Parallel selective nuclear-spin addressing for fast high-fidelity quantum gates

At a Glance

Metadata	Details
Publication Date	2021-01-20
Journal	Physical review. A/Physical review, A
Authors	Benedikt Tratzmiller, Jan F. Haase, Zhenyu Wang, Martin B. Plenio
Institutions	Universität Ulm, South China Normal University
Citations	7
Analysis	Full AI Review Included

Technical Documentation & Analysis: Fast High-Fidelity Quantum Gates via Parallel Nuclear Spin Addressing

This document analyzes the research paper “Parallel selective nuclear spin addressing for fast high-fidelity quantum gates” to provide technical specifications and align the material requirements with 6CCVD’s advanced MPCVD diamond capabilities.

Executive Summary

This research demonstrates a significant advancement in solid-state quantum computation by achieving fast, high-fidelity entangling gates between nuclear spins mediated by a Nitrogen-Vacancy (NV) center in diamond.

Core Achievement: Developed modified pulsed polarization sequences (based on PulsePol/XY-like) enabling the simultaneous, selective addressing of two distinct nuclear spin species (e.g., ²⁹Si and ¹³C) via the electron spin.
Fidelity and Speed: Achieved process fidelity exceeding 99.99% for the entangling gate, demonstrating robustness against common experimental errors (e.g., < 2% amplitude error).
Gate Time Reduction: The direct gate approach using polarization sequences reduces the total gate time by up to 50% compared to gates synthesized sequentially from electron-nuclear interactions, crucial for operating within the electron T₂ coherence limit.
Robustness: The sequences are designed to be robust against magnetic field fluctuations and control errors, making them ideal for complex quantum registers.
Material Requirement: The success of this protocol relies fundamentally on high-purity, isotopically controlled Single Crystal Diamond (SCD) to maximize the coherence time of the NV electron spin and the coupled nuclear spins.
6CCVD Value Proposition: 6CCVD provides the necessary high-coherence, optical grade SCD substrates, custom metalization, and precise polishing required to replicate and scale this advanced quantum technology.

Technical Specifications

The following hard data points were extracted from the research paper, detailing the physical parameters and performance metrics of the quantum gate protocol.

Parameter	Value	Unit	Context
NV Zero Field Splitting (D)	2π × 2.87	GHz	Electronic spin transition
Electron Rabi Frequency ($\Omega$)	(2π) 50	MHz	Microwave pulse control (Fig 2)
Nuclear Spin 1 Larmor Freq ($\omega_1$)	(2π) 2	MHz	Example: Silicon-29 (²⁹Si)
Nuclear Spin 2 Larmor Freq ($\omega_2$)	1.265 $\omega_1$	N/A	Example: Carbon-13 (¹³C)
Effective Coupling Strength ($a_1$)	(2π) 20	kHz	Electron-nuclear interaction
Effective Coupling Strength ($a_2$)	(2π) 25	kHz	Electron-nuclear interaction
Achieved Process Fidelity	>99.99	%	For ²⁹Si-¹³C entangling gate
Total Gate Time (T)	~418	µs	High-fidelity gate duration (Fig 2)
Fastest Gate Time (T)	~120	µs	Achieved by polarization sequence (Fig 4)
Amplitude Error Tolerance	< 2	%	Robustness against drive errors
Detuning Error Tolerance	< (2π) 2	MHz	Robustness against drive errors

Key Methodologies

The experiment relies on precise control over the NV center’s electron spin to mediate interactions between two distinct nuclear spins.

NV Center Initialization: The NV center spin-1 system is reduced to a two-level qubit (m_s = 0 and m_s = +1) by applying a magnetic field aligned with the NV symmetry axis.
Microwave Control Application: An external microwave drive H_mw(t) is applied to control transitions between the selected electron spin levels, characterized by a time-dependent Rabi frequency $\Omega$(t).
Pulsed Polarization Sequence: Standard sensing sequences (like CPMG or XY-family) are generalized into pulsed polarization sequences (Fig 1a, 1b) to create an effective polarization exchange interaction ($\sigma_x I_x \pm \sigma_y I_y$) between the electron spin and the nuclear spins.
Dual Resonance Tuning: Two free parameters—pulse spacing ($\tau$) and pulse phase ($\phi$)—are introduced to tune the sequence to simultaneously resonate with two arbitrary nuclear Larmor frequencies ($\omega_1$ and $\omega_2$).
Coupling Strength Manipulation: To independently tune the effective coupling strengths ($a_1, a_2$) for high-fidelity gate construction, the standard $\pi$-pulses are replaced by composite 5-$\pi$ pulses (Fig 2a), introducing additional timing parameters ($\tau_0, \tau_1, \tau_2$).
Gate Implementation: The tuned sequences realize arbitrary entangling gates (CPHASE/SWAP composition) within the nuclear spin subspace, enabling fast manipulation of noise-protected quantum states.

6CCVD Solutions & Capabilities

The successful implementation of high-fidelity NV-based quantum gates is critically dependent on the quality and customization of the diamond substrate. 6CCVD is uniquely positioned to supply the required materials and engineering services.

Research Requirement	6CCVD Solution & Capability	Technical Advantage
High Coherence Material (Essential for long T₂ times)	Optical Grade Single Crystal Diamond (SCD)	Our SCD is grown via MPCVD with ultra-low nitrogen (< 1 ppb) and precise isotopic control (e.g., < 0.1% ¹³C). This purity minimizes environmental noise, maximizing the electron T₂ and nuclear spin coherence required for >99.99% gate fidelity.
Custom Dimensions for Integration (Specific wafer size/thickness)	Custom Dimensions and Thickness Control	We supply SCD plates in custom dimensions and thicknesses (0.1µm to 500µm) and substrates up to 10mm thick, ensuring compatibility with specific microwave resonators and optical setups.
Large-Scale Quantum Simulators (Future scaling needs)	Large-Format Polycrystalline Diamond (PCD)	For applications requiring large areas or hybrid integration, 6CCVD offers high-quality PCD plates up to 125mm in diameter, polished to Ra < 5nm (inch-size).
High-Frequency Control Lines (Rabi Freq up to 50 MHz)	In-House Custom Metalization Services	We offer internal metalization capabilities (Au, Pt, Pd, Ti, W, Cu) for direct deposition onto the diamond surface. This allows engineers to fabricate high-quality microwave transmission lines necessary for applying the complex, high-speed pulsed sequences.
Surface Quality (Crucial for shallow NV centers)	Ultra-Low Roughness Polishing	Our SCD wafers are polished to achieve surface roughness Ra < 1nm, which is vital for creating high-quality, shallow NV centers via implantation and minimizing surface-related decoherence.

Engineering Support

6CCVD’s in-house PhD team specializes in the material science of diamond for quantum applications. We offer comprehensive engineering support for projects involving NV-based quantum computation, quantum sensing, and spin manipulation. We assist researchers in selecting the optimal diamond grade (SCD vs. PCD), isotopic composition, and surface preparation to meet demanding coherence and integration requirements.

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

View Original Abstract

Due to their long coherence times, nuclear spins have gained considerable attention as physical qubits. Two-qubit gates between nuclear spins of distinct resonance frequencies can be mediated by electron spins, usually employing a sequence of electron-nuclear gates. Here we present a different approach inspired by, but not limited to, NV centers in diamond and discuss possible applications. To this end we generalize external electron spin control sequences for nuclear spin initialization and hyperpolarization to achieve the simultaneous control of distinct nuclear spins via an electron spin. This approach results in efficient entangling gates that, compared to standard techniques, reduce the gate time by more than 50% when the gate time is limited by off-resonant coupling to other spins and by up to 22% when the gate time is limited by small electron-nuclear coupling.

Tech Support

Original Source

DOI: https://doi.org/10.1103/physreva.103.012607