Photonic Quantum-Accelerated Machine Learning

TL;DR

A quantum accelerator for classical machine learning is presented, using boson sampling to provide a high-dimensional quantum fingerprint for reservoir computing and demonstrates the acceleration and scalability of the scheme on a photonic quantum processing unit, providing the first experimental validation that boson-sampling-enhanced learning delivers real performance gains on actual quantum hardware.

Abstract

Machine learning is widely applied in modern society, but has yet to capitalise on the unique benefits offered by quantum resources. Boson sampling -- a quantum-interference based sampling protocol -- is a resource that is classically hard to simulate and can be implemented on current quantum hardware. Here, we present a quantum accelerator for classical machine learning, using boson sampling to provide a high-dimensional quantum fingerprint for reservoir computing. We show robust performance improvements under various conditions: imperfect photon sources down to complete distinguishability; scenarios with severe class imbalances, classifying both handwritten digits and biomedical images; and sparse data, maintaining model accuracy with twenty times less training data. Crucially, we demonstrate the acceleration and scalability of our scheme on a photonic quantum processing unit, providing the first experimental validation that boson-sampling-enhanced learning delivers real performance gains on actual quantum hardware.

Figures (7)

• Figure 1: Quantum Optical Reservoir Computing scheme. An input image (top left) from a set of potential datasets is initially processed: 1) principal component analysis (PCA, right arrow), and 2) optional linearisation from 2D to 1D (left arrow). The first $M$ components---matching the number of utilised modes---are forwarded to the boson sampling setup (thin arrow). The setup consists of photons entering a pre-circuit (top right), then a layer where the PCA phases are encoded (centre), and finally the reservoir (bottom right). The processed data is the input to the linear classifier (bottom), which finally finds the predicted classification label.
• Figure 2: MNIST classification accuracy as a function of training epochs. QORC in orange, L-SVC in blue. Training (circles, solid lines) on 60000 images, testing (squares, dashed lines) on 10000 images. For each image, the reservoir is 30000 samples. QORC outperforms the best value of L-SVC from the very first training epoch. Data points are connected for better visibility. Best performance on both models is between 50-100 epochs.
• Figure 3: MNIST classification accuracy as a function of single photon indistinguishability. QORC with $N{=}3, M{=}12$ in brown, $N{=}3, M{=}20$ in orange, and L-SVC included in black as reference. Training (circles, solid lines) on 60000 images for 100 epochs, testing (squares, dashed lines) on 10000 images. For each image, the reservoir is 30000 samples. Coloured fitted lines to guide the eye only. All accuracies for all indistinguishabilities of either reservoir size here surpass the maximal achievable training accuracy of L-SVC.
• Figure 4: QORC classification F1 score improvements on different datasets in MedMNISTv2 for 200 training epochs. Quantum reservoir: $N{=}3, M{=}20$. For each image, the reservoir is 30000 samples. OCT, OrganS, and OrganA are all greyscale images, Derma is in colour. See Supplemental Material Sec. [S5] for more details on the datasets.
• Figure 5: MNIST classification accuracy dependent on (balanced) training dataset size $n_{tr}$. L-SVC in blue squares, QORC with $N{=}3, M{=}12$ in teal triangles (ideal, no noise), purple inverted triangles (noisy, $g^{(2)}{=}1.95\%$, $\mathcal{I}{=}0$), and orange circles (QPU, $g^{(2)}{=}1.95\%$, $\mathcal{I}{=}86.36\%$). Error bars are the standard deviation on 50 subsets of training data: too small to see for large numbers of training images, but significant for smaller $n_{tr}$ and the QPU data. Grey lines show the best possible performances for train (solid) and test (dashed) accuracies with L-SVC. Training for 100 epochs, testing (dashed lines) on $n_{te}{=}10000$ images apart from QPU data, where $n_{te}=4669{-}n_{tr}$. Main: Dashed coloured lines to guide the eye only, Hill function fit: $L / (1 + (x_{50} / x)^k)$ with $(L, k, x_{50}) = (0.929, 0.61, 8.6), (0.959, 0.64, 13.3), (0.950, 0.61, 13.2), (0.964, 0.62, 13.1)$ for L-SVC and QORC (ideal, noisy, QPU), respectively. Inset: Shaded regions indicate $1\sigma$ band. No QPU data available beyond $n_{tr}=3900$.