Related papers: A vacuum-adapted approach to quantum Feynman-Kac f…
The outcome statistics of an informationally complete quantum measurement for a system in a given state can be used to evaluate the ensemble expectation of any linear operator in the same state, by averaging a function of the outcomes that…
In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures of the QS…
The fluctuations of dynamical functionals such as the empirical density and current as well as heat, work and generalized currents in stochastic thermodynamics are usually studied within the Feynman-Kac tilting formalism, which in the…
The measurement process for hidden-configuration formulations of quantum mechanics is analysed. It is shown how a satisfactory description of quantum measurement can be given in this framework. The unified treatment of hidden-configuration…
Quantum optimization, a key application of quantum computing, has traditionally been stymied by the linearly increasing complexity of gradient calculations with an increasing number of parameters. This work bridges the gap between Koopman…
We prove the existence of classical solutions to parabolic linear stochastic integro-differential equations with adapted coefficients using Feynman-Kac transformations, conditioning, and the interlacing of space-inverses of stochastic flows…
A stochastic theory for a branching process in a neutron population with two energy levels is used to assess the applicability of the differential self-interrogation Feynman-alpha method by numerically estimated reaction intensities from…
Quantum computers have attracted much attention in recent years. This is because the development of the actual quantum machine is accelerating. Research on how to use quantum computers is active in the fields such as quantum chemistry and…
In this paper, we present a novel Feynman-Kac formula and investigate learning-based methods for approximating general nonlinear time-dependent Schr\"odinger equations which may be high-dimensional. Our formulation integrates both the…
Although quantum computing holds promise to accelerate a wide range of computational tasks, the quantum simulation of quantum dynamics as originally envisaged by Feynman remains the most promising candidate for achieving quantum advantage.…
Feedback-based quantum algorithms have recently emerged as potential methods for approximating the ground states of Hamiltonians. One such algorithm, the feedback-based algorithm for quantum optimization (FALQON), is specifically designed…
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…
A stochastic filter uses a series of measurements over time to produce estimates of unknown variables based on a dynamic model. For a quantum system, such an algorithm is provided by a quantum filter, which is also known as a stochastic…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
We present a stochastic theory for the nonequilibrium dynamics of charges moving in a quantum scalar field based on the worldline influence functional and the close-time-path (CTP or in-in) coarse-grained effective action method. We…
Understanding turbulence is the key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multi-scale nature, describing the coupling between different-sized eddies in…
Gaussian wavepackets are a popular tool for semiclassical analyses of classically chaotic systems. We demonstrate that they are extremely powerful in the semiquantal analysis of such systems, too, where their dynamics can be recast in an…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…