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Title: Numerical analysis for inchworm Monte Carlo method: Sign problem and error growth
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 time, for which the inchworm Monte Carlo method shows a flatter curve than the direct application of Monte Carlo method to the classical Dyson series. To better understand the underlying mechanism of the inchworm Monte Carlo method, we distinguish two types of exponential error growth, which are known as the numerical sign problem and the error amplification. The former is due to the fast growth of variance in the stochastic method, which can be observed from the Dyson series, and the latter comes from the evolution of the numerical solution. Our analysis demonstrates that the technique of partial resummation can be considered as a tool to balance these two types of error, and the inchworm Monte Carlo method is a successful case where the numerical sign problem is effectively suppressed by such means. We first demonstrate our idea in the context of ordinary differential equations, and then provide complete analysis for the inchworm Monte Carlo method. Several numerical experiments are carried out to verify our theoretical results.  more » « less
Award ID(s):
2012286 2037263
NSF-PAR ID:
10428660
Author(s) / Creator(s):
; ;
Publisher / Repository:
American Mathematical Society
Date Published:
Journal Name:
Mathematics of Computation
Volume:
92
Issue:
341
ISSN:
0025-5718
Page Range / eLocation ID:
1141 to 1209
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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