Nonadiabatic holonomic quantum computation based on commutation relation

Nonadiabatic holonomic quantum computation has received increasing attention due to the merits of both robustness against control errors and high-speed implementation. A crucial step in realizing nonadiabatic holonomic quantum computation is to remove the dynamical phase from the total phase. For this reason, previous schemes of nonadiabatic holonomic quantum computation have to resort to the parallel transport condition, i.e., requiring the instantaneous dynamical phase to be always zero. In this paper, we put forward a strategy to design nonadiabatic holonomic quantum computation, which is based on a commutation relation rather than the parallel transport condition. Instead of requiring the instantaneous dynamical phase to be always zero, the dynamical part of the total phase is separated from the geometric part and then removed by properly choosing evolution parameters. This strategy enhances the flexibility to realize nonadiabatic holonomic quantum computation as the commutation relation is more relaxed than the parallel transport condition. It provides more options for realizing nonadiabatic holonomic quantum computation and hence allows us to optimize realizations such as the evolution time and evolution paths.Comment: 7 pages, 2 figure

Functional Electrical Stimulation mediated by Iterative Learning Control and 3D robotics reduces motor impairment in chronic stroke

Background: Novel stroke rehabilitation techniques that employ electrical stimulation (ES) and robotic technologies are effective in reducing upper limb impairments. ES is most effective when it is applied to support the patients’ voluntary effort; however, current systems fail to fully exploit this connection. This study builds on previous work using advanced ES controllers, and aims to investigate the feasibility of Stimulation Assistance through Iterative Learning (SAIL), a novel upper limb stroke rehabilitation system which utilises robotic support, ES, and voluntary effort. Methods: Five hemiparetic, chronic stroke participants with impaired upper limb function attended 18, 1 hour intervention sessions. Participants completed virtual reality tracking tasks whereby they moved their impaired arm to follow a slowly moving sphere along a specified trajectory. To do this, the participants’ arm was supported by a robot. ES, mediated by advanced iterative learning control (ILC) algorithms, was applied to the triceps and anterior deltoid muscles. Each movement was repeated 6 times and ILC adjusted the amount of stimulation applied on each trial to improve accuracy and maximise voluntary effort. Participants completed clinical assessments (Fugl-Meyer, Action Research Arm Test) at baseline and post-intervention, as well as unassisted tracking tasks at the beginning and end of each intervention session. Data were analysed using t-tests and linear regression. Results: From baseline to post-intervention, Fugl-Meyer scores improved, assisted and unassisted tracking performance improved, and the amount of ES required to assist tracking reduced. Conclusions: The concept of minimising support from ES using ILC algorithms was demonstrated. The positive results are promising with respect to reducing upper limb impairments following stroke, however, a larger study is required to confirm this