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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Vydané v:	Nature communications Ročník 10; číslo 1; s. 1571 - 9
Hlavní autori:	Marvian, Milad, Lidar, Daniel A., Hen, Itay
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	London Nature Publishing Group UK 05.04.2019 Nature Publishing Group Nature Portfolio
Predmet:	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
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Abstract	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.
AbstractList	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.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. 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. 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. 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. 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.
ArticleNumber	1571
Author	Lidar, Daniel A. Hen, Itay Marvian, Milad
Author_xml	– sequence: 1 givenname: Milad surname: Marvian fullname: Marvian, Milad email: mmarvian@mit.edu organization: Research Laboratory of Electronics, Massachusetts Institute of Technology, Department of Electrical and Computer Engineering, University of Southern California, Center for Quantum Information Science & Technology, University of Southern California – sequence: 2 givenname: Daniel A. surname: Lidar fullname: Lidar, Daniel A. organization: Department of Electrical and Computer Engineering, University of Southern California, Center for Quantum Information Science & Technology, University of Southern California, Department of Physics and Astronomy, University of Southern California, Department of Chemistry, University of Southern California – sequence: 3 givenname: Itay orcidid: 0000-0002-7009-7739 surname: Hen fullname: Hen, Itay organization: Center for Quantum Information Science & Technology, University of Southern California, Department of Physics and Astronomy, University of Southern California, Information Sciences Institute, University of Southern California
BackLink	https://www.ncbi.nlm.nih.gov/pubmed/30952854$$D View this record in MEDLINE/PubMed
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CitedBy_id	crossref_primary_10_1103_PhysRevA_105_062601 crossref_primary_10_1103_PhysRevResearch_4_043221 crossref_primary_10_1088_1361_6633_ac8c54 crossref_primary_10_1103_PhysRevA_104_052616 crossref_primary_10_1088_1742_5468_ab9e64 crossref_primary_10_1145_3639528_3639535 crossref_primary_10_1088_1361_6633_ab85b8 crossref_primary_10_1103_PhysRevResearch_2_032060 crossref_primary_10_1103_PhysRevB_107_245144 crossref_primary_10_1103_PhysRevApplied_13_034037 crossref_primary_10_1002_qute_201900108 crossref_primary_10_1088_1742_5468_abc7c7 crossref_primary_10_1103_PhysRevResearch_2_033515 crossref_primary_10_1103_PhysRevResearch_3_023080 crossref_primary_10_1109_ACCESS_2023_3323847 crossref_primary_10_1073_pnas_2006103117 crossref_primary_10_1103_PhysRevB_106_214416 crossref_primary_10_1103_PhysRevResearch_2_043032 crossref_primary_10_1103_PhysRevResearch_3_043013 crossref_primary_10_22331_q_2025_07_09_1788 crossref_primary_10_1103_jt8s_hzhd crossref_primary_10_1088_2058_9565_ac16b8 crossref_primary_10_1103_PRXQuantum_6_020312 crossref_primary_10_1088_1367_2630_ab2ee7 crossref_primary_10_1103_PhysRevA_101_012310 crossref_primary_10_1016_j_future_2024_06_012
Cites_doi	10.1017/CBO9780511614460 10.1103/PhysRevB.89.134422 10.1103/PhysRevE.97.043303 10.1103/PhysRevLett.94.170201 10.1103/PhysRevA.92.042325 10.1088/0305-4470/15/10/028 10.1016/0166-218X(84)90081-7 10.1137/140998287 10.1103/PhysRevB.93.054408 10.1103/PhysRevB.41.9301 10.1137/08072689X 10.1063/1.4936216 10.1103/PhysRevLett.117.197203 10.1093/oso/9780198517962.001.0001 10.1007/978-1-4684-2001-2_9
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Snippet	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... Non-stoquastic Hamiltonians are known to be hard to simulate due to the infamous sign problem. Here, the authors study the computational complexity of...
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SubjectTerms	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)
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Title	On the computational complexity of curing non-stoquastic Hamiltonians
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