Experimental realization of a quantum image classifier via tensor-network-based machine learning
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-09-29 |
| Journal | Photonics Research |
| Authors | Kunkun Wang, Lei Xiao, Wei Yi, Shi-Ju Ran, Peng Xue |
| Institutions | Beijing Academy of Quantum Information Sciences, Capital Normal University |
| Citations | 19 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Quantum Image Classification via Tensor Networks
Section titled âTechnical Documentation & Analysis: Quantum Image Classification via Tensor NetworksâReference Paper: Experimental realization of a quantum image classifier via tensor-network-based machine learning (arXiv:2003.08551v2)
Executive Summary
Section titled âExecutive SummaryâThis research demonstrates a significant step toward practical quantum machine learning (QML) by implementing a tensor-network (TN) based image classifier using single photonic qubits. The findings are highly relevant to the development of solid-state quantum platforms, particularly those utilizing diamond-based systems.
- Core Achievement: First experimental realization of a TN-based Machine Learning (ML) scheme using single photons for real-life image classification (MNIST dataset).
- High Accuracy: Achieved classification success rates exceeding 98% (up to 0.9910) using both three- and five-layer quantum circuit constructions.
- Qubit Efficiency: Utilized entanglement-based optimization to reduce the required Hilbert space dimension, enabling the implementation of complex circuits on only two physical qubits.
- Scalability: The scheme is explicitly designed to be scalable to multi-qubit encodings, setting the stage for multi-class classification.
- Platform Agnostic Potential: The methodology is confirmed to be transferable and highly amenable to solid-state quantum platforms, specifically mentioning Nitrogen-Vacancy (NV) centers in diamond, which requires high-purity Single Crystal Diamond (SCD) materials.
- Methodology: The classifier relies on mapping classical image features to quantum states, training a Matrix Product State (MPS) classifier, and translating the optimized tensors into qubit-efficient quantum circuits implemented via interferometry.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the experimental results and numerical simulations:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Maximum Classification Success Rate | 0.9910 | Dimensionless | Five-layer construction, Testing Set |
| Minimum Classification Success Rate | 0.9820 | Dimensionless | Three-layer construction (Estimated) |
| Total Image Features (N) | 784 | Pixels/Components | MNIST image size |
| Retained Feature Qubits (Nâ) | 3 or 5 | Qubits | After entanglement-based optimization |
| Physical Qubit Count | 2 | Qubits | Operational and Classifier qubits |
| Total Photon Count (per image) | > 104 | Photons | Required for estimation/Poissonian statistics |
| Single-Photon Generation Rate | 2 x 104 | Photons/second | Pump power setting |
| Three-Layer Dephasing Rate (η) | 0.9977 | Dimensionless | Estimated numerical fit |
| Five-Layer Dephasing Rate (η) | 0.9926 | Dimensionless | Estimated numerical fit |
| Wave Plate Setting Angle Uncertainty | ± 1.588° (Max) | Degrees (°) | Three-layer construction |
Key Methodologies
Section titled âKey MethodologiesâThe experimental realization of the TN-based quantum classifier involves a hybrid classical-quantum approach, broken down into the following key steps:
- Classical Data Mapping: Classical gray-scale images (N = 784 pixels) are transformed into frequency components using Discrete Cosine Transformation (DCT), and then mapped to a product state of N qubits in the quantum Hilbert space.
- Matrix Product State (MPS) Training: A supervised TN-based ML algorithm is used to train a Matrix Product State (MPS) classifier on the training set of the MNIST dataset.
- Entanglement-Based Feature Extraction: The entanglement entropy of the MPS is calculated. Only a small number of core feature qubits (Nâ = 3 or 5) exhibiting the largest entanglement entropy are retained, dramatically reducing the required Hilbert space dimension.
- Quantum Circuit Translation: The optimized, reduced MPS tensors are translated into a quantum circuit consisting of unitary gates acting on Nâ qubits.
- Qubit-Efficient Implementation: The circuit is further simplified to act on only two physical qubits (Operational and Classifier qubits) using single-photon interferometry networks.
- Gate Implementation: Single-qubit gates (U1) are realized using Half-Wave Plates (HWPs). Two-qubit gates (Ui, i = 2, 3) are realized through cascaded interferometers consisting of HWPs and Beam Displacers (BDs).
- Classification Readout: The classification result is accessed via projective measurements (Ïz) on the output classifier qubit.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe successful demonstration of this TN-based ML scheme using photons provides a direct blueprint for implementation on solid-state platforms, particularly those leveraging the exceptional coherence properties of Nitrogen-Vacancy (NV) centers in diamond. 6CCVD is uniquely positioned to supply the foundational materials required to transition this research from photonics to robust, scalable solid-state quantum systems.
Applicable Materials for Quantum ML Platforms
Section titled âApplicable Materials for Quantum ML PlatformsâTo replicate or extend this research using solid-state NV centers, engineers require ultra-high purity diamond materials.
| Application Requirement | 6CCVD Material Recommendation | Technical Specification |
|---|---|---|
| Quantum Qubit Host | Optical Grade Single Crystal Diamond (SCD) | Ultra-low nitrogen concentration (Type IIa) and low strain, essential for maximizing NV center coherence time (T2) and fidelity in quantum operations. |
| High-Density Integration | Polycrystalline Diamond (PCD) Substrates | Available up to 125mm diameter, providing large area platforms for scaling up complex quantum circuits and integrated photonics. |
| Shallow NV Creation | SCD Plates (Thin Film) | Thickness control from 0.1”m to 500”m, allowing precise creation of shallow NV centers near the surface for efficient coupling to external fields or nanophotonic structures. |
| Boron Doping | Boron-Doped Diamond (BDD) | Available for electrochemical or sensing applications related to quantum readout or control layers, with thickness control from 0.1”m to 500”m. |
Customization Potential for Advanced Quantum Circuits
Section titled âCustomization Potential for Advanced Quantum CircuitsâThe complexity of the interferometric network (HWPs, BDs, CBSs) suggests that future solid-state implementations will require precise on-chip control structures. 6CCVD offers comprehensive customization capabilities to meet these demands:
- Custom Dimensions and Geometry: We provide MPCVD diamond plates and wafers up to 125mm (PCD) and custom substrates up to 10mm thick. We offer precision laser cutting and shaping services to integrate diamond components into existing experimental setups.
- Ultra-Precision Polishing: Achieving high optical coupling and minimizing scattering losses is critical for NV center readout. Our SCD polishing achieves surface roughness of Ra < 1nm, and inch-size PCD achieves Ra < 5nm.
- Integrated Metalization: Quantum control often requires on-chip microwave and RF structures. 6CCVD offers internal metalization capabilities, including deposition of Au, Pt, Pd, Ti, W, and Cu stacks, enabling the fabrication of high-quality transmission lines directly onto the diamond surface for qubit manipulation.
Engineering Support
Section titled âEngineering Supportâ6CCVDâs in-house PhD team specializes in the material science of MPCVD diamond for quantum applications. We can assist researchers in selecting the optimal diamond specifications (e.g., isotopic purity, controlled doping levels, specific crystallographic orientation) necessary to maximize the coherence time and operational fidelity for similar Tensor Network Machine Learning projects utilizing NV centers.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly. We offer global shipping (DDU default, DDP available) to ensure timely delivery of critical materials worldwide.
View Original Abstract
Quantum machine learning aspires to overcome intractability that currently limits its applicability to practical applications. However, quantum machine learning itself is limited by low effective dimensions achievable in state-of-the-art experiments. Here, we demonstrate highly successful classifications of real-life images using photonic qubits, combining a quantum tensor-network representation of hand-written digits and entanglement-based optimization. Specifically, we focus on binary classification for hand-written zeroes and ones, whose features are cast into the tensor-network representation, further reduced by optimization based on entanglement entropy and encoded into two-qubit photonic states. We then demonstrate image classification with a high success rate exceeding 98%, through successive gate operations and projective measurements. Although we work with photons, our approach is amenable to other physical realizations such as nitrogen-vacancy centers, nuclear spins, and trapped ions, and our scheme can be scaled to efficient multi-qubit encodings of features in the tensor-product representation, thereby setting the stage for quantum-enhanced multi-class classification.
Tech Support
Section titled âTech SupportâOriginal Source
Section titled âOriginal SourceâReferences
Section titled âReferencesâ- 2020 - Tensor Network Contractions [Crossref]