Quantum error correction of spin quantum memories in diamond under a zero magnetic field

At a Glance

Metadata	Details
Publication Date	2022-04-27
Journal	Communications Physics
Authors	Takaya Nakazato, Raustin Reyes, Nobuaki Imaike, Kazuyasu Matsuda, Kazuya Tsurumoto
Institutions	Yokohama National University
Citations	17
Analysis	Full AI Review Included

Technical Documentation & Analysis: Zero-Field Quantum Error Correction in Diamond NV Centers

Reference: Nakazato et al., Quantum error correction of spin quantum memories in diamond under a zero magnetic field, Communications Physics (2022) 5:102.

Executive Summary

This research successfully demonstrates fault-tolerant quantum memory operation using Nitrogen-Vacancy (NV) centers in diamond, achieving a critical milestone for scalable quantum networks and hybrid quantum computing architectures.

Zero-Field Operation: Quantum Error Correction (QEC) was achieved under a completely zero magnetic field, eliminating the primary obstacle for integrating spin-based quantum memories with magnetic-field-sensitive superconducting qubits.
Three-Qubit QEC: The demonstration utilized a three-qubit code (one ¹⁴N nuclear spin memory qubit and two surrounding ¹³C nuclear spin ancilla qubits) to protect against bit-flip and phase-flip errors.
High Fidelity: The QEC process yielded high average state fidelities of 75.4% (bit-flip) and 74.6% (phase-flip) against intentionally generated errors.
Material Requirement: The experiment relied on high-purity Type IIa Chemical Vapor Deposition (CVD) diamond, confirming the necessity of ultra-low defect density Single Crystal Diamond (SCD) for long-coherence quantum applications.
Long Coherence Times: The nuclear spins exhibited exceptional coherence, with the ¹⁴N spin lasting over 10 seconds and ¹³C spin pairs lasting approximately 1.9 minutes.
Advanced Control: High-fidelity manipulation was enabled by holonomic Controlled-Z (C-Z) gates and GRAPE (gradient ascent pulse engineering)-optimized microwave pulses.

Technical Specifications

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

Parameter	Value	Unit	Context
Diamond Material	High-Purity Type IIa CVD Diamond	N/A	Substrate for NV center creation.
Crystal Orientation	<100>	N/A	Specified orientation for growth.
Operating Temperature	5	K	Required for maximizing electron spin coherence (T₂).
Magnetic Field Condition	Zero (Canceled)	N/A	Achieved via 3D coil system to cancel residual fields.
¹⁴N Nuclear Spin Coherence Time	>10	seconds	Demonstrated long-lived quantum memory.
¹³C Nuclear Spin Pair Coherence Time	~1.9	minutes	Exceptional memory lifetime observed.
Zero-Field Splitting (D₀)	2.877	MHz	NV electron spin transition frequency.
¹⁴N Hyperfine Splitting	2.2	MHz	Used for memory qubit manipulation.
¹³C₁ Hyperfine Splitting	1.14	MHz	Strongly coupled ancilla qubit.
¹³C₂ Hyperfine Splitting	0.33	MHz	Strongly coupled ancilla qubit.
GHZ Entanglement Fidelity	78	%	Classical correlation confirmed for three nuclear spins.
QEC Fidelity (Bit-Flip Error)	75.4	%	Average state fidelity after error correction.
QEC Fidelity (Phase-Flip Error)	74.6	%	Average state fidelity after error correction.

Key Methodologies

The experiment required stringent material preparation and precise control techniques to achieve zero-field QEC:

Material Preparation: A high-purity Type IIa CVD-grown Single Crystal Diamond (SCD) with <100> orientation was used, containing a single, naturally occurring NV center.
Cryogenic Cooling: The sample was cooled to 5 K to extend the electron spin coherence time, which is necessary for high-fidelity quantum operations.
Zero-Field Cancellation: A three-dimensional coil system was employed to cancel all residual magnetic fields (including the geomagnetic field). The zero-field condition was verified by maximizing the spin-echo coherence time.
Microwave Delivery: Two orthogonal copper wires were attached directly to the sample surface to deliver microwaves with arbitrary polarization for spin manipulation.
Optical Control: A 515 nm green laser was used for charge and electron spin initialization, and 637 nm red lasers were used for resonant excitation and spin measurement (ODMR).
Gate Implementation: Universal quantum gates (Hadamard, Pauli-X/Y) and the holonomic Controlled-Z (C-Z) gate were implemented using the geometric phase, conditioned on the NV electron spin state.
Pulse Optimization: The GRAPE algorithm was used to optimize microwave waveforms, ensuring robust, high-fidelity manipulation of the nuclear spins, particularly the strongly coupled ¹³C isotopes.

6CCVD Solutions & Capabilities

This groundbreaking research highlights the critical role of high-quality CVD diamond in advancing fault-tolerant quantum computation. 6CCVD is uniquely positioned to supply and customize the materials required to replicate, scale, and extend this zero-field QEC work.

Applicable Materials

Research Requirement	6CCVD Material Recommendation	Technical Rationale
High-Purity Type IIa Diamond	Optical Grade Single Crystal Diamond (SCD)	Our SCD features ultra-low nitrogen and defect concentrations (< 1 ppb), guaranteeing the long intrinsic T₂ coherence times (seconds to minutes) necessary for nuclear spin quantum memory.
Ancilla Qubit Integration	Custom ¹³C-Enriched SCD	For scaling beyond naturally occurring ¹³C, 6CCVD can supply SCD substrates isotopically enriched with ¹³C, allowing for controlled placement and density of ancilla qubits, optimizing hyperfine coupling strength.
Zero-Field Integration	High-Purity Polycrystalline Diamond (PCD)	For large-scale quantum network interfaces, our high-quality PCD (up to 125mm diameter) offers a cost-effective platform for distributed quantum repeaters, maintaining high purity standards.
Qubit Readout/Control	Boron-Doped Diamond (BDD)	BDD films can be integrated as electrodes or conductive layers for advanced electrical control and readout of NV centers, facilitating complex quantum circuits.

Customization Potential

The success of this zero-field QEC relies on precise material geometry and integration. 6CCVD offers comprehensive customization services to meet these stringent engineering demands:

Custom Dimensions and Thickness: We provide SCD plates from 0.1 µm films up to 500 µm wafers, and substrates up to 10 mm thick. This allows researchers to select the optimal thickness for NV creation (via implantation or in-situ growth) and subsequent device integration.
Crystallographic Orientation: While the paper used <100>, 6CCVD supplies SCD cut and polished to specific orientations (<100>, <111>, <110>), enabling optimization of NV alignment and strain engineering for specific quantum protocols.
Advanced Metalization: The experiment required copper wires for microwave delivery. 6CCVD offers in-house deposition of critical thin-film metals (Au, Pt, Pd, Ti, W, Cu) directly onto diamond substrates, essential for creating microwave waveguides, superconducting contacts, or integrated control circuitry.
Ultra-Smooth Polishing: Our SCD polishing achieves surface roughness (Ra) below 1 nm, minimizing surface defects that can introduce noise and degrade coherence, particularly critical for high-fidelity, zero-field operations.

Engineering Support

6CCVD’s in-house PhD team specializes in diamond material science for quantum applications. We provide expert consultation on:

Material Selection: Assisting researchers in selecting the optimal purity, isotopic enrichment (e.g., ¹³C or ¹²C), and crystal orientation for NV center creation and zero-field QEC experiments.
Integration Strategy: Advising on metalization schemes and substrate preparation for seamless integration with external components, such as superconducting circuits or microwave antennas.
Global Logistics: We ensure reliable, global shipping (DDU default, DDP available) of sensitive diamond materials, supporting international research collaborations.

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/s42005-022-00875-6