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We discuss a projector Monte Carlo method for quantum spin models formulated in the valence bond basis, using the S=1/2 Heisenberg antiferromagnet as an example. Its singlet ground state can be projected out of an arbitrary basis state as…
We show how information on the uniformity properties of a point set employed in numerical multidimensional integration can be used to improve the error estimate over the usual Monte Carlo one. We introduce a new measure of (non-)uniformity…
For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced by approximations to a distribution's inverse cumulative distribution function. These approximations are…
X-ray dose constantly gains interest in the interventional suite. With dose being generally difficult to monitor reliably, fast computational methods are desirable. A major drawback of the gold standard based on Monte Carlo (MC) methods is…
We investigate operator dynamics and entanglement growth in dual-unitary circuits, a class of locally scrambled quantum systems that enables efficient simulation beyond the exponential complexity of the Hilbert space. By mapping the…
Monte Carlo simulations are performed in classical phase space for a one-dimensional quantum harmonic crystal. Symmetrization effects for spinless bosons and fermions are quantified. The algorithm is tested for a range of parameters against…
The Monte Carlo method is a powerful technique for computing thermodynamic magnetic states of otherwise unsolvable spin Hamiltonians, but the method becomes computationally prohibitive with increasing number of spins and the simulation 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…
We present a new Monte Carlo algorithm based on the Stochastic Approximation Monte Carlo (SAMC) algorithm for directly calculating the density of states. The proposed method is Stochastic Approximation with a Dynamic update factor (SAD)…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
A method is proposed to handle the sign problem in the simulation of systems having indefinite or complex-valued measures. In general, this new approach, which is based on renormalisation blocking, is shown to yield statistical errors…
Quantum Monte-Carlo simulations of hybrid quantum-classical models such as the double exchange Hamiltonian require calculating the density of states of the quantum degrees of freedom at every step. Unfortunately, the computational…
In simulations of crystals, unlike liquids or gases, it may happen that the properties of the studied system depend not only on the volume of the simulation cell but also on its shape. For such cases it is desirable to change the shape of…
The problem of estimating the probability p=P(g(X<0) is considered when X represents a multivariate stochastic input of a monotone function g. First, a heuristic method to bound p is formally described, involving a specialized design of…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
This study presents new closed-form estimators for the Dirichlet and the Multivariate Gamma distribution families, whose maximum likelihood estimator cannot be explicitly derived. The methodology builds upon the score-adjusted estimators…
A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…
Wave-function Monte Carlo methods are an important tool for simulating quantum systems, but the standard method cannot be used to simulate decoherence in continuously measured systems. Here we present a new Monte Carlo method for such…
Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…
Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique…