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Numerical simulation is an important non-perturbative tool to study quantum field theories defined in non-commutative spaces. In this contribution, a selection of results from Monte Carlo calculations for non-commutative models is…
The quantum phase transition of the one-dimensional long-range transverse-field Ising model is explored by combining the quantum Monte Carlo method and stochastic parameter optimization, specifically achieved by tuning correlation ratios so…
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo…
Solutions to many-body problem instances often involve an intractable number of degrees of freedom and admit no known approximations in general form. In practice, representing quantum-mechanical states of a given Hamiltonian using available…
Modeling the dynamics of a quantum system connected to the environment is critical for advancing our understanding of complex quantum processes, as most quantum processes in nature are affected by an environment. Modeling a macroscopic…
Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of…
Quantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. In this review, we focus on the electronic structure QMC, i.e., methods relevant for systems described by the electron-ion…
Quantum annealing is a generic solver of the optimization problem that uses fictitious quantum fluctuation. Its simulation in classical computing is often performed using the quantum Monte Carlo simulation via the Suzuki--Trotter…
Non-Hermitian quantum systems exhibit unique properties and hold significant promise for diverse applications, yet their dynamical simulation poses a particular challenge due to intrinsic openness and non-unitary evolution. Here, we…
In a number of classical statistical-physical models, there exists a characteristic dimensionality called the upper critical dimension above which one observes the mean-field critical behavior. Instead of constructing high-dimensional…
Quantum Monte Carlo simulations are powerful and versatile tools for the quantum many-body problem. In addition to the usual calculations of energies and eigenstate observables, quantum Monte Carlo simulations can in principle be used to…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…
We present a numerical method to simulate the dynamics of continuous-variable quantum many-body systems. Our approach is based on custom neural-network many-body quantum states. We focus on dynamics of two-dimensional quantum rotors and…
A review of the Loop Algorithm, its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a Quantum Monte Carlo procedure which employs nonlocal changes of worldline configurations,…
Quantum computers have a potential for solving quantum chemistry problems with higher accuracy than classical computers. Quantum computing quantum Monte Carlo (QC-QMC) is a QMC with a trial state prepared in quantum circuit, which is…
An efficient Quantum Monte Carlo algorithm for the simulation of bosonic systems on a lattice in a grand canonical ensemble is proposed. It is based on the mapping of bosonic models to the spin models in the limit of the infinite total spin…
Due to the intrinsic complexity of the quantum many-body problem, quantum Monte Carlo algorithms and their corresponding Monte Carlo configurations can be defined in various ways. Configurations corresponding to few Feynman diagrams often…
Quantum Monte Carlo (QMC) methods offer exact solutions for quantum many-body systems but face severe limitations in fermionic systems like atomic nuclei due to the sign problem. While sign-problem-free QMC algorithms exist and provide…
We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed…
We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical…