Related papers: The Loop Algorithm
It has been shown that the Metropolis algorithm can be implemented on quantum computers in a way that avoids the sign problem. However, flat histogram techniques are often preferred as they don't suffer from the same limitations that…
Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems. As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its application to most fermion systems…
The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the…
Stochastic processes play a fundamental role in physics, mathematics, engineering and finance. One potential application of quantum computation is to better approximate properties of stochastic processes. For example, quantum algorithms for…
We give a brief discussion of the recently developed Constrained-Path Monte Carlo Method. This method is a quantum Monte Carlo technique that eliminates the fermion sign problem plaguing simulations of systems of interacting electrons. The…
Quantum spin systems with strong geometric restrictions give rise to rich quantum phases such as valence bond solids and spin liquid states. However, the geometric restrictions often hamper the application of sophisticated numerical…
Hamiltonian simulation is one of the most promising paths toward quantum advantage. Most prior approaches to Hamiltonian simulation circuit synthesis focus on local rewrite rules and low-level optimizations, and give limited attention to…
Present quantum Monte Carlo codes use statistical techniques adapted to find the amplitude of a quantum system or the associated eigenvalues. Thus, they do not use a true physical random source. It is demonstrated that, in fact, quantum…
In recent years, a better understanding of the Monte Carlo method has provided us with many new techniques in different areas of statistical physics. Of particular interest are so called cluster methods, which exploit the considerable…
Simple feedback loops, inspired from extremum-seeking, are proposed to lock a probe-frequency to the transition frequency of a single quantum system following quantum Monte-Carlo trajectories. Two specific quantum systems are addressed, a…
We review efficient Monte Carlo methods for simulating quantum systems which couple to a dissipative environment. A brief introduction of the Caldeira-Leggett model and the Monte Carlo method will be followed by a detailed discussion of…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Self-learning Monte Carlo method [arXiv:1610.03137, 1611.09364] is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we implement this method in the framework of determinantal…
An efficient O(N) cluster Monte Carlo method for Ising models with long-range interactions is presented. Our novel algorithm does not introduce any cutoff for interaction range and thus it strictly fulfills the detailed balance. The…
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…
Simulating stochastic systems with feedback control is challenging due to the complex interplay between the system's dynamics and the feedback-dependent control protocols. We present a single-step-trajectory probability analysis to…
Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the…
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…
Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of…
Quantum annealing aims to provide a faster method for finding the minima of complicated functions, compared to classical computing, so there is an increasing interest in the relaxation dynamics of quantum spin systems. Moreover, it is known…