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Affine variables, which have the virtue of preserving the positive-definite character of matrix-like objects, have been suggested as replacements for the canonical variables of standard quantization schemes, especially in the context of…
A study of the artificial neural network representation of quantum many-body states is presented. The locality and entanglement properties of states for shallow and deep quantum neural networks are investigated in detail. By introducing the…
Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last…
Neural networks have been proposed as efficient numerical wavefunction ansatze which can be used to variationally search a wide range of functional forms for ground state solutions. These neural network methods are also advantageous in that…
The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less…
Neural quantum states (NQS) provide a flexible and highly expressive parameterization of wave functions for strongly correlated problems in quantum chemistry. Despite rapid advances in network architectures, the evaluation of electronic…
The neural mechanisms supporting flexible relational inferences, especially in novel situations, are a major focus of current research. In the complementary learning systems framework, pattern separation in the hippocampus allows rapid…
A fundamental problem in quantum many-body physics is that of finding ground states of local Hamiltonians. A number of recent works gave provably efficient machine learning (ML) algorithms for learning ground states. Specifically, [Huang et…
Based on the {\it nonlinear coherent states} method, a general and simple algebraic formalism for the construction of \textit{`$f$-deformed intelligent states'} has been introduced. The structure has the potentiality to apply to systems…
We initiate the study of neural-network quantum state algorithms for analyzing continuous-variable lattice quantum systems in first quantization. A simple family of continuous-variable trial wavefunctons is introduced which naturally…
A classification of multipartite entanglement in qubit systems is introduced for pure and mixed states. The classification is based on the robustness of the said entanglement against partial trace operation. Then we use current machine…
Non-classical correlations can be regarded as resources for quantum information processing. However, the classification problem of non-classical correlations for quantum states remains a challenge, even for finite-size systems. Although…
The brain must robustly store a large number of memories, corresponding to the many events encountered over a lifetime. However, the number of memory states in existing neural network models either grows weakly with network size or recall…
A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to…
Due to the exponential growth of the Hilbert space dimension with system size, the simulation of quantum many-body systems has remained a persistent challenge until today. Here, we review a relatively new class of variational states for the…
We consider the problem of designing a machine learning-based model of an unknown dynamical system from a finite number of (state-input)-successor state data points, such that the model obtained is also suitable for optimal control design.…
In this paper we present a hybrid neural network augmented physics-based modeling (APBM) framework for Bayesian nonlinear latent space estimation. The proposed APBM strategy allows for model adaptation when new operation conditions come…
Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial…
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…
Finding the precise location of quantum critical points is of particular importance to characterise quantum many-body systems at zero temperature. However, quantum many-body systems are notoriously hard to study because the dimension of…