Freiburg 2019 – wissenschaftliches Programm
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FM: Fall Meeting
FM 17: Quantum Computation: Simulation I
FM 17.6: Talk
Montag, 23. September 2019, 17:45–18:00, 1010
Easing the Monte Carlo Sign Problem — •Dominik Hangleiter1, Ingo Roth1, Daniel Nagaj2, and Jens Eisert1 — 1FU Berlin, 14195 Berlin — 2Slovak Academy of Sciences, Bratislava, Slovakia
Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems -- their phase transitions, their ground and thermal state properties -- but also quantum circuit simulation. However, QMC methods face the severe limitation of a `sign problem' for many quantum systems, in particular so for fermionic systems. Here, we introduce a novel universal and versatile framework for `easing the sign problem' by local basis changes in practical condensed-matter applications, realising that it is a basis-dependent property. We introduce the optimisation problem of finding the basis in which the sign problem is smallest by means of minimizing the positive part of the Hamiltonian matrix. We then demonstrate that this problem is practically feasible using geometric optimization methods by the example of frustrated ladder systems, showing that the sign problem can be greatly reduced. Complementing this pragmatic mindset, as our main rigorous result we show that easing the sign problem can be a computationally hard task, even in situations in which deciding whether an exact solution exists can be done efficiently.