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We establish a physically meaningful representation of a quantum energy density for use in Quantum Monte Carlo calculations. The energy density operator, defined in terms of Hamiltonian components and density operators, returns the correct…
This Dissertation presents results of a thorough study of ultracold bosonic and fermionic gases in three-dimensional and quasi-one-dimensional systems. Although the analyses are carried out within various theoretical frameworks…
In this Ph.D. thesis quantum Monte Carlo methods are applied to investigate the properties of a number of ultracold quantum systems. In Chapter 1 we discuss the analytical approaches and approximations used in the subsequent Chapters; also…
Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in…
Variational Monte Carlo (VMC) methods are used to sample classically from distributions corresponding to quantum states which have an efficient classical description. VMC methods are based on performing a number of steps of a Markov chain…
The VB-QMC method is presented in this chapter. It consists of using in quantum Monte Carlo (QMC) approaches with a wave function expressed as a usually short expansion of classical Valence-Bond (VB) structures supplemented by a Jastrow…
Chiral effective field theory (EFT) enables a systematic description of low-energy hadronic interactions with controlled theoretical uncertainties. For strongly interacting systems, quantum Monte Carlo (QMC) methods provide some of the most…
It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons,…
Heavy quark thermalization in the quark-gluon plasma (QGP) is one of the most promising phenomena for understanding the strong interaction, where their energy loss and momentum broadening at low momentum can be well described by a…
On the base of Diffusion Monte-Carlo method it is developed a new Complex Diffusion Monte-Carlo (CDMC) method allowing to simulate the quantum systems with complex wave function. There are no approximations on the calculation of modulus and…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a…
We study beryllium dihydride (BeH$_2$) and acetylene (C$_2$H$_2$) molecules using real-space diffusion Monte Carlo (DMC) method. The molecules serve as perhaps the simplest prototypes that illustrate the difficulties with biases in the…
All-electron Fixed-node Diffusion Monte Carlo (FN-DMC) calculations for the nonrelativistic ground-state energy of the water molecule at equilibrium geometry are presented. The determinantal part of the trial wavefunction is obtained from a…
The projective quantum Monte Carlo (PQMC) algorithms are among the most powerful computational techniques to simulate the ground state properties of quantum many-body systems. However, they are efficient only if a sufficiently accurate…
Quantum computers (QCs) must implement quantum error correcting codes (QECCs) to protect their logical qubits from errors, and modeling the effectiveness of QECCs on QCs is an important problem for evaluating the QC architecture. The…
We present a simple and general formalism to compute efficiently the derivatives of a multi-determinant Jastrow-Slater wave function, the local energy, the interatomic forces, and similar quantities needed in quantum Monte Carlo. Through a…
Quasi-Monte Carlo (QMC) is a powerful method for evaluating high-dimensional integrals. However, its use is typically limited to distributions where direct sampling is straightforward, such as the uniform distribution on the unit hypercube…
Quantum-mechanical methods are widely used for understanding molecular interactions throughout biology, chemistry, and materials science. Quantum diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple…
Fixed-node diffusion Monte Carlo (FNDMC) is a stochastic quantum many-body method that has a great potential in electronic structure theory. We examine how FNDMC satisfies exact constraints, linearity and derivative discontinuity of total…