Related papers: Targeting Eigenstates by "Simulated Measurements" …
The aim of this article is to propose a new reduced-order modelling approach for parametric eigenvalue problems arising in electronic structure calculations. Namely, we develop nonlinear reduced basis techniques for the approximation of…
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
We present a variational algorithm for fault tolerant quantum computing to solve a system of linear equations which directly maximises the parameters of the target fidelity. This so-called measurement test algorithm can be applied to any…
Trotter decomposition provides a simple approach to simulating open quantum systems by decomposing the Lindbladian into a sum of individual terms. While it is established that Trotter errors in Hamiltonian simulation depend on nested…
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…
Recent progress in quantum simulation and algorithms has demonstrated a rapid expansion in capabilities. The search continues for new techniques and applications to exploit quantum advantage. Here we propose an innovative method to…
We propose a marginal likelihood strategy within the Kennedy-O'Hagan (KOH) Bayesian framework, where a Gaussian process (GP) models the discrepancy between a physical system and its simulator. Our approach introduces a novel marginalized…
A misunderstanding of entangled states has spawned decades of concern about quantum measurements and a plethora of quantum interpretations. The "measurement state" or "Schrodinger's cat state" of a superposed quantum system and its detector…
One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…
Ab-initio simulations of multiple heavy quarks propagating in a Quark-Gluon Plasma are computationally difficult to perform due to the large dimension of the space of density matrices. This work develops machine learning algorithms to…
We explore an unconventional bridge between quantum mechanical density matrices and sound by mapping elements of the density matrix and their phases to auditory signals, thus introducing a framework for Open Quantum Sonification. Employing…
It is shown that the operator sum representation for non-Markovian dynamics and the Lindblad master equation in Markovian limit can be derived from a formal solution to quantum Liouville equation for a qubit system in the presence of…
We present a collection of methods to simulate entangled dynamics of open quantum systems governed by the Lindblad equation with tensor network methods. Tensor network methods using matrix product states have been proven very useful to…
Non-equilibrium steady states are a focal point of research in the study of open quantum systems. Previous variational algorithms for searching these steady states have suffered from resource-intensive implementations due to vectorization…
The so-called Born-Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows to effectively separate fast and slow degrees of freedom and thus treating electrons and nuclei at different mathematical…
Solving the time-dependent Schr\"odinger equation is an important application area for quantum algorithms. We consider Schr\"odinger's equation in the semi-classical regime. Here the solutions exhibit strong multiple-scale behavior due to a…
We consider a toy model for the study of monitored dynamics in a many-body quantum systems. We study the stochastic Schrodinger equation resulting from the continuous monitoring with a rate $\Gamma$ of a random hermitian operator chosen at…
It is assumed that in a measurement the system under study interacts with a macroscopic measuring apparatus, in such a way that the density matrix of the measured system evolves according to the Lindblad equation. Under an assumption of…
Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of…
Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schr\"odinger…