Two-local qubit Hamiltonians: when are they stoquastic?

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.

arXiv comment24 pages

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• Expressive power of complex-valued restricted Boltzmann machines for solving non-stoquastic Hamiltonians
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• Effective Hamiltonians for interacting superconducting qubits -- local basis reduction and the Schrieffer-Wolff transformation
• Determining QMC simulability with geometric phases
• A Quantum N-Queens Solver
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• All you need is spin: SU(2) equivariant variational quantum circuits based on spin networks
• Improving nonstoquastic quantum annealing with spin-reversal transformations
• A rapidly mixing Markov chain from any gapped quantum many-body system
• Validating a Two Qubit Non-Stoquastic Hamiltonian in Quantum Annealing
• Simultaneous Stoquasticity
• StoqMA vs. MA: the power of error reduction
• Classical Simulation of High Temperature Quantum Ising Models