Paul Warburton (UCL)
Quantum Annealing – Beyond the Transverse-Field Ising Model
Quantum annealing with the transverse-field Ising model (TFIM) has been shown experimentally to give excellent performance at the 5000-qubit level for approximate solutions to problems in quantum simulation [1]. For exact solutions to combinatorial optimisation problems, however, the annealing rate is limited by the minimum gap. The gap occurs at an avoided level crossing (or equivalently at a quantum phase transition) and results in an annealing time which typically scales exponentially with system size.
Here we numerically show that using terms that go beyond the TFIM can enhance the minimum gap, potentially leading to reduced anneal times and/or fewer errors. In particular we show that the addition of XX interaction terms (which couple states separated by a Hamming distance of two) leads to improved scaling of the gap minimum for maximum weighted independent set problems on both a toy bipartite graph [2] and random Erdős-Renyi graphs [3]. We further show how an effective Hamiltonian involving XX interactions can be implemented using only the conventional set of TFIM fields and couplers – i.e. X, Z and ZZ [4].
This work was performed in collaboration with Natasha Feinstein, Bobby Banks, Roopayan Ghosh, Luca Nutricati and Sougato Bose.
[1] King et al. Science 388 199(2025) [2] Feinstein, PAW et al. Phys. Rev. A 110 042609 (2024) [3] Nutricati, PAW et al. arXiv:2409.16350 (2024) [4] Banks, PAW et al., arXiv:2503.16663 (2025)