The sign problem, non-stoquasticity and everything in between

ORAL  · Invited

Abstract

The quantum Monte Carlo sign problem has been rightfully recognized as one of the grand challenges of computational physics. This problem encapsulates our inability to develop a proper understanding of many important quantum many-body phenomena in physics, chemistry and well beyond. Despite its centrality, the circumstances under which the sign problem arises or can be resolved as well as its interplay with the related notion of `non-stoquasticity' are often not very well understood. In this talk, I will attempt to elucidate the circumstances under which the sign problem emerges and clear up some of the confusion surrounding this intricate computational phenomenon. Making use of the recently introduced off-diagonal series expansion quantum Monte Carlo technique, I will discuss a sufficient and necessary condition for the simulability of quantum many-body Hamiltonians and provide a construction for non-stoquastic, yet sign-problem-free and hence QMC-simulable, quantum many-body models.

*The research is based upon work (partially) supported by the Office of the Director of National Intelligence (ODNI), Intelligence AdvancedResearch Projects Activity (IARPA) and the Defense Advanced Research Projects Agency (DARPA), via the U.S. Army Research Officecontract W911NF-17-C-0050. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarilyrepresenting the official policies or endorsements, either expressed or implied, of the ODNI, IARPA, DARPA, or the U.S. Government. The U.S. Governmentis authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon.

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Publication: [1] I. Hen, ``Determining quantum Monte Carlo simulability with geometric phases'', Physical Review Research 3, 023080 (2021).
[2] M. Marvian, D. A. Lidar and I. Hen, ``On the Computational Complexity of Curing Non-Stoquastic Hamiltonians'', Nature Communications 10, 1571 (2019).
[3] J. Klassen, M. Marvian, S. Piddock, M. Ioannou, I. Hen and B. Terhal, ``Hardness and Ease of Curing the Sign Problem for Two-Local Qubit Hamiltonians'', SIAM J. Comput., 49(6), 1332–1362 (2020).
[4] L. Gupta and I. Hen, ``Elucidating the interplay between non-stoquasticity and the sign problem'', Advanced Quantum Technologies. arXiv:1910.13867 (2019).
[5] I. Hen, Resolution of the Sign Problem for a Frustrated Triplet of Spins, Phys. Rev. E 99, 033306 (2019).

Presenters

  • Itay Hen

    • University of Southern California

Authors

  • Itay Hen

    • University of Southern California