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6CCVD Research

Experimental realization of a quantum image classifier via tensor-network-based machine learning

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2021-09-29
JournalPhotonics Research
AuthorsKunkun Wang, Lei Xiao, Wei Yi, Shi-Ju Ran, Peng Xue
InstitutionsBeijing Computational Science Research Center, Beijing Academy of Quantum Information Sciences
Citations19
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”

This research presents the first experimental demonstration of a Tensor-Network-Based Machine Learning (TN-ML) scheme using single photons for real-life image classification, addressing the critical challenge of high Hilbert-space dimensionality in quantum computing.

  • Core Achievement: Successful binary classification of hand-written digits (“0” and “1”) from the MNIST dataset, achieving an experimental success rate exceeding 98%.
  • Efficiency Breakthrough: The scheme utilizes entanglement-based optimization to dramatically reduce the required feature space from 784 pixels to only 3 or 5 feature qubits, making implementation feasible on current quantum hardware.
  • Qubit Minimization: A qubit-efficient quantum circuit design allows the classifier to operate using only two physical qubits (operational and classifier qubits) via single-photon interferometry.
  • Hybrid Approach: The classifier is trained and optimized classically using Matrix Product States (MPS), and the resulting unitary gates are then implemented experimentally using photonic qubits.
  • Robustness Confirmed: The trained classifier successfully recognized poorly written digits that were not included in the original MNIST dataset, demonstrating high confidence and accuracy.
  • Platform Versatility: Although demonstrated with photons, the TN-ML approach is general and scalable to other platforms, including nitrogen-vacancy (NV) centers, nuclear spins, and trapped ions, paving the way for quantum-enhanced multi-class classification.

Technical Specifications

Section titled “Technical Specifications”
ParameterValueUnitContext
Original Feature Space (N)784PixelsInput dimension for MNIST images.
Retained Feature Qubits (N)3 or 5QubitsReduced dimension after entanglement-based optimization (3-layer or 5-layer construction).
Operational Qubits (N’)2QubitsPhysical qubits used in the final quantum circuit (classifier and operational).
Experimental Success Rate>98%Achieved for classifying all testing images of “0” and “1”.
Highest Theoretical Accuracy0.9910N/AAchieved using the 5-layer construction.
Estimated Success Rate (Lowest)0.9820N/AScheme B, 3-layer construction, accounting for experimental imperfections.
Total Photon Count>104PhotonsMinimum count required for reliable classification per image.
Single-Photon Generation Rate~2 x 104Photons/sRate used during the experiment.
Measurement Time3sFixed measurement time per image classification.
Estimated Dephasing Rate (Ρ)0.9977N/AFor 3-layer construction, characterizing noise due to Beam Displacer misalignment.
Feature EncodingPolarization/Spatial ModesN/AClassifier qubit encoded in polarization (H/V); Operational qubit encoded in spatial modes (upper/lower).

Key Methodologies

Section titled “Key Methodologies”

The experimental realization follows a hybrid classical-quantum approach, leveraging Tensor Network (TN) optimization to minimize the required quantum resources.

  1. Classical Data Preprocessing:

    • Classical gray-scale images (N=784 pixels) are transformed into a data-sparse frequency space using Discrete-Cosine Transformation (DCT).
    • The resulting frequency components are mapped to quantum feature states (product states of N qubits).

  2. Tensor Network Training and Optimization:

    • A Matrix Product State (MPS) classifier is trained classically using supervised learning on the MNIST training set, optimizing the tensors to minimize the loss function.
    • Feature Extraction: Entanglement entropy is calculated for all feature qubits in the MPS. Only the 3 or 5 features exhibiting the largest entanglement entropy are retained, drastically reducing the feature space dimension (N=784 to N=3 or 5).

  3. Quantum Circuit Translation:

    • The optimized, reduced MPS tensors are translated into a sequence of unitary gates (Ui) acting on the retained feature qubits.
    • The tensors are constrained to satisfy right-to-left orthogonal conditions, ensuring the gates are isometries.

  4. Qubit-Efficient Implementation (Single-Photon Interferometry):

    • The circuit is implemented using a qubit-efficient scheme, requiring only two physical qubits: a classifier qubit (encoded in photon polarization) and an operational qubit (encoded in spatial modes).
    • Gate Realization: Single-qubit gates (U1) are realized via Half-Wave Plates (HWPs). Two-qubit gates (Ui) are realized using cascaded interferometers composed of HWPs and Beam Displacers (BDs).
    • Feature Input: The extracted features of an image are input sequentially by measuring the operational qubit at different times.

  5. Classification Readout:

    • The final classification result is obtained through projective measurements (σz) on the output classifier qubit, yielding probabilities P0 and P1 corresponding to the “0” and “1” categories.

Commercial Applications

Section titled “Commercial Applications”

The demonstrated TN-ML scheme offers a path toward practical quantum machine learning applications, particularly where data complexity exceeds the capacity of current noisy, intermediate-scale quantum (NISQ) devices.

  • Quantum Computing Hardware Development:

    • Provides a benchmark and validation scheme for qubit-efficient circuit design and implementation on various platforms (photonic circuits, superconducting circuits, trapped ions, NV centers).
    • Accelerates the development of quantum algorithms that efficiently handle large classical datasets by minimizing required qubit count.

  • Advanced Pattern Recognition and AI:

    • Optical Character Recognition (OCR): Direct application for robust, high-accuracy classification of hand-drawn or noisy images.
    • Multi-Class Classification: The scheme is readily extendable to multi-category problems by utilizing multiple degrees of freedom in photons (e.g., orbital angular momentum, time-bin) or higher-level qudits.

  • Quantum Sensing and Metrology:

    • The TN framework, known for its interpretability and ability to model entanglement, can be applied to optimize quantum sensors and measurements in noisy environments.

  • Data Compression and Feature Engineering:

    • The entanglement-based feature extraction methodology provides a powerful tool for identifying the most relevant features in high-dimensional classical data, useful across classical and quantum ML pipelines.
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 “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2020 - Tensor Network Contractions [Crossref]

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