Quantum annealing with ²Σ molecules

Quantum annealing (QA) has been considered as a practical quantum algorithm for NP-complete and NP-hard optimization problems. While most of the QA devices currently in use are based on superconducting circuits using stoquastic Hamiltonians, Quantum Monte Carlo algorithms can efficiently simulate stoquastic dynamics and therefore no exponential speed-up is expected from these systems. Ultracold molecules in optical lattices have been recently considered as platforms for quantum simulation. ²Σ molecules display an avoided crossing in the spin-rotational energy levels when placed in superimposed DC electric and magnetic fields. Dipole-dipole interactions between molecules in rotational states close to the avoided crossing lead to an XXZ model which can be tuned from an XY model at the crossing to an Ising model away from the crossing. In this work, we propose two architectures for quantum annealers based on ²Σ molecules placed in superimposed electric and magnetic fields. Qubits can be designed using pairs of molecules in combined DC fields or molecules in microwave fields. The latter results in a non-stoquastic Hamiltonian during the annealing.