD)	Available for integration where conductive diamond layers are needed for specialized electrical control or sensing applications.

Customization Potential

The transition to scalable quantum registers (simulated up to 6 qubits) necessitates precise engineering beyond standard substrates.

Custom Dimensions and Thickness: 6CCVD provides SCD plates with thicknesses ranging from $0.1\ \mu\text{m}$ to $500\ \mu\text{m}$, and substrates up to 10mm thick, allowing for optimal thermal management and optical access required for NV center experiments.
Surface Preparation: Achieving high-fidelity control requires minimal surface defects. 6CCVD offers superior polishing services, ensuring surface roughness $R_a < 1\ \text{nm}$ on SCD, critical for maintaining near-surface NV coherence.
Integrated Control Structures: The control scheme relies on precise MW pulsing. 6CCVD offers in-house custom metalization (Au, Pt, Pd, Ti, W, Cu) directly deposited onto the diamond surface, enabling the fabrication of high-frequency coplanar waveguides (CPWs) for efficient on-chip MW delivery to the NV centers.

Engineering Support

The paper identifies that scalable systems require a minimum electron spin $T_2^*$ of $\approx 30\ \mu\text{s}$. Achieving and exceeding this threshold is a material science challenge.

Coherence Optimization: 6CCVD’s in-house PhD team specializes in optimizing MPCVD growth recipes to control impurity incorporation and isotopic ratios, directly impacting $T_2$ and $T_2^*$. We assist researchers in selecting the ideal material specifications (e.g., nitrogen concentration, ${}^{12}\text{C}$ enrichment level) necessary for similar NV Center Quantum Computing projects.
Global Logistics: We ensure reliable global shipping (DDU default, DDP available) for time-sensitive research projects, guaranteeing the prompt delivery of specialized diamond materials worldwide.

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

View Original Abstract

Hybrid quantum registers, such as electron-nuclear spin systems, have emerged as promising hardware for implementing quantum information and computing protocols in scalable systems. Nevertheless, the coherent control of such systems still faces challenges. Particularly, the lower gyromagnetic ratios of the nuclear spins cause them to respond slowly to control fields, resulting in gate times that are generally longer than the coherence time of the electron. Here, we demonstrate a scheme for circumventing this problem by indirect control: we apply a small number of short pulses only to the electron and let the full system undergo free evolution under the hyperfine coupling between the pulses. Using this scheme, we realize robust quantum gates in an electron-nuclear spin system, including a Hadamard gate on the nuclear spin and a controlled-NOT gate with the nuclear spin as the target qubit. The durations of these gates are shorter than the electron coherence time, and thus additional operations to extend the system coherence time are not needed. Our demonstration serves as a proof of concept for achieving efficient coherent control of electron-nuclear spin systems, such as nitrogen vacancy centers in diamond. Our scheme is still applicable when the nuclear spins are only weakly coupled to the electron.