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For model-based estimation methods, the modeling that is as close to reality as possible makes a vital estimation result. In simple applications, it is sufficient to model a system with a single state space model. However, there are…
A set of new exact ground states of the generalized Hubbard models in arbitrary dimensions with explicitly given parameter regions is presented. This is based on a simple method for constructing exact ground states for homogeneous quantum…
For $d \ge 2$ and all $q\geq q_{0}(d)$ we give an efficient algorithm to approximately sample from the $q$-state ferromagnetic Potts and random cluster models on finite tori $(\mathbb Z / n \mathbb Z )^d$ for any inverse temperature…
We investigate the properties of quantum annealing applied to the random field Ising model in one, two and three dimensions. The decay rate of the residual energy, defined as the energy excess from the ground state, is find to be…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
A ubiquitous problem in quantum physics is to understand the ground-state properties of many-body systems. Confronted with the fact that exact diagonalisation quickly becomes impossible when increasing the system size, variational…
Rotating-wave approximation and its validity in multi-state quantum systems are studied through analytic approach. Their applicability is also verified from the viewpoint of generic states by the use of direct numerical integrations of the…
Ising formulations are widely utilized to solve combinatorial optimization problems, and a variety of quantum or semiconductor-based hardware has recently been made available. In combinatorial optimization problems, the existence of local…
We describe an efficient Monte Carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models. The density of states is modified at each step when the energy…
A huge number of independent true ground-state configurations is calculated for two-, three- and four-dimensional +- J spin-glass models. Using the genetic cluster-exact approximation method, system sizes up to N=20^2,8^3,6^4 spins are…
Optimization problems frequently appear in any scientific domain. Most of the times, the corresponding decision problem turns out to be NP-hard, and in these cases genetic algorithms are often used to obtain approximated solutions. However,…
Quantum computing is believed to be particularly useful for the simulation of chemistry and materials, among the various applications. In recent years, there have been significant advancements in the development of near-term quantum…
We introduce a method that generates ground-state ansatzes for quantum many-body systems which are both analytically tractable and accurate over wide parameter regimes. Our approach leverages a custom symbolic language to construct tensor…
Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
The simulation of the dynamics of a system coupled to a low-temperature environment is a promising application of quantum computers to determine ground-state properties of physical systems. However, this approach requires not only the…
We present a method for finding individual excited states' energy stationary points in complete active space self-consistent field theory that is compatible with standard optimization methods and highly effective at overcoming difficulties…
We consider deterministic and {\em randomized} quantum algorithms simulating $e^{-iHt}$ by a product of unitary operators $e^{-iA_jt_j}$, $j=1,...,N$, where $A_j\in\{H_1,...,H_m\}$, $H=\sum_{i=1}^m H_i$ and $t_j > 0$ for every $j$.…
State selective field ionization detection techniques in physics require a specific progression through a complicated atomic state space to optimize state selectivity and overall efficiency. For large principle quantum number n, the…
Quantum circuit partitioning (QCP) is a hybrid quantum-classical approach that aims to simulate large quantum systems on smaller quantum computers. A quantum computation is divided into smaller subsystems and results of measurements on…