Built on

T. F. Gonzalez, “Clustering to minimize the maximum intercluster distance,” Theoretical Computer Science
1985
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N. J. Cerf and O. C. Martin, “Projection Monte Carlo methods : an algorithmic analysis,” International Journal of Modern Physics C
1995
Earlier work this paper cites.
M. Grassl, M. Rötteler, and T. Beth, “Computing local invariants of quantum-bit systems,” Phys. Rev. A
1998
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N. Linden, S. Popescu, and A. Sudbery, “Nonlocal Parameters for Multiparticle Density Matrices,” Physical Review Letters
1999
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S. Sorella and L. Capriotti, “Green function Monte Carlo with stochastic reconfiguration: An effective remedy for the sign problem,” Physical Review B - Condensed Matter and Materials Physics
2000
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R. F. Bishop and D. J. J. Farnell, “Marshall-Peierls sign rules, the quantum monte carlo method, and frustration,” International Journal of Modern Physics B
2001
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Y. Makhlin, “Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations,” Quantum Information Processing
2002
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C. Wu and S.-C. Zhang, “Sufficient condition for absence of the sign problem in the fermionic quantum monte carlo algorithm,” Phys. Rev. B
2005
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S. Bravyi, D. P. DiVincenzo, R. I. Oliveira, and B. M. Terhal, “The Complexity of Stoquastic Local Hamiltonian Problems,” Quantum Information and Computation
2008
Earlier work this paper cites.

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2018

Two-local qubit Hamiltonians: when are they stoquastic?

Klassen, Joel, Terhal, Barbara M.

Understand

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.

Built on

T. F. Gonzalez, “Clustering to minimize the maximum intercluster distance,” Theoretical Computer Science
1985
Earlier work this paper cites.
N. J. Cerf and O. C. Martin, “Projection Monte Carlo methods : an algorithmic analysis,” International Journal of Modern Physics C
1995
Earlier work this paper cites.
M. Grassl, M. Rötteler, and T. Beth, “Computing local invariants of quantum-bit systems,” Phys. Rev. A
1998
Earlier work this paper cites.
N. Linden, S. Popescu, and A. Sudbery, “Nonlocal Parameters for Multiparticle Density Matrices,” Physical Review Letters
1999
Earlier work this paper cites.
S. Sorella and L. Capriotti, “Green function Monte Carlo with stochastic reconfiguration: An effective remedy for the sign problem,” Physical Review B - Condensed Matter and Materials Physics
2000
Earlier work this paper cites.
R. F. Bishop and D. J. J. Farnell, “Marshall-Peierls sign rules, the quantum monte carlo method, and frustration,” International Journal of Modern Physics B
2001
Earlier work this paper cites.
Y. Makhlin, “Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations,” Quantum Information Processing
2002
Earlier work this paper cites.
C. Wu and S.-C. Zhang, “Sufficient condition for absence of the sign problem in the fermionic quantum monte carlo algorithm,” Phys. Rev. B
2005
Earlier work this paper cites.
S. Bravyi, D. P. DiVincenzo, R. I. Oliveira, and B. M. Terhal, “The Complexity of Stoquastic Local Hamiltonian Problems,” Quantum Information and Computation
2008
Earlier work this paper cites.