相关论文: Optimally chosen Nakajima-Zwanzig master equation …

We investigate the exact solution, perturbation theory and master equation of open system dynamics based on our serial studies on quantum mechanics in general quantum systems [An Min Wang, quant-ph/0611216 and quant-ph/0611217]. In a…

The dynamics of finite dimension open quantum systems is studied with the help of the simplest possible form of projection operators, namely the ones which project only onto one dimensional subspaces. The simplicity of the action of the…

A programmable quantum processor is a fundamental model of quantum computation. In this model, any quantum channel can be approximated by applying a fixed universal quantum operation onto an input state and a quantum `program' state, whose…

We derive a new expansion of the Heisenberg equation of motion based on the projection operator method proposed by Shibata, Hashitsume and Shing\=u. In their projection operator method, a certain restriction is imposed on the initial state.…

We propose a mixed-configuration approximation based on single-band impurity solvers to efficiently study nonequilibrium multi-orbital systems at moderate computational cost. In this work, we merge the approach with the so-called auxiliary…

The generalized quantum master equation provides a powerful framework for non-Markovian dynamics of open quantum systems. However, the accurate and efficient evaluation of the memory kernel remains a challenge. In this work, we introduce a…

We present a non-equilibrium quantum master equation for a driven open quantum system in the presence of a continuously applied electromagnetic field. Starting from a driven Caldeira-Leggett (CL) model in which the external electromagnetic…

The time-convolutionless master equation provides a general framework to model non-Markovian dynamics of an open quantum system with a time-local generator. A diagrammatic representation is developed and proven for the perturbative…

We introduce the neural tangent kernel (NTK) regime for two-layer neural operators and analyze their generalization properties. For early-stopped gradient descent (GD), we derive fast convergence rates that are known to be minimax optimal…

In this work, we adopt the Gradient Projection Method (GPM) to problems of quantum control. For general $N$-level closed and open quantum systems, we derive the corresponding adjoint systems and gradients of the objective functionals, and…

In his lectures at College de France, P.L. Lions introduced the concept of Master equation, see [5] for Mean Field Games. It is introduced in a heuristic fashion, from the system of partial differential equations, associated to a Nash…

We study the analytically solvable Ising model of a single qubit system coupled to a spin bath. The purpose of this study is to analyze and elucidate the performance of Markovian and non-Markovian master equations describing the dynamics of…

The next few years will be exciting as prototype universal quantum processors emerge, enabling implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware…

In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…

Computing many eigenpairs of the Schr{\"o}dinger operator presents a computational bottleneck in large-scale quantum simulations due to the global communication overhead of explicit orthogonalization. To address this issue, we propose a…

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…

The quantum master equation (QME), used to describe the Markov process of interaction between atoms and field, has a number of significant drawbacks. It is extremely memory intensive, and also inapplicable to the case of long-term memory in…

Consistent weighted least square estimators are proposed for a wide class of nonparametric regression models with random regression function, where this real-valued random function of $k$ arguments is assumed to be continuous with…

Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…

We analyze the mean-field limit of a stochastic Schr{\"o}dinger equation arising in quantum optimal control and mean-field games, where N interacting particles undergo continuous indirect measurement. For the open quantum system described…