On the computational complexity of curing non-stoquastic Hamiltonians

Quantum many-body systems whose Hamiltonians are non-stoquastic, i.e., have positive off-diagonal matrix elements in a given basis, are known to pose severe limitations on the efficiency of Quantum Monte Carlo algorithms designed to simulate them, due to the infamous sign problem. We study the compu...

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Bibliographic Details
Published in:Nature communications Vol. 10; no. 1; pp. 1571 - 9
Main Authors: Marvian, Milad, Lidar, Daniel A., Hen, Itay
Format: Journal Article
Language:English
Published: London Nature Publishing Group UK 05.04.2019
Nature Publishing Group
Nature Portfolio
Subjects:
639/766/483
639/766/483/3926
639/766/483/481
639/766/483/640
Algorithms
Complexity
Computation
Computer applications
Computer simulation
Curing
Decomposition
Humanities and Social Sciences
multidisciplinary
Qubits (quantum computing)
Science
Science (multidisciplinary)
ISSN:2041-1723, 2041-1723
Online Access:Get full text
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Summary:Quantum many-body systems whose Hamiltonians are non-stoquastic, i.e., have positive off-diagonal matrix elements in a given basis, are known to pose severe limitations on the efficiency of Quantum Monte Carlo algorithms designed to simulate them, due to the infamous sign problem. We study the computational complexity associated with ‘curing’ non-stoquastic Hamiltonians, i.e., transforming them into sign-problem-free ones. We prove that if such transformations are limited to single-qubit Clifford group elements or general single-qubit orthogonal matrices, finding the curing transformation is NP-complete. We discuss the implications of this result. Non-stoquastic Hamiltonians are known to be hard to simulate due to the infamous sign problem. Here, the authors study the computational complexity of transforming such Hamiltonians into stoquastic ones and prove that the task is NP-complete even for the simplest class of transformations.
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ISSN:2041-1723
2041-1723
DOI:10.1038/s41467-019-09501-6