Macroscopic quantum tunneling (MQT), where an extensive number of quantum degrees of freedom change configuration simultaneously to cross a large intermediate energy barrier, is a spectacular, and elusive, phenomenon in many-body physics. In the first part of the talk, we build on the concept of Symphonic Tunneling introduced in Mossi et al (arXiv:2306.10632), where MQT is accelerated by tuning oscillating fields based on details of the underlying system, to consider very high frequency drives. We consider the ferromagnetic N-spin transition in transverse field Ising models. I will discuss the theoretical derivation of tunneling rates in 1d, and show numerical studies obtained in higher dimensions. As MQT transitions also act as a bottleneck to quantum optimization algorithms, accelerating MQT is of significant scientific and practical interest. In the second part of the talk, I will introduce a new quantum algorithm called IST-SAT (Iterative Symphonic Tunneling for Boolean Satisfiability Problems) which circumvents computing gradients and parameter optimization. I will share benchmarking results of the IST-SAT algorithm on sets of doubly hard MAX-3-XORSAT instances, which are exponentially difficult for both exact and approximate optimization for all known classical and quantum methods. We expect that methods from symphonic tunneling and IST-SAT are generic and should generalize to other quantum optimization problems which are bottlenecked by exponentially small gaps and first-order transitions.
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