Preserving entanglement in a solid-spin system using quantum autoencoders

At a Glance

Metadata	Details
Publication Date	2022-09-26
Journal	Applied Physics Letters
Authors	Feifei Zhou, Yu Tian, Yumeng Song, Chu-Dan Qiu, Xiangyu Wang
Institutions	Hefei University of Technology, Zhejiang Lab
Citations	8
Analysis	Full AI Review Included

Technical Documentation & Analysis: Preserving Entanglement in Solid-Spin Systems

This document analyzes the research paper “Preserving Entanglement in a Solid-Spin System Using Quantum Autoencoders” and outlines how 6CCVD’s advanced MPCVD diamond materials and engineering services are ideally suited to replicate, extend, and scale this critical quantum memory technology.

Executive Summary

The research successfully demonstrates a novel method for preserving quantum entanglement in a solid-state system, leveraging the unique properties of Nitrogen-Vacancy (NV) centers in diamond.

Core Achievement: Entanglement lifetime of Bell states in a solid-spin system (NV electron and ¹⁴N nuclear spins) was extended by three orders of magnitude.
Performance Metric: Lifetime increased from $2.22 \pm 0.43$ µs (unencoded) to $3.03 \pm 0.56$ ms (encoded).
Methodology: A Hybrid Quantum-Classical Autoencoder (HQCA) was trained to compress the fragile electron-nuclear entanglement into the robust, long-coherence ¹⁴N nuclear spin subspace.
Technical Advantage: HQCA optimization inherently compensates for control imperfections and decoherence effects common in complex solid-spin systems, avoiding the need for extensive prior noise characterization.
Material Requirement: The experiment relies fundamentally on the high-quality spin properties and long coherence times provided by the diamond lattice structure.
6CCVD Value Proposition: 6CCVD provides the ultra-high purity Single Crystal Diamond (SCD) substrates, custom dimensions, and integrated metalization required for high-fidelity NV quantum memory devices.

Technical Specifications

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

Parameter	Value	Unit	Context
Unencoded Entanglement Lifetime	2.22 ± 0.43	µs	Bell state free evolution
CNOT Decoupled Lifetime	2.53 ± 0.76	ms	Traditional decoupling method
Autoencoder Encoded Lifetime	3.03 ± 0.56	ms	Encoded into ¹⁴N nuclear spin
Lifetime Improvement Factor	3 Orders of Magnitude	N/A	Autoencoder vs. Unencoded
Static Magnetic Field (B_z)	≈ 52	mT	Applied along the NV axis
Excitation Wavelength	532	nm	Green laser source for polarization
Fluorescence Detection Range	650 to 800	nm	Detected by Avalanche Photodiode (APD)
Microwave Pulse Duration ($t$)	800	ns	Fixed duration for $U_{\epsilon}$ encoder pulses
Final Encoder Amplitude ($B_1$)	0.164	V	Optimized AWG voltage peak-peak
Final Electron Spin Probability ($P_{	0\rangle}$)	> 0.93	N/A
RF/MW Delivery Structure Thickness	100	µm	$\Omega$-type ring on coverslip

Key Methodologies

The experiment utilized a hybrid quantum-classical approach (HQCA) implemented on a bulk diamond NV center system.

Material Preparation: Experiments were performed using NV centers in bulk diamond integrated into a home-built Optically Detected Magnetic Resonance (ODMR) system.
Spin Initialization: A 532 nm green laser and a static magnetic field ($B_z \approx 52$ mT) were used to achieve simultaneous optical polarization of both the electron spin (qubit 1) and the ¹⁴N nuclear spin (qubit 2).
Quantum Control Hardware: Microwave (MW) and radio-frequency (RF) signals were generated using an IQ-modulation system (AWG/VSG) and delivered to the sample via a slot-line structure featuring a 100 µm thick $\Omega$-type ring.
Encoder Design: The quantum autoencoder ($U_{\epsilon}$) was defined as a Parameterized Quantum Circuit (PQC) consisting of two MW pulses ($MW_1, MW_2$), each fixed at 800 ns duration, applied only to the electron spin.
HQCA Optimization: The encoder parameters ($B_1, B_2$) were iteratively optimized using gradient descent. The cost function was the average probability ($P$) that the electron spin occupies $|0\rangle$, measured directly on the quantum processor (NV center).
Entanglement Verification: The performance of the trained autoencoder was verified by comparing the coherence lifetime of the Bell state under three conditions: unencoded free evolution, CNOT-decoupled evolution, and autoencoder-encoded evolution.

6CCVD Solutions & Capabilities

This research highlights the critical need for high-quality, customized diamond substrates for advanced quantum information processing (QIP). 6CCVD is uniquely positioned to supply the materials and engineering services necessary to advance this work from fundamental research to scalable quantum memory prototypes.

Applicable Materials

To replicate and extend this high-fidelity entanglement preservation research, 6CCVD recommends the following materials:

Optical Grade Single Crystal Diamond (SCD): Essential for minimizing lattice defects and maximizing the electron spin coherence time ($T_2$), which is crucial for high-fidelity quantum gates and HQCA optimization.
High-Purity SCD Substrates: Required for creating well-isolated NV centers, whether through native incorporation or controlled ion implantation.
Custom Substrates (up to 10 mm thick): For integration into specialized ODMR setups requiring specific thermal or mechanical properties.

Customization Potential

The experimental setup requires precise integration of control electronics onto the diamond surface. 6CCVD offers comprehensive services to meet these needs:

Research Requirement	6CCVD Capability	Engineering Specification
High-Fidelity Quantum Control	Ultra-Smooth Polishing	SCD surfaces polished to Ra < 1 nm to minimize surface noise and maximize optical coupling efficiency.
On-Chip RF/MW Delivery	Custom Metalization Services	Internal capability to deposit multi-layer metal stacks (e.g., Ti/Pt/Au, Cu) for fabricating slot-line or $\Omega$-type ring structures directly onto the diamond surface.
Custom Dimensions	Precision Laser Cutting & Shaping	Supply of custom-sized plates/wafers up to 125 mm (PCD) or custom SCD plates up to 500 µm thick, ensuring compatibility with specific confocal microscopy objectives (like the 60×, NA 1.42 used here).
Boron Doping (Future Extension)	Boron-Doped Diamond (BDD)	For researchers exploring alternative quantum systems or integrated electrodes, 6CCVD offers BDD films up to 500 µm thick.

Engineering Support

The success of the HQCA method relies on minimizing experimental errors and optimizing complex pulse sequences. 6CCVD’s in-house PhD team specializes in the material science of solid-state quantum systems. We can assist researchers in selecting the optimal diamond grade, orientation, and surface termination for similar NV Quantum Memory projects, ensuring the highest possible $T_2$ coherence times and gate fidelities.

We offer global shipping (DDU default, DDP available) to ensure your critical materials arrive safely and efficiently, regardless of your location.

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

View Original Abstract

Entanglement, as a key resource for modern quantum technologies, is extremely fragile due to the decoherence. Here, we show that a quantum autoencoder, which is trained to compress a particular set of quantum entangled states into a subspace that is robust to decoherence, can be employed to preserve entanglement. The training process is based on a hybrid quantum-classical approach to improve the efficiency in building the autoencoder and reduce the experimental errors during the optimization. Using nitrogen-vacancy centers in diamond, we demonstrate that the entangled states between the electron and nuclear spins can be encoded into the nucleus subspace, which has much longer coherence time. As a result, lifetime of the Bell states in this solid-spin system is extended from 2.22 ± 0.43 μs to 3.03 ± 0.56 ms, yielding a three orders of magnitude improvement. The quantum autoencoder approach is universal, paving the way of utilizing long lifetime nuclear spins as immediate-access quantum memories in quantum information tasks.

Tech Support

Original Source

DOI: https://doi.org/10.1063/5.0120060