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

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.

References in corpus (6)

• Mathematical Foundation of Quantum Annealing
• Quantum annealing with antiferromagnetic fluctuations
• Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stochastic Hamiltonians
• Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics
• Experimental demonstration of perturbative anticrossing mitigation using non-uniform driver Hamiltonians
• Why and when is pausing beneficial in quantum annealing?