Related papers: Neural Controlled Differential Equations with Quan…
The Schrodinger equation describes how quantum states evolve according to the Hamiltonian of the system. For physical systems, we have it that the Hamiltonian must be a Hermitian operator to ensure unitary dynamics. For anti-Hermitian…
We construct, for any finite dimension $n$, a new hidden measurement model for quantum mechanics based on representing quantum transition probabilities by the volume of regions in projective Hilbert space. For $n=2$ our model is equivalent…
Numerous lines of experimental, numerical and analytical evidence indicate that it is surprisingly easy to locate optimal controls steering quantum dynamical systems to desired objectives. This has enabled the control of complex quantum…
A nano-rod under compression, which is capacitively coupled to a Cooper-pair box, can be modeled in terms of a quartic oscillator linearly interacting with a tunnelling pseudo-spin. We have integrated numerically the quantum dynamics of…
The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than…
We study and compare the time evolutions of concurrence and quantum discord in a driven system of two interacting qubits prepared in a generic Werner state. The~corresponding quantum dynamics is exactly treated and manifests the appearance…
Quantum Physics-Informed Neural Networks (QPINNs) integrate quantum computing and machine learning to impose physical biases on the output of a quantum neural network, aiming to either solve or discover differential equations. The approach…
The neural Ordinary Differential Equation (ODE) model has shown success in learning complex continuous-time processes from observations on discrete time stamps. In this work, we consider the modeling and forecasting of time series data that…
The concept of dynamical hidden symmetries in the physics of electron tunneling through composite quantum dots (CQD) and quantum ladders (QL) is developed and elucidated. Quite generally, dynamical symmetries are realizable in the space of…
The control of flying quantum bits (qubits) carried by traveling quantum fields is crucial for coherent information transmission in quantum networks. In this paper, we develop a general framework for modeling the generation, catching and…
Modeling continuous dynamical systems from discretely sampled observations is a fundamental problem in data science. Often, such dynamics are the result of non-local processes that present an integral over time. As such, these systems are…
This paper explores a simple question: can we model the internal transformations of a neural network using dynamical systems theory? We introduce Koopman autoencoders to capture how neural representations evolve through network layers,…
A quantum computer is proposed in which information is stored in the two lowest electronic states of doped quantum dots (QDs). Many QDs are located in a microcavity. A pair of gates controls the energy levels in each QD. A Controlled Not…
The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests…
The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the non-trivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that…
The double slits experiment is a basic phenomenon, which allows to explain principal behaviour of quantum systems. However, textbooks present static pictures of corresponding interference patterns. At the same time, modern computer software…
We propose in this paper a gradient-type dynamical system to solve the problem of maximizing quantum observables for finite dimensional closed quantum ensembles governed by the controlled Liouville-von Neumann equation. The asymptotic…
We propose a new numerical scheme of evolution for the Einstein equations using the discrete variational derivative method (DVDM). We derive the discrete evolution equation of the constraint using this scheme and show the constraint…
Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the…
A classical computer simulating Schrodinger dynamics of a quantum system requires resources which scale exponentially with the size of the system, and is regarded as inefficient for such purposes. However, a quantum computer made up of a…