Related papers: Emergent Quantumness in Neural Networks

Fast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically (ontologically) evolving systems one can still define a conserved quantum energy.…

Robust control design for quantum systems is a challenging and key task for practical technology. In this work, we apply neural networks to learn the control problem for the semiclassical Schr\"odinger equation, where the control variable…

Neural networks have emerged as a promising paradigm for quantum information processing, yet they confront the challenge of generating training datasets with sufficient size and rich diversity, which is particularly acute when dealing with…

In this short paper, we show how a quantum nonlocal effect of far-apart wavepackets in the Schrodinger picture of wavefunctions is replaced by a local instability problem when considering the hydrodynamical formulation of quantum mechanics,…

A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…

Accurate numerical solutions for the Schr\"odinger equation are of utmost importance in quantum chemistry. However, the computational cost of current high-accuracy methods scales poorly with the number of interacting particles. Combining…

The classical limit of quantum mechanics, formally investigated through frameworks like strict deformation quantization, remains a profound area of inquiry in the philosophy of physics. This paper explores a computational approach employing…

A key open question in quantum computation is what advantages quantum neural networks (QNNs) may have over classical neural networks (NNs), and in what situations these advantages may transpire. Here we address this question by studying the…

[New and updated results were published in Nature Chemistry, doi:10.1038/s41557-020-0544-y.] The electronic Schr\"odinger equation describes fundamental properties of molecules and materials, but can only be solved analytically for the…

Solving the Schr\"odinger equation is key to many quantum mechanical properties. However, an analytical solution is only tractable for single-electron systems. Recently, neural networks succeeded at modeling wave functions of many-electron…

We train a generative language model on the randomized local measurement data collected from Schr\"odinger's cat quantum state. We demonstrate that the classical reality emerges in the language model due to the information bottleneck:…

A stochastic Euler equation is proposed, describing the motion of a particle density, forced by the random action of virtual photons in vacuum. After time averaging, the Euler equation is reduced to the Reynolds equation, well studied in…

A nonlinear extension of Schr\"odinger's wave equation is proposed that ensures non-signaling by keeping linear the evolution of \textit{coordinate-diagonal} elements of the density matrix. The equation contains a negative kinetic energy…

We introduce a unified framework -- Quantum Neural Ordinary and Partial Differential Equations (QNODEs and QNPDEs) -- which extends the continuous-time formalism of classical neural ordinary and partial differential equations into quantum…

It is known that the Schroedinger equation may be derived from a hydrodynamic model in which the Lagrangian position coordinates of a continuum of particles represent the quantum state. Using Routh\s method of ignorable coordinates it is…

We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schr\"odinger equation is mapped onto a…

As quantum machine-learning architectures mature, a central challenge is no longer their construction, but identifying the regimes in which they offer practical advantages over classical approaches. In this work, we introduce a framework…

Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but…

We regard the real and imaginary parts of the Schrodinger wave function as canonical conjugate variables.With this pair of conjugate variables and some other 2n pairs, we construct a quadratic Hamiltonian density. We then show that the…

Neural networks are being used to improve the probing of the state spaces of many particle systems as approximations to wavefunctions and in order to avoid the recurring sign problem of quantum monte-carlo. One may ask whether the usual…