Exponential acceleration of collective quantum tunneling in the transverse field Ising model using high frequency AC drives (Part 1)*

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. Because MQT rates generically decay exponentially in system size, they are naturally very slow, and extremely sensitive to noise, control error and other similar issues. As MQT transitions also act as a bottleneck to quantum optimization algorithms, accelerating MQT is of significant scientific and practical interest. In this talk, we build on the concept of Symphonic Tunneling introduced in Mossi et al (arXiv:2306.10632), where MQT is accelerated by tuning AC 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, and show that if the amplitude and frequency of the drive is allowed to increase logarithmically in system size, the collective tunneling rate between ferromagnetic states can cross over from exponential to polynomial (empirically, linear) in system size, without meaningfully heating the system. We discuss the theoretical derivation of this effect in 1d, and its extension to higher dimensions.