Related papers: Stochastic wave function approach to generalized m…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
A method is presented for the systematic derivation of a hierarchy of coupled equations for the computation of two-time correlation functions of operators for open many-body quantum systems. We show how these systems of equations can be…
A tilted Liouville-master equation in Hilbert space is presented for Markovian open quantum systems. We demonstrate that it is the unraveling of the tilted quantum master equation. The latter is widely used in the analysis and calculations…
Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the…
The Monte Carlo wave function method or the quantum trajectory/jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to…
We propose an optimized algorithm for the numerical simulation of two-time correlation functions by means of stochastic wave functions. As a first application, we investigate the two-time correlation function of a nonlinear optical…
Stochastic unravelings provide a useful way to represent open quantum system dynamics in terms of pure state realizations, and have been widely studied both from a fundamental and from a computational point of view. They were initially…
Based on a fundamental identity for stochastic hyperbolic-like operators, we derive in this paper a global Carleman estimate (with singular weight function) for stochastic wave equations. This leads to an observability estimate for…
Stochastic quantization is applied to derivation of the equations for the Wilson loops and generating functionals of the Wilson loops in the large-N limit. These equations are treated both in the coordinate and momentum representations. In…
In this paper, we investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. In our prequel paper, we introduced an input model in which Lindblad operators are encoded into pure quantum…
The master equation for a linear open quantum system in a general environment is derived using a stochastic approach. This is an alternative derivation to that of Hu, Paz and Zhang, which was based on the direct computation of path…
Non-Markovian quantum state diffusion provides a wavefunction-based framework for modeling open quantum systems. In this work, we introduce a novel machine learning approach based on an operator construction algorithm. This algorithm…
The Lindblad master equation for an open quantum system with a Hamiltonian containing an arbitrary potential is written as an equation for the Wigner distribution function in the phase space representation. The time derivative of this…
The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…
It is shown that evolution of an open quantum system can be exactly described in terms of wave function which obeys Schrodinger equation with randomly varying parameters whose statistics is universally determined by separate dynamics of the…
A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…
In this paper we present a stochastic homogenization result for a class of Hilbert space evolutionary gradient systems driven by a quadratic dissipation potential and a $\Lambda$-convex energy functional featuring random and rapidly…
We introduce a variational hybrid classical-quantum algorithm to simulate the Lindblad master equation and its adjoint for time-evolving Markovian open quantum systems and quantum observables. Our method is based on a direct representation…
We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for…