(Spiking) Neural Network Quantum States

Complex quantum many-body systems build the foundation of state of the art quantum computation and quantum simulation devices. Yet, theoretical studies of such systems are limited by the so-called curse of dimensionality: the Hilbert space grows exponentially with the number of qubits involved, making exact solutions computationally prohibitive. To tackle this task, we use artificial neural networks as variational ansätze that are trained to represent wave function amplitudes of quantum systems.

Since the wave function enables the evaluation of any observable, a well-trained neural network representation allows for the computation of ground state energies, magnetizations, or quantum correlations, and thus enables the study of phase diagrams and phase transitions. Additionally, neural network wave function ansätze can be used to explore real-time dynamics. In order to find ground state representations of a given system Hamiltonian, a variational Monte Carlo method can be used to optimize the network parameters such that the energy expectation value is minimized.

While multiple artificial neural network architectures, such as convolutional neural networks, restricted Boltzmann machines, recurrent neural networks, or transformer models, have been proven to be powerful wave function ansätze, we aim to further increase the computational efficiency of neural network quantum state representations by exploring advanced network architectures. This includes the investigation of the MLP-Mixer architecture—a model originally designed for vision tasks—as a highly expressive and scalable network architecture.

Furthermore, we aim to investigate the performance of spiking neural networks for quantum state representation, which allow for implementations on neuromorphic hardware. Such devices, which emulate the behaviour of the human brain, have proven powerful in first proof-of-principle works on representing quantum states on spiking neuromorphic hardware. Based on those initial results, which demonstrated an accelerated sample generation and a significantly reduced energy consumption compared to simulations on conventional computers, we aim to develop optimized quantum state representation ansätze to enable energy-efficient and scalable quantum simulation, particularly for time-dependent processes or deployment on specialized hardware.