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We develop a time-dependent variational Monte Carlo (t-VMC) method for quantum dynamics of strongly correlated electrons. The t-VMC method has been recently applied to bosonic systems and quantum spin systems. Here, we propose a…
We present a unified theory of the variational Monte Carlo (VMC) and determinant quantum Monte Carlo (DQMC) methods using a novel density matrix formulation of VMC. We introduce an efficient algorithm for VMC to compute correlation…
Recently, Syljuasen and Sandvik proposed a new framework for constructing algorithms of quantum Monte Carlo simulation. While it includes new classes of powerful algorithms, it is not straightforward to find an efficient algorithm for a…
On the base of a Feynman-Kac--type formula involving Poisson stochastic processes, recently a Monte Carlo algorithm has been introduced, which describes exactly the real- or imaginary-time evolution of many-body lattice quantum systems. We…
We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove…
Modern quantum Monte Carlo (QMC) methods often capture electron correlation through both explicitly correlating Jastrow factors and small to mid-sized configuration interaction (CI) expansions. Here, we study the additional optimization…
Multi-orbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to…
We present a new method for the optimization of large configuration interaction (CI) expansions in the quantum Monte Carlo (QMC) framework. The central idea here is to replace the non-orthogonal variational optimization of CI coefficients…
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 present general principles for the design and analysis of unbiased Monte Carlo estimators in a wide range of settings. Our estimators posses finite work-normalized variance under mild regularity conditions. We apply our estimators to…
We introduce an extension of the time-dependent variational Monte Carlo (tVMC) method that adaptively controls the expressivity of the variational quantum state during the simulation of the dynamics. This adaptive tVMC (atVMC) approach is…
Arrays of Rydberg atoms are a powerful platform to realize strongly-interacting quantum many-body systems. A common Rydberg Hamiltonian is free of the sign problem, meaning that its equilibrium properties are amenable to efficient…
When a system undergoes a quantum phase transition, the ground-state wave-function shows a change of nature, which can be monitored using the fidelity concept. We introduce two Quantum Monte Carlo schemes that allow the computation of…
The implementation of optimal statistical inference protocols for high-dimensional quantum systems is often computationally expensive. To avoid the difficulties associated with optimal techniques, here I propose an alternative approach to…
Variational quantum algorithms are promising tools for near-term quantum computers as their shallow circuits are robust to experimental imperfections. Their practical applicability, however, strongly depends on how many times their circuits…
The directed-loop quantum Monte Carlo method is generalized to the case of retarded interactions. Using the path integral, fermion-boson or spin-boson models are mapped to actions with retarded interactions by analytically integrating out…
A quantum Monte Carlo method combining update of the loop algorithm with the global flip of the world line is proposed as an efficient method to study the magnetization process in an external field, which has been difficult because of…
The problem of estimating certain distributions over $\{0,1\}^d$ is considered here. The distribution represents a quantum system of $d$ qubits, where there are non-trivial dependencies between the qubits. A maximum entropy approach is…
We present a fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of systems with long-range interactions that reproduces the dynamics of a standard implementation exactly, i.e., the generated configurations and…
An extended ensemble Monte Carlo algorithm is proposed by introducing a violation of the detailed balance condition to the update scheme of the inverse temperature in simulated tempering. Our method, irreversible simulated tempering, is…