Related papers: A quantum Karhunen-Loeve expansion and quadratic-e…
This paper is concerned with a filtering problem for a class of nonlinear quantum stochastic systems with multichannel nondemolition measurements. The system-observation dynamics are governed by a Markovian Hudson-Parthasarathy quantum…
We establish the potential of continuous-variable Gaussian states of linear dynamical systems for machine learning tasks. Specifically, we consider reservoir computing, an efficient framework for online time series processing. As a…
We develop a system of non-linear stochastic evolution equations that describes the continuous measurements of quantum systems with mixed initial state. We address quantum systems with unbounded Hamiltonians and unbounded interaction…
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…
In the framework of the Heisenberg picture, an alternative derivation of the reduced density matrix of a driven dissipative quantum harmonic oscillator as the prototype of an open quantum system is investigated. The reduced density matrix…
We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic…
We show that the usual master equation formalism of Markovian open quantum systems is completely equivalent to a certain state vector formalism. The state vector of the system satisfies a given frictional Schr\"odinger equation except for…
One of the most important topics in quantum scientific computing is solving differential equations. In this paper, generalized quantum functional expansion (QFE) framework is proposed. In the QFE framework, a functional expansion of…
Large classes of multi-dimensional Gaussian processes can be enhanced with stochastic Levy area(s). In a previous paper, we gave sufficient and essentially necessary conditions, only involving variational properties of the covariance.…
We present a time-linear scaling method to simulate open and correlated quantum systems out of equilibrium. The method inherits from many-body perturbation theory the possibility to choose selectively the most relevant scattering processes…
The dynamics of excitonic energy transfer in molecular complexes triggered by interaction with laser pulses offers a unique window into the underlying physical processes. The absorbed energy moves through the network of interlinked pigments…
We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…
In this work we introduce a phase-space description based on the positive P representation for bosonic fields interacting with a system of quantum emitters. The formalism is applicable to collective light-matter interactions and open…
Quantum state smoothing is a technique for assigning a valid quantum state to a partially observed dynamical system, using measurement records both prior and posterior to an estimation time. We show that the technique is greatly simplified…
We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian)…
In the present paper, a stochastic Taylor expansion of some functional applied to the solution process of an It\^o or Stratonovich stochastic differential equation with a multi-dimensional driving Wiener process is given. Therefore, the…
We delve into the use of photonic quantum computing to simulate quantum mechanics and extend its application towards quantum field theory. We develop and prove a method that leverages this form of Continuous-Variable Quantum Computing…
We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional formalism combined with a two-time Hubbard-Stratonovich transformation allows us…
We study a simplified scheme of $k$ coupled autocatalytic reactions, previously introduced by Togashi and Kaneko. The role of stochastic fluctuations is elucidated through the use of the van Kampen system-size expansion and the results…
We present a nonlinear stochastic Schroedinger equation for pure states describing non-Markovian diffusion of quantum trajectories. It provides an unravelling of the evolution of a quantum system coupled to a finite or infinite number of…