Glassy phase of optimal quantum control

We study the problem of preparing a quantum many-body system from an initial to a target state by optimizing the fidelity over the family of hang-hang protocols. We present compelling numerical evidence for a universal spin-glasslikc transition controlled by the protocol time duration. The glassy critical point is marked by a proliferation of protocols with close-to-optimal fidelity and with a true optimum that appears exponentially difficult to locate. Using a machine learning (ML) inspired framework based on the manifold learning algorithm t-distributed stochastic neighbor embedding, we are able to visualize the geometry of the high-dimensional control landscape in an effective low-dimensional representation. Across the transition, the control landscape features an exponential number of clusters separated by extensive barriers, which bears a strong resemblance with replica symmetry breaking in spin glasses and random satisfiahility problems. We further show that the quantum control landscape maps onto a disorder-free classical Ising model with frustrated nonlocal, multibody interactions. Our work highlights an intricate but unexpected connection between optimal quantum control and spin glass physics, and shows how tools from ML can be used to visualize and understand glassy optimization landscapes.

Jaar van publicatie:2019

Trefwoorden:A1 Journal article

BOF-keylabel:ja

BOF-publication weight:6

CSS-citation score:2

Auteurs:International

Authors from:Higher Education

Toegankelijkheid:Open