Taming the Dynamical Sign Problem in Diagrammatic Algorithms for Open Quantum Systems

Explore the challenges and recent advancements in numerical simulations for open quantum system dynamics in this conference talk by Jianfeng Lu from Duke University Mathematics. Delve into diagrammatic algorithms, focusing on the interplay between the dynamical sign problem and error amplification in numerical integration. Discover how partial resummation techniques can balance these errors and learn about the inchworm Monte Carlo method's success in suppressing the numerical sign problem. Gain insights into various approaches, mathematical frameworks, and numerical examples presented throughout the talk, including the Brick Theorem, propagator analysis, and integral differential interpretations.

Intro
Example
Different approaches
Price to pay
Framework
Notation
Naming time
Bad propagator
Applying perturbation theory
Simplifying assumptions
The Brick Theorem
The Full Propagator
The Hamiltonian
Propagator
Bb
Analytical sign problem
The inchworm
Interim expansion
Mathematical terminologies
Integral differential interpretation
OD representation
Natural numerical scheme
Interim diagram
Numerical examples
Can we do something better
Design a better numerical scheme
A good starting point