Related papers: Expressibility of neural quantum states: a Walsh-c…
Neural network quantum states emerge as a promising tool for solving quantum many-body problems. However, its successes and limitations are still not well-understood in particular for Fermions with complex sign structures. Based on our…
By universal formulas we understand parameterized analytic expressions that have a fixed complexity, but nevertheless can approximate any continuous function on a compact set. There exist various examples of such formulas, including some in…
Entanglement of high-dimensional and multipartite quantum systems offer promising perspectives in quantum information processing. However, the characterization and measure of such kind of entanglement is of great challenge. Here we consider…
Neural-network quantum states (NQS) are powerful neural-network ans\"atzes that have emerged as promising tools for studying quantum many-body physics through the lens of the variational principle. These architectures are known to be…
Transformer networks have achieved remarkable empirical success across a wide range of applications, yet their theoretical expressive power remains insufficiently understood. In this paper, we study the expressive capabilities of…
Neural Quantum States (NQS) are powerful tools used to represent complex quantum many-body states in an increasingly wide range of applications. However, despite their popularity, at present only a rudimentary understanding of their…
The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states,…
The dimension of a quantum state is traditionally seen as the number of superposed distinguishable states in a given basis. We propose an absolute, i.e.~basis-independent, notion of dimensionality for ensembles of quantum states. It is…
Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently complex network theory has been applied to quantum systems, where complex…
Quantum neural networks (QNNs) based on parametrized quantum circuits are promising candidates for machine learning applications, yet many architectures lack clear connections to classical models, potentially limiting their ability to…
The success of deep networks has been attributed in part to their expressivity: per parameter, deep networks can approximate a richer class of functions than shallow networks. In ReLU networks, the number of activation patterns is one…
Generalized Additive Models (GAMs) are commonly considered *interpretable* within the ML community, as their structure makes the relationship between inputs and outputs relatively understandable. Therefore, it may seem natural to…
One of the central problems in quantum mechanics is to determine the ground state properties of a system of electrons interacting via the Coulomb potential. Since its introduction by Hohenberg, Kohn, and Sham, Density Functional Theory…
Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…
Most existing expressivity theories for neural networks assume exact real arithmetic, whereas practical neural networks are executed under finite-precision floating-point arithmetic with implementation-dependent execution semantics. Recent…
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…
Variational methods have proven to be excellent tools to approximate ground states of complex many body Hamiltonians. Generic tools like neural networks are extremely powerful, but their parameters are not necessarily physically motivated.…
Learning quantum states from measurement data is a central problem in quantum information and computational complexity. In this work, we study the problem of learning to generate mixed states on a finite-dimensional lattice. Motivated by…
Unitary recurrent neural networks (URNNs) have been proposed as a method to overcome the vanishing and exploding gradient problem in modeling data with long-term dependencies. A basic question is how restrictive is the unitary constraint on…
Complex adaptive learning is intelligent. It is adaptive, learns in feedback loops, and generates hidden patterns as many individuals, elements or particles interact in complex adaptive systems (CAS). CAS highlights adaptation in life and…