801 research outputs found
Mitigating sign problem by automatic differentiation
As an intrinsically-unbiased method, quantum Monte Carlo (QMC) is of unique
importance in simulating interacting quantum systems. Unfortunately, QMC often
suffers from the notorious sign problem. Although generically curing sign
problem is shown to be hard (NP-hard), sign problem of a given quantum model
may be mitigated (sometimes even cured) by finding better choices of simulation
scheme. A universal framework in identifying optimal QMC schemes has been
desired. Here, we propose a general framework using automatic differentiation
(AD) to automatically search for the best continuously-parameterized QMC
scheme, which we call "automatic differentiable sign mitigation" (ADSM). We
further apply the ADSM framework to the honeycomb lattice Hubbard model with
Rashba spin-orbit coupling and demonstrate ADSM's effectiveness in mitigating
its sign problem. For the model under study, ADSM leads a significant power-law
acceleration in computation time (the computation time is reduced from to
the order of with ).Comment: 4.1 pages + supplemental materials, 4 figure
Automatic Differentiable Monte Carlo: Theory and Application
Differentiable programming has emerged as a key programming paradigm
empowering rapid developments of deep learning while its applications to
important computational methods such as Monte Carlo remain largely unexplored.
Here we present the general theory enabling infinite-order automatic
differentiation on expectations computed by Monte Carlo with unnormalized
probability distributions, which we call "automatic differentiable Monte Carlo"
(ADMC). By implementing ADMC algorithms on computational graphs, one can also
leverage state-of-the-art machine learning frameworks and techniques to
traditional Monte Carlo applications in statistics and physics. We illustrate
the versatility of ADMC by showing some applications: fast search of phase
transitions and accurately finding ground states of interacting many-body
models in two dimensions. ADMC paves a promising way to innovate Monte Carlo in
various aspects to achieve higher accuracy and efficiency, e.g. easing or
solving the sign problem of quantum many-body models through ADMC.Comment: 11.5 pages + supplemental materials, 4 figure
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