Neural network enhanced hybrid quantum many-body dynamics

Ying Zhen Yang, Huaixin Cao, Zhanjun Zhang

Ruiyang Zhou, Saubhik Sarkar, Sougato Bose +1 more

The integration of quantum computing and machine learning has emerged as a promising frontier in computational science. We present a hybrid protocol which combines classical neural networks with non-equilibrium dynamics of a quantum many-body system for image classification. This architecture leverages classical neural networks to efficiently process high-dimensional data and encode it effectively on a quantum many-body system, overcoming a challenging task towards scaled up quantum computation. The quantum module further capitalizes on the discriminative properties of many-body quantum dynamics to enhance classification accuracy. By mapping images from distinct classes to nearly-orthogonal quantum states, the system maximizes separability in the Hilbert space, enabling robust classification. We evaluate the performance of our model on several benchmark datasets with various number of features and classes. Moreover, we demonstrate the key role of the quantum module in achieving high classification accuracy which cannot be accomplished by the classical neural network alone. This showcases the potential of our hybrid protocol for achieving practical quantum advantage and paves the way for future advancements in quantum-enhanced computational techniques.

Rouven Koch, José Luis Lado

Computing dynamical distributions in quantum many-body systems represents one of the paradigmatic open problems in theoretical condensed matter physics. Despite the existence of different techniques both in real-time and frequency space, computational limitations often dramatically constrain the physical regimes in which quantum many-body dynamics can be efficiently solved. Here we show that the combination of machine-learning methods and complementary many-body tensor network techniques substantially decreases the computational cost of quantum many-body dynamics. We demonstrate that combining kernel polynomial techniques and real-time evolution, together with deep neural networks, allows to compute dynamical quantities faithfully. Focusing on many-body dynamical distributions, we show that this hybrid neural-network many-body algorithm, trained with single-particle data only, can efficiently extrapolate dynamics for many-body systems without prior knowledge. Importantly, this algorithm is shown to be substantially resilient to numerical noise, a feature of major importance when using this algorithm together with noisy many-body methods. Ultimately, our results provide a starting point towards neural-network powered algorithms to support a variety of quantum many-body dynamical methods, that could potentially solve computationally expensive many-body systems in a more efficient manner.

Matija Medvidović, Javier Robledo Moreno

Liam B. Schramm

Ruiyang Zhou, Abolfazl Bayat

In this work, we numerically demonstrate the performance of our recent hybrid classical-quantum algorithm for image classification using four different data sets. This hybrid algorithm combines a classical neural network with nonequilibrium dynamics of a many-body system. The goal is to benefit from the flexibility of neural networks in dealing with large feature sets and leverage the fast non-equilibrium manybody dynamics for discriminating quantum states. The classical neural network performs task-aware dimensionality reduction while its parameters are optimized according to a cost function which is obtained by a quantum module. The large input images are compressed to a very few numbers at the output of the neural network. Those numbers are used as the strength of local magnetic fields in a many-body system whose Hamiltonian is described by an Ising Hamiltonian in the transverse field. Thus, the dynamics of such system encodes every image into a quantum state. The classical neural network is optimized in such a way that the images from the same class are mapped to quantum states which have high fidelity with each other while images from different classes are mapped to orthogonal states. We numerically evaluate the approach on four datasets, including PathMNIST, BloodMNIST, OCTMNIST, and PneumoniaMNIST. For benchmarking, we compare the performance of the protocol against classification accuracy of a pure classical neural network whose complexity is comparable with the classical module in our protocol. Across datasets, the hybrid protocol consistently improves test accuracy, with the magnitude of gains depending on modality and task complexity. Increasing the number of qubits, neural network depth, and training size can enhance the accuracy of the protocol. Together, these results position quantum dynamics as an effective feature engine for computer vision, and outline design guidelines for resource-efficient hybrid protocols.