Quantum Random Features Achieve 89.3% Accuracy on Fashion-Mnist with Scalable Qubits

Researchers are tackling a significant hurdle in quantum machine learning: the need for complex and resource-intensive circuits to process data. Akitada Sakurai, Aoi Hayashi, and William John Munro, from the Okinawa Institute of Science and Technology Graduate University, alongside Kae Nemoto, present a novel approach using Quantum Random Features and Dynamical Random Features. These lightweight models, inspired by classical techniques, generate high-dimensional representations without the need for extensive optimisation, offering a pathway towards scalable quantum algorithms. Their work demonstrates that these features reproduce classical random Fourier feature behaviour and, crucially, achieve up to 89.3% accuracy on the Fashion-MNIST dataset, matching or exceeding classical performance with reduced qubit demands, thereby bridging the gap between theoretical potential and practical implementation?

By measuring in the computational basis, the research establishes a probability distribution with 2N components forming the quantum feature map, effectively leveraging the potential of an N-qubit system. The team adopted a modified version of random Fourier features, interpreting it as a two-layer neural network with fixed, randomly initialised weights, creating a clear connection between classical kernel methods and quantum circuit architectures. The team engineered a layered quantum data-encoding circuit designed to reproduce the spectral characteristics of RFF without constructing a full 2N weight matrix. Each layer incorporates Z-rotation encoding, embedding data via single-qubit Rz(θ) gates, where angles θ are computed from a random matrix W ∈R(NL)×d with entries drawn from N(0, σ2/NL) alongside a bias vector b sampled uniformly from [0, β). Spectral scrambling is then realised through either a fixed random permutation matrix Pπ for QRF or Hamiltonian evolution under an Ising-type model for QDRF, enriching the accessible frequency spectrum.

Measuring in the computational basis yields a probability distribution forming the quantum feature map, with β = π p 3/NL set to prevent probability condensation and maintain correspondence with the RFF formulation. Experiments employed a random frequency representation, Θ = BW ·x, mirroring WRFF in the RFF model, where B is constructed from diagonal elements of Pauli operators σz combined with the permutation operator Pπ. The team demonstrated that as the number of layers, L, increases, the composite transformation BW asymptotically approaches the statistical properties of WRFF, finding that L ≈20 provides a close approximation. This design achieves a substantial reduction in preprocessing cost, scaling as O(NLd), as L is typically much smaller than 2N for large qubit counts.

To further enhance experimental feasibility, the study replaced Pπ in QRF with naturally realisable unitary evolutions generated by a long-range transverse-field Ising model, defined by H = X i>j J |i −j|α σi zσj z + g X i σi x, with parameters α = 1.5, g/J = 1.0, and Jt = 3.5. Numerical simulations benchmarked RFF, QRF, and QDRF using the Fashion-MNIST dataset, comprising 60,000 training and 10,000 testing grayscale images normalised to the range [0, 1]. Results showed that QRF attains up to 89. This performance was achieved using a layered quantum data-encoding circuit that reproduces the spectral characteristics of RFF without constructing a full 2N weight matrix. The team measured the performance of QRF and QDRF across varying numbers of layers (L) and qubits (N). Results demonstrate that QRF achieves 86% testing accuracy with N=11 qubits and L=20 layers, while QDRF reaches 89% under the same conditions. Specifically, the models exhibited a testing accuracy of approximately 0.82 for N=9, increasing to 0.90 for N=15, indicating a positive correlation between qubit count and performance. Measurements confirm that the overall preprocessing cost of the QRF model scales as O(NLd), a substantial reduction compared to the classical RFF formulation, particularly when L is significantly smaller than 2N. The authors acknowledge that achieving high performance may necessitate careful alignment of the models. Furthermore, the output dimensions of QERC are constrained by the number of qubits, requiring dimensionality reduction techniques that can be fundamentally limited, particularly for high-resolution data. Future research will focus on task-specific spectral engineering and a more formal characterisation of expressivity, sample complexity, and generalisation performance. These advancements aim to deepen understanding of how spectral structure governs quantum feature mappings and will potentially broaden applications to areas such as time-series forecasting, generative modelling, and reinforcement learning.