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We develop Monte Carlo methods for sampling random states and corresponding bit strings in qubit systems. To this end, we derive exact probability density functions that yield the Porter-Thomas distribution in the limit of large systems. We…
An appropriate iterative scheme for the minimization of the energy, based on the variational Monte Carlo (VMC) technique, is introduced and compared with existing stochastic schemes. We test the various methods for the 1D Heisenberg ring…
Development of exponentially scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, is a useful algorithm that allows…
Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although…
We have employed the steepest descent method to optimise the variational ground state quantum Monte Carlo wave function for He, Li, Be, B and C atoms. We have used both the direct energy minimisation and the variance minimisation…
A new Monte Carlo method is proposed for fermion systems interacting with classical degrees of freedom. To obtain a weight for each Monte Carlo sample with a fixed configuration of classical variables, the moment expansion of the density of…
We present a continuous-variable photonic quantum algorithm for the Monte Carlo evaluation of multi-dimensional integrals. Our algorithm encodes n-dimensional integration into n+3 modes and can provide a quadratic speedup in runtime…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
We reformulate the projected imaginary-time evolution of Full Configuration Interaction Quantum Monte Carlo in terms of a Lagrangian minimization. This naturally leads to the admission of polynomial complex wavefunction parameterizations,…
We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained and the position at a given (constant) time of an exponentially tempered L\'evy process. The algorithm, based on…
The computation of determinants plays a central role in diagrammatic Monte Carlo algorithms for strongly correlated systems. The evaluation of large numbers of determinants can often be the limiting computational factor determining the…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
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…
The paper proposes Monte Carlo algorithms for the computation of the information rate of two-dimensional source/channel models. The focus of the paper is on binary-input channels with constraints on the allowed input configurations. The…
By decomposing the important sampled imaginary time Schr\"odinger evolution operator to fourth order with positive coefficients, we derived a number of distinct fourth order Diffusion Monte Carlo algorithms. These sophisticated algorithms…
Many-electron problems pose some of the greatest challenges in computational science, with important applications across many fields of modern science. Fermionic quantum Monte Carlo (QMC) methods are among the most powerful approaches to…
Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales…
Quantum Monte Carlo (QMC) methods are one of the most important tools for studying interacting quantum many-body systems. The vast majority of QMC calculations in interacting fermion systems require a constraint to control the sign problem.…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
Quantum Monte Carlo (QMC) methods are often used to calculate properties of many body quantum systems. The main cost of many QMC methods, for example the variational Monte Carlo (VMC) method, is in constructing a sequence of Slater matrices…