Related papers: Discrete Approximation of Quantum Stochastic Model…
We derive the fluctuation theorem for quantum-state statistics that can be obtained when we initially measure the total energy of a quantum system at thermal equilibrium, let the system evolve unitarily, and record the quantum-state data…
The de Finetti representation theorem for continuous variable quantum system is first developed to approximate an N-partite continuous variable quantum state with a convex combination of independent and identical subsystems, which requires…
Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning", to study their stable convergence…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
Path integrals are usually formulated in discrete Euclidean time using the Trotter formula. We propose a new method to study discrete quantum systems, in which we work directly in the Euclidean time continuum. The method is of general…
As a primary contribution, we present a convergence theorem for stochastic iterations, and in particular, Q-learning iterates, under a general, possibly non-Markovian, stochastic environment. Our conditions for convergence involve an…
Applicability of Feynman path integral approach to numerical simulations of quantum dynamics in real time domain is examined. Coherent quantum dynamics is demonstrated with one dimensional test cases (quantum dot models) and performance of…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
We show that a large class of stochastic heat equations can be approximated by systems of interacting stochastic differential equations. As a consequence, we prove various comparison principles extending earlier results. Among other things,…
In this work, we present different representations of Khuri-Treiman equation, the advantage and disadvantage of each representations are discussed. Using a toy model for scattering amplitude, we study the sensitivity of solution of KT…
We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…
We simulate the time evolution of collective neutrino oscillations in two-flavor settings on a quantum computer. We explore the generalization of Trotter-Suzuki approximation to time-dependent Hamiltonian dynamics. The trotterization steps…
One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc, in order to accelerate the process of discovery. It is important to ask: Can this be achieved…
Most of physical experiments are usually described as repeated measurements of some random variables. The experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared…
This paper describes a simple, causally deterministic model of quantum measurement based on an amplitude threshold detection scheme. Surprisingly, it is found to reproduce many phenomena normally thought to be uniquely quantum in nature. To…
We prove pathwise convergence of the layerwise evolution of tokens in a finite-depth, finite-width transformer model with MultiLayer Perceptron (MLP) blocks to a continuous-time stochastic interacting particle system. We also identify the…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
We study a variation of the Trotter-Suzuki decomposition, in which a Hamiltonian exponential is approximated by an ordered product of two-qubit operator exponentials such that the Trotter step size is enhanced for a small number of terms.…