Experimental unsupervised learning of non-Hermitian knotted phases with solid-state spins
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2022-09-24 |
| Journal | npj Quantum Information |
| Authors | Yefei Yu, Li-Wei Yu, Wengang Zhang, Huili Zhang, Xiaolong Ouyang |
| Institutions | ShangHai JiAi Genetics & IVF Institute, Tsinghua University |
| Citations | 47 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Non-Hermitian Topological Phases in Diamond NV Centers
Section titled âTechnical Documentation & Analysis: Non-Hermitian Topological Phases in Diamond NV CentersâExecutive Summary
Section titled âExecutive SummaryâThis research successfully demonstrates the autonomous classification of exotic non-Hermitian topological phases using unsupervised machine learning implemented on a solid-state quantum simulator.
- Platform: The experiment utilizes the Nitrogen-Vacancy (NV) center in a single crystal diamond (SCD) coupled to a nearby 13C nuclear spin, serving as a two-qubit quantum simulator.
- Achievement: Experimental implementation of the non-Hermitian twister Hamiltonian, which hosts peculiar knotted topological phases (Hopf link, Unknot, Unlink).
- Methodology: The non-Hermitian dynamics were simulated using the dilation method, generating a high-fidelity, unlabeled experimental data set via 3552 non-unitary evolutions.
- Performance: Achieved high-fidelity state preparation, with >97.2% of prepared states exhibiting a fidelity (F) greater than 0.985.
- Classification: The diffusion map method was successfully applied to cluster the raw experimental data into the three distinct topological phases without a priori knowledge of the system.
- Material Requirement: The high-fidelity results rely critically on the use of high-quality, low-strain single crystal diamond (Type IIa) with controlled isotopic purity.
- Core Value: This work validates unsupervised machine learning as a robust tool for classifying unknown topological phases in solid-state quantum systems, paving the way for autonomous discovery in quantum materials science.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the experimental implementation using the NV center platform:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Diamond Material Type | Single Crystal (Type IIa) | N/A | <100>-oriented substrate |
| Carbon Isotope Abundance | 1.1 | % | Natural 13C abundance |
| Hyperfine Strength (NV-13C) | 13.7 | MHz | Coupling strength to nearby nuclear spin |
| Electron Spin Coherence Time (T2*) | 3.0 | ”s | Measured via Ramsey interferometry (Room Temp) |
| Laser Wavelength | 532 | nm | Green laser for spin initialization and readout |
| Laser Excitation Power | 80 | ”W | Used for photoluminescence (PL) excitation |
| PL Rate | 460 | kcps | Photon count rate of the NV center |
| Static Magnetic Field (Bz) | â 480 | Gauss | Applied along the NV axis for ESLAC polarization |
| Prepared State Fidelity (F) | > 0.985 | N/A | Achieved for >97.2% of 1184 prepared states |
| Non-Unitary Evolution Time | â 1.2 | ”s | Time required for state decay to target eigenstate |
| Topological Phases Classified | 3 | N/A | Hopf link, Unknot, Unlink |
Key Methodologies
Section titled âKey MethodologiesâThe experimental simulation and classification relied on precise control over the solid-state spin system and advanced data analysis techniques:
- Material Preparation: A <100>-oriented Type IIa single crystal diamond (natural 13C abundance) was used. A Solid Immersion Lens (SIL) was fabricated on the surface via Focused Ion Beam (FIB) to enhance the photon collection efficiency of the preselected NV center.
- Spin Initialization: The system was initialized via optical pumping using a 532 nm laser, followed by rotations to prepare the initial state |Κ(0)>. Nuclear spins were polarized using Excited-State Level Anticrossing (ESLAC) under a static magnetic field (Bz â 480 Gauss).
- Hamiltonian Implementation: The non-Hermitian twister Hamiltonian H(k) was simulated using the dilation method 98,101, which maps the non-unitary evolution of the target electron spin (He) onto the unitary evolution of the coupled electron-nuclear spin system (He,n).
- Coherent Control: Microwave (MW) and Radio Frequency (RF) pulses, generated by an Arbitrary Waveform Generator (AWG) and IQ-mixer, were used to coherently manipulate the electron and nuclear spins, controlling the Hamiltonian parameters m1,2 and momentum k.
- Data Acquisition: An unlabeled data set of 37 samples was generated by varying the parameter m1 and sweeping the discrete momentum ki across the first Brillouin zone, requiring 3552 non-unitary evolutions.
- Unsupervised Learning: The experimental right eigenstates (|R1> and |R2>) were transformed into unit Hamiltonian vectors. The diffusion map method 94-96 was then applied to cluster these vectors based on connectivity, successfully identifying the three distinct knotted topological phases.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe successful replication and extension of this cutting-edge quantum simulation require diamond materials with exceptional purity, precise isotopic control, and superior surface qualityâall core specialties of 6CCVD.
Applicable Materials for Quantum Simulation
Section titled âApplicable Materials for Quantum SimulationâTo achieve the high coherence times (T2* = 3.0 ”s) and low-noise environment necessary for high-fidelity non-unitary dynamics, 6CCVD recommends the following materials:
| Material Grade | Specification | Application Context |
|---|---|---|
| Optical Grade Single Crystal Diamond (SCD) | Ultra-low Nitrogen Concentration (< 1 ppb) | Essential for maximizing electron spin coherence time (T2) and minimizing decoherence in solid-state quantum simulators. |
| Isotopically Purified SCD | 13C Abundance < 0.1% | Reduces the nuclear spin bath noise, significantly extending T2 and T2* beyond the 3.0 ”s achieved in the paper (natural abundance 1.1% 13C). |
| SCD with Controlled 13C Doping | Custom 13C concentration (e.g., 0.5% to 5%) | Required for studies that specifically rely on coupling to nearby nuclear spins (like the 13C ancilla used here) for multi-qubit simulation. |
| Boron-Doped Diamond (BDD) | Custom doping levels (p-type) | Applicable for extending this research into non-Hermitian topological phases relevant to electrochemistry or superconducting quantum devices. |
Customization Potential
Section titled âCustomization Potentialâ6CCVDâs advanced MPCVD growth and post-processing capabilities directly address the engineering challenges inherent in NV center experiments, such as the need for custom optics and integrated control structures:
- Custom Dimensions and Substrates:
- We provide SCD plates with thicknesses ranging from 0.1 ”m up to 500 ”m, and SCD substrates up to 10 mm thick, allowing for robust mounting and integration into confocal systems.
- We offer custom laser cutting services to produce substrates with unique geometries required for specialized setups (e.g., micro-pillars or cantilever structures).
- Surface Engineering and Polishing:
- The fabrication of the Solid Immersion Lens (SIL) used in the experiment demands an atomically flat surface. 6CCVD guarantees Polishing to Ra < 1 nm for SCD, ensuring minimal optical scattering and high-fidelity optical access necessary for high-NA collection.
- Integrated Metalization:
- For future integrated quantum circuits requiring on-chip control, 6CCVD offers in-house custom metalization stacks, including Au, Pt, Pd, Ti, W, and Cu. This capability is crucial for fabricating high-frequency microwave (MW) coplanar waveguides (CPW) directly on the diamond surface to deliver the control pulses used in the simulation.
Engineering Support
Section titled âEngineering Supportâ6CCVDâs in-house PhD team can assist with material selection and optimization for similar Solid-State Quantum Simulation projects. We provide consultation on:
- Optimizing diamond growth recipes to achieve specific NV center densities and charge states.
- Selecting the appropriate isotopic purity to meet target coherence times (T2) for complex quantum dynamics.
- Designing custom metalization layouts for integrated quantum control systems.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Abstract Non-Hermiticity has widespread applications in quantum physics. It brings about distinct topological phases without Hermitian counterparts, and gives rise to the fundamental challenge of phase classification. Here, we report an experimental demonstration of unsupervised learning of non-Hermitian topological phases with the nitrogen-vacancy center platform. In particular, we implement the non-Hermitian twister model, which hosts peculiar knotted topological phases, with a solid-state quantum simulator consisting of an electron spin and a nearby 13 C nuclear spin in a nitrogen-vacancy center in diamond. By tuning the microwave pulses, we efficiently generate a set of experimental data without phase labels. Furthermore, based on the diffusion map method, we cluster this set of experimental raw data into three different knotted phases in an unsupervised fashion without a priori knowledge of the system, which is in sharp contrast to the previously implemented supervised learning phases of matter. Our results showcase the intriguing potential for autonomous classification of exotic unknown topological phases with experimental raw data.