Two-local qubit Hamiltonians: when are they stoquastic?

Joel Klassen; Barbara M. Terhal

doi:10.22331/q-2019-05-06-139

Two-local qubit Hamiltonians: when are they stoquastic?

Joel Klassen¹ and Barbara M. Terhal^1,2

¹QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands
²Institute for Theoretical Nanoelectronics, Forschungszentrum Juelich, D-52425 Juelich, Germany

Published:	2019-05-06, volume 3, page 139
Eprint:	arXiv:1806.05405v3
Doi:	https://doi.org/10.22331/q-2019-05-06-139
Citation:	Quantum 3, 139 (2019).

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Abstract

We examine the problem of determining if a 2-local Hamiltonian is stoquastic by local basis changes. We analyze this problem for two-qubit Hamiltonians, presenting some basic tools and giving a concrete example where using unitaries beyond Clifford rotations is required in order to decide stoquasticity. We report on simple results for $n$-qubit Hamiltonians with identical 2-local terms on bipartite graphs. Our most significant result is that we give an efficient algorithm to determine whether an arbitrary $n$-qubit XYZ Heisenberg Hamiltonian is stoquastic by local basis changes.

► BibTeX data

@article{Klassen2019twolocalqubit,
  doi = {10.22331/q-2019-05-06-139},
  url = {https://doi.org/10.22331/q-2019-05-06-139},
  title = {Two-local qubit {H}amiltonians: when are they stoquastic?},
  author = {Klassen, Joel and Terhal, Barbara M.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {139},
  month = may,
  year = {2019}
}

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[4] Gioele Consani and Paul A Warburton, "Effective Hamiltonians for interacting superconducting qubits: local basis reduction and the Schrieffer–Wolff transformation", New Journal of Physics 22 5, 053040 (2020).

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[8] Joel Klassen, Milad Marvian, Stephen Piddock, Marios Ioannou, Itay Hen, and Barbara M. Terhal, "Hardness and Ease of Curing the Sign Problem for Two-Local Qubit Hamiltonians", SIAM Journal on Computing 49 6, 1332 (2020).

[9] A. Ciani and B. M. Terhal, "Stoquasticity in circuit QED", Physical Review A 103 4, 042401 (2021).

[10] Eleni Marina Lykiardopoulou, Alex Zucca, Sam A. Scivier, and Mohammad H. Amin, "Improving nonstoquastic quantum annealing with spin-reversal transformations", Physical Review A 104 1, 012619 (2021).

[11] I. Ozfidan, C. Deng, A.Y. Smirnov, T. Lanting, R. Harris, L. Swenson, J. Whittaker, F. Altomare, M. Babcock, C. Baron, A.J. Berkley, K. Boothby, H. Christiani, P. Bunyk, C. Enderud, B. Evert, M. Hager, A. Hajda, J. Hilton, S. Huang, E. Hoskinson, M.W. Johnson, K. Jooya, E. Ladizinsky, N. Ladizinsky, R. Li, A. MacDonald, D. Marsden, G. Marsden, T. Medina, R. Molavi, R. Neufeld, M. Nissen, M. Norouzpour, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, M. Reis, T. Prescott, C. Rich, Y. Sato, G. Sterling, N. Tsai, M. Volkmann, W. Wilkinson, J. Yao, and M.H. Amin, "Demonstration of a Nonstoquastic Hamiltonian in Coupled Superconducting Flux Qubits", Physical Review Applied 13 3, 034037 (2020).

[12] Adrian Chapman and Steven T. Flammia, "Characterization of solvable spin models via graph invariants", Quantum 4, 278 (2020).

[13] Valentin Torggler, Philipp Aumann, Helmut Ritsch, and Wolfgang Lechner, "A Quantum N-Queens Solver", Quantum 3, 149 (2019).

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