Experimental demonstration of adversarial examples in learning topological phases

At a Glance

Metadata	Details
Publication Date	2022-08-25
Journal	Nature Communications
Authors	Huili Zhang, Si Jiang, Xin Wang, Wengang Zhang, Xianzhi Huang
Institutions	ShangHai JiAi Genetics & IVF Institute, Tsinghua University
Citations	10
Analysis	Full AI Review Included

Technical Documentation: MPCVD Diamond for NV Center Quantum Simulation

Executive Summary

This research utilizes the Nitrogen-Vacancy (NV) center in diamond as a robust, solid-state quantum simulator to investigate the reliability of machine learning (ML) classifiers when applied to experimental data for identifying topological phases.

Core Achievement: Experimental demonstration of “adversarial examples”—tiny, carefully crafted perturbations—that successfully deceive neural network classifiers designed to identify topological phases (specifically, Hopf insulators).
Material Requirement: The experiment relies critically on high-quality, low-defect Single Crystal Diamond (SCD) to host the NV center, ensuring the long coherence times and low noise environment necessary for quantum simulation.
Vulnerability Identified: Experimental noise is shown to be more likely to act as an adversarial perturbation when the input data percentage is reduced, highlighting a crucial trade-off between data efficiency and classifier robustness in real-world quantum experiments.
Fabrication Necessity: The setup required precise micro-fabrication, including the creation of a Solid Immersion Lens (SIL) with a 6.74 µm diameter on the diamond surface to enhance photon collection efficiency (NA = 1.49 objective).
6CCVD Value Proposition: 6CCVD provides the necessary Electronic Grade SCD substrates, custom dimensions, ultra-low surface roughness (Ra < 1nm), and in-house metalization/fabrication capabilities required to replicate and advance this solid-state quantum platform.
Topological Integrity: Crucially, the adversarial perturbations did not alter the fundamental topological properties (Hopf index or topological link) of the simulated phase, confirming that the ML classifier failed to capture the underlying physical principles.

Technical Specifications

The following hard data points were extracted from the experimental setup and results, demonstrating the stringent material and operational requirements of the NV center platform.

Parameter	Value	Unit	Context
Quantum Platform	NV Center	N/A	Solid-state quantum simulator
Laser Wavelength	532	nm	Diode laser for spin initialization
Laser Excitation Time	3	µs	Initialization pulse duration
Static Magnetic Field (B₀)	472	Gauss	Permanent magnet, aligned to NV axis
MW Carrier Frequencies	Two orthogonal 100	MHz	Used for Hamiltonian modulation
Adiabatic Passage Time	1500	ns	Total time for quantum evolution
Solid Immersion Lens (SIL) Diameter	6.74	µm	Fabricated on diamond for collection enhancement
Objective Numerical Aperture (NA)	1.49	N/A	Oil-immersed objective lens
Fluorescence Count Rate	~260	kcps	Under 0.25 mW laser excitation
Signal-to-Noise Ratio (SNR)	~100:1	N/A	Photon detection quality
Classification Fidelity (Legitimate Sample)	99.68(31)	%	High confidence classification
Classification Fidelity (Adversarial Sample)	99.23(26)	%	High confidence classification, despite misprediction
Hopf Index (Theory, N→∞)	-2, 1, 0	N/A	For h = 0.5, 2, and 3.2, respectively
Surface Roughness Requirement (Implied)	Ra < 1	nm	Necessary for high-fidelity optical coupling (6CCVD standard)

Key Methodologies

The experiment utilized a highly controlled solid-state quantum simulation protocol implemented on the NV center platform.

Material Selection and Fabrication: A high-quality diamond sample containing a single NV center was used. A Solid Immersion Lens (SIL) with a 6.74 µm diameter was fabricated on the surface to enhance the collection of emitted photons.
Spin Initialization and Polarization: The electron spin state was initialized using a 3 µs pulse from a 532 nm laser. A static magnetic field of 472 Gauss was applied, precisely aligned to the NV symmetry axis, enabling dynamic polarization of the nuclear spin.
Hamiltonian Simulation: The three-dimensional Hopf insulator Hamiltonian was simulated using the electron subspace spanned by the |0> and |-1> states. This was controlled via Microwave (MW) modulation, programmed using two orthogonal 100 MHz carrier signals.
Adiabatic Evolution: The quantum state was evolved adiabatically over a total time of 1500 ns, ensuring the system remained in the ground state throughout the simulation of the momentum-space Hamiltonian.
Quantum State Tomography: The density matrix (ρ) was measured at various points in the momentum grid (k-space) by counting spin-dependent photon numbers, allowing for full characterization of the simulated phase.
Adversarial Example Generation: Adversarial perturbations were generated using optimization algorithms (e.g., Projected Gradient Descent and Differential Evolution) to create tiny, high-fidelity modifications to the measured density matrices that specifically mislead the trained neural network classifier.
Topological Invariant Calculation: The Hopf index (χ) was calculated directly from the experimentally measured data using a conventional discretization scheme over a 10 x 10 x 10 momentum grid, confirming that the adversarial examples did not alter the true topological invariant.

6CCVD Solutions & Capabilities

The successful execution of this advanced quantum simulation relies on ultra-high-purity diamond substrates and precision engineering capabilities that are core to 6CCVD’s expertise. We offer materials and services specifically tailored to meet the stringent requirements of NV center research and solid-state quantum computing.

Applicable Materials for Replication and Extension

To replicate or extend this research into more complex quantum simulations or sensing applications, 6CCVD recommends the following materials:

Material Grade	Specification	Application Context
Electronic Grade SCD	Ultra-low nitrogen content (< 1 ppb N), low strain, high purity.	Essential for maximizing NV center coherence time (T₂) and minimizing spectral diffusion, crucial for high-fidelity quantum simulation.
Controlled N-Doped SCD	Precise, low-level nitrogen doping (e.g., 1-5 ppm) during growth.	Allows for controlled creation of NV centers at desired densities, optimizing the trade-off between single-spin isolation and ensemble sensing.
Optical Grade SCD	High transmission across UV-IR spectrum, Ra < 1 nm polishing.	Required for efficient 532 nm laser delivery and high-NA photon collection through the substrate.

Customization Potential for NV Platforms

The paper highlights the need for specialized geometry (SIL fabrication) and precise optical coupling. 6CCVD’s in-house engineering capabilities directly address these requirements:

Custom Dimensions and Thickness: We provide SCD plates and wafers up to 125mm (PCD) and custom thicknesses from 0.1 µm to 500 µm (SCD). We can supply substrates pre-cut to specific dimensions required for integration into confocal microscope stages.
Ultra-Precision Polishing: Achieving high-fidelity optical coupling (NA = 1.49 objective) demands exceptional surface quality. 6CCVD guarantees Ra < 1 nm polishing on SCD substrates, minimizing scattering losses and maximizing photon collection efficiency.
Micro-Fabrication Support: While the researchers fabricated the 6.74 µm Solid Immersion Lens (SIL) themselves, 6CCVD offers custom laser cutting and patterning services to define precise geometries, including mesa structures or pre-forms for SIL fabrication, streamlining the device integration process.
Advanced Metalization: For integrating MW control lines (as used for the 100 MHz carrier signals) or thermal management layers, 6CCVD provides internal metalization services, including Au, Pt, Pd, Ti, W, and Cu deposition, directly onto the diamond surface with high precision.

Engineering Support

6CCVD’s in-house PhD team specializes in the material science of diamond for quantum applications. We offer consultation services to assist researchers in:

Material Selection: Optimizing the diamond grade (e.g., nitrogen concentration, isotopic purity) to achieve target coherence times (T₂) for specific quantum simulation or quantum sensing projects.
Defect Engineering: Advising on post-growth processing (e.g., electron irradiation and annealing) necessary for high-yield NV center creation.
Integration Challenges: Providing technical guidance on mounting, thermal management, and surface preparation for integrating diamond into complex cryogenic or high-power optical setups.

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/s41467-022-32611-7