Related papers: Expressibility of neural quantum states: a Walsh-c…
We establish a direct connection between general tensor networks and deep feed-forward artificial neural networks. The core of our results is the construction of neural-network layers that efficiently perform tensor contractions, and that…
Simulating quantum many-body dynamics on classical computers is a challenging problem due to the exponential growth of the Hilbert space. Artificial neural networks have recently been introduced as a new tool to approximate quantum-many…
The challenge of quantum many-body problems comes from the difficulty to represent large-scale quantum states, which in general requires an exponentially large number of parameters. Recently, a connection has been made between quantum…
A naive classical representation of an n-qubit state requires specifying exponentially many amplitudes in the computational basis. Past works have demonstrated that classical neural networks can succinctly express these amplitudes for many…
Neural Network Quantum States (NQS) represent quantum wavefunctions by artificial neural networks. Here we study the wavefunction access provided by NQS defined in [Science, \textbf{355}, 6325, pp. 602-606 (2017)] and relate it to results…
Adaptive quantum circuits, leveraging measurements and classical feedback, significantly expand the landscape of realizable quantum states compared to their non-adaptive counterparts, enabling the preparation of long-range entangled states…
The classical approach to measure the expressive power of deep neural networks with piecewise linear activations is based on counting their maximum number of linear regions. This complexity measure is quite relevant to understand general…
We study deep neural networks with polynomial activations, particularly their expressive power. For a fixed architecture and activation degree, a polynomial neural network defines an algebraic map from weights to polynomials. The image of…
Neural quantum states are a promising framework for simulating many-body quantum dynamics, as they can represent states with volume-law entanglement. As time evolves, the neural network parameters are typically optimized at discrete time…
Neural-network quantum states (NQS) have become a powerful tool in many-body physics. Of the numerous possible architectures in which neural-networks can encode amplitudes of quantum states the simplicity of the Restricted Boltzmann Machine…
Entanglement depth quantifies how many qubits share genuine multipartite entanglement, but certification typically relies on tailored witnesses or full tomography, both of which scale poorly with system size. We recast entanglement-depth…
In this work, we address the question whether a sufficiently deep quantum neural network can approximate a target function as accurate as possible. We start with simple but typical physical situations that the target functions are physical…
Artificial neural networks have been recently introduced as a general ansatz to compactly represent many- body wave functions. In conjunction with Variational Monte Carlo, this ansatz has been applied to find Hamil- tonian ground states and…
Variational wavefunctions offer a practical route around the exponential complexity of many-body Hilbert spaces, but their expressive power is often sharply constrained. Matrix product states, for instance, are efficient but limited to area…
The hybrid quantum-classical algorithm is actively examined as a technique applicable even to intermediate-scale quantum computers. To execute this algorithm, the hardware efficient ansatz is often used, thanks to its implementability and…
The benefits of depth in feedforward neural networks are well known: composing multiple layers of linear transformations with nonlinear activations enables complex computations. While similar effects are expected in recurrent neural…
In recent years, neural network quantum states (NNQS) have emerged as powerful tools for the study of quantum many-body systems. Electronic structure calculations are one such canonical many-body problem that have attracted significant…
We study the expressivity of sparse maxout networks, where each neuron takes a fixed number of inputs from the previous layer and employs a, possibly multi-argument, maxout activation. This setting captures key characteristics of…
Deep neural networks (DNNs) have emerged as a popular mathematical tool for function approximation due to their capability of modelling highly nonlinear functions. Their applications range from image classification and natural language…
Neural quantum states (NQS) provide flexible and compact wavefunction parameterizations for numerical studies of quantum many-body physics. In particular, NQS aim to circumvent the exponential scaling of the Hilbert space by compressing…