| Metadata | Details |
|---|
| Publication Date | 2022-09-24 |
| Journal | npj Quantum Information |
| Authors | Yefei Yu, Li-Wei Yu, Wengang Zhang, Huili Zhang, Xiaolong Ouyang |
| Institutions | Tsinghua University, ShangHai JiAi Genetics & IVF Institute |
| Citations | 47 |
| Analysis | Full AI Review Included |
- Core Achievement: Successful experimental demonstration of unsupervised machine learning (UML) for classifying exotic non-Hermitian (NH) topological phases using raw, unlabeled data.
- Platform: A solid-state quantum simulator based on a Nitrogen-Vacancy (NV) center in diamond, utilizing the electron spin (target) and a nearby 13C nuclear spin (ancilla).
- Model Simulated: The NH twister Hamiltonian, which hosts distinct topological phases indexed by knot structures (Hopf link, Unknot, Unlink).
- Implementation Method: The dilation method was employed to map the non-unitary NH dynamics onto a larger, unitary Hermitian system, achieving high state preparation fidelity (F > 0.985 for >97% of samples).
- Learning Algorithm: The Diffusion Map method clustered the experimental data samples into three distinct topological categories, matching theoretical predictions precisely.
- Significance: This work validates UML as a robust, autonomous tool for identifying unknown topological phases in complex quantum systems, even in the presence of experimental noise and imperfections.
| Parameter | Value | Unit | Context |
|---|
| Diamond Substrate Type | Type IIa, <100>-oriented | N/A | Single crystal diamond used for NV center platform. |
| 13C Natural Abundance | 1.1 | % | Isotope abundance in the diamond sample. |
| Laser Wavelength (Excitation) | 532 | nm | Green laser used for spin state initialization and readout. |
| Laser Power (Excitation) | 80 | ”W | Power used for photoluminescence (PL) excitation. |
| PL Collection Rate | 460 | kcps | Photoluminescence rate of the NV center. |
| Static Magnetic Field (Bz) | ~480 | Gauss | Applied along the NV axis for nuclear spin polarization (ESLAC). |
| 13C Hyperfine Strength | 13.7 | MHz | Coupling strength between electron and nuclear spin. |
| Electron Spin Coherence Time (T2) | 3.0 | ”s | Measured via standard Ramsey interferometry. |
| Non-unitary Evolution Time | ~1.2 | ”s | Time required for the electron spin state to decay to the target eigenstate. |
| State Preparation Fidelity (F) | >0.985 | N/A | Achieved for >97.2% of the 1184 prepared eigenstates. |
| AOM On/Off Ratio | 105:1 | N/A | Enhanced ratio for green laser pulse modulation. |
| Diffusion Map Variance (Δ) | 0.08 | N/A | Parameter used in the Gaussian kernel function for clustering. |
- System Initialization: The NV center electron spin (target) and the neighboring 13C nuclear spin (ancilla) were polarized to the state |0e>|â>n using optical pumping and the Excited-State Level Anti-Crossing (ESLAC) technique under a ~480 Gauss magnetic field.
- Hamiltonian Implementation (Dilation): The non-Hermitian twister Hamiltonian H(k) was simulated by mapping its non-unitary dynamics to a larger, unitary Hermitian Hamiltonian He,n governing the coupled electron-nuclear system. This mapping was realized using precisely controlled microwave (MW) pulses (MW1,2).
- Data Generation: An unlabeled data set of 37 samples was generated by systematically varying the parameter m1 of the twister Hamiltonian (while fixing m2 = 0.6). The momentum k was varied discretely across the first Brillouin zone.
- Eigenstate Preparation: The right eigenstates (|R1> and |R2>) corresponding to the NH phases were prepared by exploiting the non-unitary time evolution. The system naturally decays to the eigenstate with the largest imaginary part of the eigenvalue in the long-time limit (~1.2 ”s).
- Input Vector Transformation: The measured eigenstates were transformed into unit Hamiltonian vectors (x) using the biorthogonal relation and anti-commutator trace operation (Equation 2).
- Unsupervised Clustering: The Diffusion Map method was applied to the unlabeled input vectors (x). This method calculates the Gaussian kernel value distribution (K) to measure local similarity and constructs a diffusion matrix (P).
- Dimension Reduction and Classification: The eigenvectors corresponding to the largest eigenvalues of the diffusion matrix were used to project the data into a low-dimensional space, successfully clustering the samples into three distinct topological phases (Hopf link, Unknot, Unlink).
- Quantum Simulation and Materials Discovery: Provides a validated, robust methodology for autonomously classifying complex topological phases (NH or Hermitian) in quantum materials, accelerating the discovery of new phases without reliance on prior theoretical models.
- Solid-State Quantum Computing: Utilizes the NV center platform, a leading candidate for solid-state qubits. The precise MW/RF control and high-fidelity state preparation techniques developed are essential for building scalable quantum processors.
- Quantum Sensing and Metrology: The NV centerâs long coherence time (T2 = 3.0 ”s) and high-fidelity control make it ideal for high-sensitivity magnetometry, thermometry, and electric field sensing.
- Advanced Diamond Substrates (Relevant to 6ccvd.com): Requires high-quality, low-defect single crystal diamond (Type IIa) for optimal NV center performance and long coherence times. The fabrication of Solid Immersion Lenses (SILs) via Focused Ion Beam (FIB) is a critical step in enhancing photon collection efficiency for commercial quantum devices.
- Machine Learning Hardware Acceleration: Demonstrates the practical application of unsupervised learning algorithms (Diffusion Map) in experimental physics, paving the way for integrated autonomous control and analysis systems in future quantum laboratories.
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.