Nonstoquastic Hamiltonians and Quantum Annealing of an Ising Spin Glass

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We study the role of Hamiltonian complexity in the performance of quantum annealers.

• We consider two general classes of annealing Hamiltonians: stoquastic ones, which can be simulated efficiently using the quantum Monte Carlo algorithm, and nonstoquastic ones, which cannot be treated efficiently.
• We implement the latter by adding antiferromagnetically coupled two-spin driver terms to the traditionally studied transverse-field Ising model, and compare their performance to that of similar stoquastic Hamiltonians with ferromagnetically coupled additional terms.
• We focus on a model of long-range Ising spin glass as our problem Hamiltonian and carry out the comparison between the annealers by numerically calculating their success probabilities in solving random instances of the problem Hamiltonian in systems of up to 17 spins.