title: Quantum brachistochrone curves as geodesics: obtaining accurate minimum-time protocols for the control of quantum systems.
abstract: Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the brachistochrone problem, and apply this method to two examples demonstrating its power.
authors.affiliation: Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.|Department of Physics, University of Massachusetts at Boston, Boston, Massachusetts 02125, USA.|Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803, USA.
authors.forename: Xiaoting
authors.initials: X
authors.lastname: Wang
authors.affiliation: Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.|Dipartimento di Fisica, Università Degli Studi di Torino and INFN, Sezione di Torino, I-10125 Torino, Italy.|Institute for Scientific Interchange Foundation, I-10126 Torino, Italy.
authors.forename: Michele
authors.initials: M
authors.lastname: Allegra
authors.affiliation: Department of Physics, University of Massachusetts at Boston, Boston, Massachusetts 02125, USA.|Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803, USA.
authors.forename: Kurt
authors.initials: K
authors.lastname: Jacobs
authors.affiliation: Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.|Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Seth
authors.initials: S
authors.lastname: Lloyd
authors.affiliation: Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Cosmo
authors.initials: C
authors.lastname: Lupo
authors.affiliation: Google Research, Venice, California 90291, USA.
authors.forename: Masoud
authors.initials: M
authors.lastname: Mohseni