Related papers: Neural Controlled Differential Equations with Quan…
Quantum simulation is known to be capable of simulating certain dynamical systems in continuous time -- Schrodinger's equations being the most direct and well-known -- more efficiently than classical simulation. Any linear dynamical system…
We show that the discrete-time evolution of an open quantum system generated by a single quantum channel $T$ can be embedded in the discrete-time evolution of an enlarged closed quantum system, i.e. we construct a unitary dilation of the…
Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…
We present a novel approach (DyNODE) that captures the underlying dynamics of a system by incorporating control in a neural ordinary differential equation framework. We conduct a systematic evaluation and comparison of our method and…
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a…
We propose a neural control method to provide guaranteed stabilization for mechanical systems using a novel negative imaginary neural ordinary differential equation (NINODE) controller. Specifically, we employ neural networks with desired…
We present a simple new way - called Schrodingerisation - to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial…
We investigate optimal control strategies for state to state transitions in a model of a quantum dot molecule containing two active strongly interacting electrons. The Schrodinger equation is solved nonperturbatively in conjunction with…
We consider the problem of an electron tunneling between two coupled quantum dots, a two-state quantum system (qubit), using a low-transparency point contact (PC) or tunnel junction as a detector continually measuring the position of the…
A few modified textbook Rayleigh-Schr\"{o}dinger perturbative representations of bound states are reviewed. They were all inspired by an adaptive re-split of the Hamiltonian, using nonstandard bases and the flexibility of normalization of…
Robust and high-precision quantum control is extremely important but challenging for the functionization of scalable quantum computation. In this paper, we show that this hard problem can be translated to a supervised machine learning task…
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides a new operator-theoretic representation of classical dynamics by combining ergodic theory with quantum…
The linearity of quantum mechanics leads, under the assumption that the wave function offers a complete description of reality, to grotesque situations famously known as Schroedinger's cat. Ways out are either adding elements of reality or…
The combined quantum electron-nuclear dynamics is often associated with the Born-Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent…
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…
This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter…
Quantum emitters coupled to one-dimensional waveguides constitute a paradigmatic quantum-optical platform for exploring collective phenomena in open quantum many-body systems. For appropriately spaced emitters, they realize the Dicke model,…
A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function…
We model the dynamics of a closed quantum system brought out of mechanical equilibrium, undergoing a non-driven, spontaneous, thermodynamic transformation. In particular, we consider a quantum particle in a box with a moving and insulating…
A general framework for analyzing the topology of quantum channels of single-particle systems is developed to find a class of genuinely dynamical topological phases that can be realized by means of discrete quantum feedback control. We…