Related papers: The sign problem and the Lefschetz thimble
We develop a new numerical scheme which allows precise solution of coherent tunneling problems, i.e., problems with exponentially small transition amplitudes between quasidegenerate states. We explain how this method works for the…
In Monte Carlo simulation, lattice field theory with a $\theta$ term suffers from the sign problem. This problem can be circumvented by Fourier-transforming the topological charge distribution $P(Q)$. Although this strategy works well for…
Towards a solution to the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the…
Quantum Monte Carlo simulations of quantum many body systems are plagued by the Fermion sign problem. The computational complexity of simulating Fermions scales exponentially in the projection time $\beta$ and system size. The sign problem…
We consider the numerical analysis of the inchworm Monte Carlo method, which is proposed recently to tackle the numerical sign problem for open quantum systems. We focus on the growth of the numerical error with respect to the simulation…
The Worldvolume Hybrid Monte Carlo method (WV-HMC method) [arXiv:2012.08468] is a reliable and versatile algorithm towards solving the sign problem. Similarly to the tempered Lefschetz thimble method, this method removes the ergodicity…
Diagrammatic Monte Carlo approach is applied to a problem of a single spin-down fermion resonantly interacting with the sea of ideal spin-up fermions. On one hand, we develop a generic, sign-problem tolerant, method of exact numerical…
This is an introductory level review of recent applications of resurgent trans-series and Picard-Lefschetz theory to quantum mechanics and quantum field theory. Resurgence connects local perturbative data with global topological structure.…
Quantum Monte Carlo is one of the most promising approaches for dealing with large-scale quantum many-body systems. It has played an extremely important role in understanding strongly correlated physics. However, two fundamental problems,…
The quantum theory of antiferromagnetism in metals is necessary for our understanding of numerous intermetallic compounds of widespread interest. In these systems, a quantum critical point emerges as external parameters (such as chemical…
A quantum implementation of the Stochastic Series Expansion (SSE) Monte Carlo method is proposed, and it is shown that quantum SSE offers significant advantages over classical implementations of SSE. In particular, for problems where…
The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is a reliable and versatile algorithm for addressing the numerical sign problem. It resolves the ergodicity issues commonly encountered in Lefschetz thimble-based…
Quantum computing is a promising way to systematically solve the longstanding computational problem, the ground state of a many-body fermion system. Many efforts have been made to realise certain forms of quantum advantage in this problem,…
We present a quantum Monte Carlo algorithm for the simulation of general quantum and classical many-body models within a single unifying framework. The algorithm builds on a power series expansion of the quantum partition function in its…
Recently there has been remarkable progress in solving the sign problem, which occurs in investigating statistical systems with a complex weight. The two promising methods, the complex Langevin method and the Lefschetz thimble method, share…
In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the…
Neural quantum states (NQS) are a promising approach to study many-body quantum physics. However, they face a major challenge when applied to lattice models: Convolutional networks struggle to converge to ground states with a nontrivial…
This paper presents a method for alleviating sign problems in lattice path integrals, including those associated with finite fermion density in relativistic systems. The method makes use of information gained from some systematic expansion…
Monte Carlo is one of the most useful methods to study the quantum Hall problems. In this paper, we introduce a fast lattice Monte Carlo method based on a mathematically exact reformulation of the torus quantum Hall problems from continuum…
The sign problem is the fundamental limitation to quantum Monte Carlo simulations of the statistical mechanics of interacting fermions. Determinant quantum Monte Carlo (DQMC) is one of the leading methods to study lattice models such as the…