Fast quantum communication in linear networks

¹ U.S. Army Research Laboratory, Computational and Information Sciences Directorate - Adelphi, MD 20783, USA
² Department of Physics, University of Massachusetts at Boston - Boston, MA 02125, USA
³ Hearne Institute for Theoretical Physics, Louisiana State University - Baton Rouge, LA 70803, USA
⁴ Department of Automation, Tsinghua University & Center for Quantum Information Science and Technology, TNList - Beijing, 100084, China
⁵ Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, Qatar Foundation Doha, Qatar
⁶ Department of Chemistry, Princeton University - Princeton, NJ 08544, USA

Received: 4 February 2016
Accepted: 2 June 2016

Abstract

Here we consider the speed at which quantum information can be transferred between the nodes of a linear network. Because such nodes are linear oscillators, this speed is also important in the cooling and state preparation of mechanical oscillators, as well as in frequency conversion. We show that if there is no restriction on the size of the linear coupling between two oscillators, then there exist control protocols that will swap their respective states with high fidelity within a time much shorter than a single oscillation period. Standard gradient search methods fail to find these fast protocols. We were able to do so by augmenting standard search methods with a path-tracing technique, demonstrating that this technique has remarkable power to solve time-optimal control problems, as well as confirming the highly challenging nature of these problems. As a further demonstration of the power of path tracing, first introduced by Moore Tibbets et al. (Phys. Rev. A, 86 (2012) 062309), we apply it to the generation of entanglement in a linear network.