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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[10] 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).

[11] Tameem Albash, "Validating a two-qubit nonstoquastic Hamiltonian in quantum annealing", Physical Review A 101 1, 012310 (2020).

[12] Dorit Aharonov and Alex B. Grilo, "Stoquastic PCP vs. Randomness", arXiv:1901.05270.

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