Validating Large-Scale Quantum Machine Learning: Efficient Simulation of Quantum Support Vector Machines Using Tensor Networks

TL;DR

This work tackles the exponential barriers of simulating large-scale QSVMs on classical hardware by leveraging tensor-network representations via the cuQuantum SDK and cuTensorNet. It demonstrates near-quadratic scaling in practice, enabling simulations up to 784 qubits with seconds-scale runtime on a single GPU and linear MPI scalability across multiple GPUs. The authors validate the framework on MNIST and Fashion-MNIST, showing competitive binary and multiclass classifications and highlighting the practical impact of quantum-kernel methods for high-dimensional data. The results provide a robust validation tool for quantum-HPC research and establish a scalable pathway toward combining quantum algorithms with high-performance computing resources.

Abstract

We present an efficient tensor-network-based approach for simulating large-scale quantum circuits, demonstrated using Quantum Support Vector Machines (QSVMs). Our method effectively reduces exponential runtime growth to near-quadratic scaling with respect to the number of qubits in practical scenarios. Traditional state-vector simulations become computationally infeasible beyond approximately 50 qubits; in contrast, our simulator successfully handles QSVMs with up to 784 qubits, completing simulations within seconds on a single high-performance GPU. Furthermore, by employing the Message Passing Interface (MPI) in multi-GPU environments, the approach shows strong linear scalability, reducing computation time as dataset size increases. We validate the framework on the MNIST and Fashion MNIST datasets, achieving successful multiclass classification and emphasizing the potential of QSVMs for high-dimensional data analysis. By integrating tensor-network techniques with high-performance computing resources, this work demonstrates both the feasibility and scalability of large-qubit quantum machine learning models, providing a valuable validation tool in the emerging Quantum-HPC ecosystem.

Figures (14)

• Figure 1: QSVM Simulator: Optimizes quantum kernel estimation and learning, enhancing phase operation and objective evaluation, leading to swift and precise classification outcomes.
• Figure 2: (a) Tensor network formulation of a quantum circuit. (b) Contraction paths determine the computational and memory costs of tensor network simulations: The upper path results in higher costs.
• Figure 3: Building blocks of the cuTensorNet library.
• Figure 4: (a) The QSVM pipeline showcases the quantum circuit transformation of input data into feature space quantum states. (b) A schematic of the QSVM circuit.
• Figure 5: Computational complexity of QSVM simulation. The left graph demonstrates that simulation time scales exponentially with the number of qubits, as $O(2^n)$, while the right graph shows that the number of quantum circuits required scales quadratically with data size, as $O(n^2)$.