| Autor: |
Day AGR; Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA., Bukov M; Department of Physics, University of California, Berkeley, California 94720, USA., Weinberg P; Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA., Mehta P; Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA., Sels D; Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.; Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA.; Theory of Quantum and Complex Systems, Universiteit Antwerpen, B-2610 Antwerpen, Belgium. |
| Abstrakt: |
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 bang-bang protocols. We present compelling numerical evidence for a universal spin-glasslike 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 satisfiability 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. |
