Eigenvalue-invariant transformation of Ising problem for anti-crossing mitigation in quantum annealing

TL;DR

This paper introduces the Energy Landscape Transformation of Ising Problems (ELTIP), which effectively mitigates anti-crossing in quantum annealing, outperforming non-stoquastic Hamiltonians in reducing annealing time for certain problems.

Contribution

The paper proposes ELTIP, a novel eigenvalue-invariant transformation method that eliminates anti-crossing in quantum annealing, enhancing adiabaticity and reducing annealing time.

Findings

ELTIP removes anti-crossing in tested problems.

Non-stoquastic Hamiltonian reduces anti-crossing when energy gap is small.

ELTIP shortens annealing time more effectively than non-stoquastic Hamiltonian.

Abstract

We have proposed the energy landscape transformation of Ising problems (ELTIP), which changes the combination of the state and eigenvalue without changing all the original eigenvalues [arXiv:2202.05927]. We study how the ELTIP affects the anti-crossing between two levels of the ground and first excited states during quantum annealing. We use a 5-spin maximum-weighted independent set for the problem to numerically investigate the anticrossing. For comparison, we introduce a non-stoquastic Hamiltonian that adds antiferromagnetic interaction to the normal transverse magnetic field. Annealing with the non-stoquastic Hamiltonian is effective for difficult problems. The non-stoquastic Hamiltonian mitigates the anti-crossing when only the energy gap between the ground state and the first excited state of the final state is small. When the ELTIP is used, the anti-crossing disappears. For the problems investigated in this paper, the ELTIP shortens the annealing time to guarantee adiabatic change more than the non-stoquastic Hamiltonian.