Related papers: The Loop Algorithm
A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously…
The combination of continuum Many-Body Quantum physics and Monte Carlo methods provide a powerful and well established approach to first principles calculations for large systems. Replacing the exact solution of the problem with a…
We present an efficient computational approach to sample the histories of nonlinear stochastic processes. This framework builds upon recent work on casting a $d$-dimensional stochastic dynamical system into a $d+1$-dimensional equilibrium…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
For spin rotational symmetric models with a positive-definite high-temperature expansion of the partition function, a stochastic sampling of the series expansion upon partial resummation becomes logically equivalent to sampling an…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
We present a new class of algorithms for performing valence-bond quantum Monte Carlo of quantum spin models. Valence-bond quantum Monte Carlo is a T=0 Monte Carlo method based on sampling of a set of operator-strings that can be viewed as…
We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable | after the Heisenberg evolution associated with the…
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…
Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of general and efficient update algorithm for large size systems close to phase transition or with…
Monte Carlo simulations of lattice quantum field theories on Lefschetz thimbles are non trivial. We discuss a new Monte Carlo algorithm based on the idea of computing contributions to the functional integral which come from complete flow…
Recently, a diffusion Monte Carlo algorithm was applied to the study of spin dependent interactions in condensed matter. Following some of the ideas presented therein, and applied to a Hamiltonian containing a Rashba-like interaction, a…
We consider generalizations of the classical inverse problem to Bayesien type estimators, where the result is not one optimal parameter but an optimal probability distribution in parameter space. The practical computational tool to compute…
Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in…
A possible solution of the notorious sign problem preventing direct Monte Carlo calculations for systems with non-zero chemical potential is to deform the integration region in the complex plane to a Lefschetz thimble. We investigate this…
This work develops novel error expansions with computable leading order terms for the global weak error in the tau-leap discretization of pure jump processes arising in kinetic Monte Carlo models. Accurate computable a posteriori error…
Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…
Computations of chemical systems' equilibrium properties and non-equilibrium dynamics have been suspected of being a "killer app" for quantum computers. This review highlights the recent advancements of quantum algorithms tackling complex…
Continuous-time determinantal algorithm is proposed for the quantum Monte Carlo simulation of the interacting fermions. The scheme does not invoke Hubbard-Stratonovich transformation. The fermionic action is divided into two parts. One of…
The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the…