Related papers: Design nearly optimal quantum algorithm for linear…
The open Tavis--Cummings model consists of $N$ quantum emitters interacting with a common cavity mode, accounts for losses and decoherence, and is frequently explored for quantum information processing and designing quantum devices. As $N$…
We present a quantum algorithm based on the Generalized Quantum Master Equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the…
We develop a Lindblad framework for quantum stochastic thermodynamics to study the nonequilibrium thermodynamics of open quantum systems. Our approach adopts the local quantum detailed balance condition, ensuring thermodynamic consistency…
We compare two approaches to open quantum systems, namely, the non-Hermitian dynamics and the Lindblad master equation. In order to deal with more general dissipative phenomena, we propose the unified master equation that combines the…
Dynamical systems appear in nearly every aspect of the physical world. As such, understanding the properties of dynamical systems is of great importance. Typically, a dynamical system is described by a system of ordinary differential…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
Recent advances in quantum computing and their increased availability has led to a growing interest in possible applications. Among those is the solution of partial differential equations (PDEs) for, e.g., material or flow simulation.…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
With the advent of ultra-high power lasers the nonlinear nature of the vacuum of quantum electrodynamics (QED) can be probed. Due to the highly nonlinear structure of the underlying equations new numerical algorithms are required. A…
We develop an optimal control algorithm for robust quantum gate preparation in open environments with the state of the quantum system represented using the Lindblad master equation. The algorithm is based on adaptive linearization and…
Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…
Quantum simulation on emerging quantum hardware is a topic of intense interest. While many studies focus on computing ground state properties or simulating unitary dynamics of closed systems, open quantum systems are an interesting target…
We present a Bayesian algorithm to identify generators of open quantum system dynamics, described by a Lindblad master equation, that are compatible with measured experimental data. The algorithm, based on a Markov Chain Monte Carlo…
We construct quantum algorithms to compute physical observables of nonlinear PDEs with M initial data. Based on an exact mapping between nonlinear and linear PDEs using the level set method, these new quantum algorithms for nonlinear…
We consider the natural generalization of the Schr\"{o}dinger equation to Markovian open system dynamics: the so-called the Lindblad equation. We give a quantum algorithm for simulating the evolution of an $n$-qubit system for time $t$…
In open quantum systems, a basic question at the interface of quantum information, statistical physics, and many-body dynamics is how well can one infer the structure of noise and dissipation generators from finite-time measurement…