Hypothesis testing of quantum Monte Carlo simulations

Jincheng Zhang

The Riemann Hypothesis, a long-standing unsolved problem in number theory, remains one of the most challenging mathematical puzzles. Traditional methods struggle to efficiently explore the vast solution space, hindering progress towards a definitive proof. This paper proposes a novel approach utilizing quantum-enhanced Riemann Hypothesis testing, specifically employing a hybrid quantum-classical algorithm. We hypothesize that quantum superposition, coupled with probabilistic error correction, can dramatically accelerate the search for solutions and provide novel insights into the hypothesis. The core mechanism involves a 'Quantum Monte Carlo' simulation, refined with classical optimization, designed to effectively navigate the hypothesis space. This work offers a potential paradigm shift in the testing process, potentially unlocking new avenues for investigation and pushing the boundaries of number-theoretic research.

Matthias Troyer, Philipp Werner, Adolfo Avella +1 more

Hyeonseong Jung, Shiho Kim

Fran�ois Delyon, B. Bernu, Markus Holzmann

Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time-discretized diffusion process. We present a robust and practical method to determine the effective variance of general observables and show how to verify the equilibrium hypothesis by the Kolmogorov-Smirnov test. We then derive scaling laws of the efficiency illustrated by variational Monte Carlo calculations on the two-dimensional electron gas.

Kurt Binder, Dieter W. Heermann

Fei Lin, Jurij Šmakov, Erik Schwartz Sørensen +2 more

We generalize the imaginary-chemical-potential quantum Monte Carlo (QMC) method proposed by Dagotto [Phys. Rev. B 41, R811 (1990)] to systems without particle-hole symmetry. The generalized method is tested by comparing the results of the QMC simulations and exact diagonalization on small Hubbard molecules, such as tetrahedron and truncated tetrahedron. Results of the application of the method to the C60 Hubbard molecule are discussed.