Yimin Ge

Chunbiao Gan, Haihui Yuan, Shixi Yang et al.

This paper presents a systematic approach to exponentially stabilize the periodic orbits of multi-domain hybrid systems arising from 3D bipedal walking. Firstly, the method of Poincare sections is extended to the hybrid systems with multiple domains. Then, based on the properties of the Poincare maps, a continuous piecewise feedback control strategy is presented, and three methods are furthermore given to design the controller parameters based on the developed theorems. By those design methods, the controller parameters in each continuous phase can be designed independently, which allows the strategy to be applied to hybrid systems with multiple domains. Finally, the proposed strategy is illustrated by a simulation example. To show that the proposed strategy is not limited to bipedal robots with left-right symmetry property which is assumed in some previous works, an underactuated 3D bipedal robot with asymmetric walking gait is considered.

Vedran Dunjko, Yimin Ge, J. Ignacio Cirac

Suppose we have a small quantum computer with only M qubits. Can such a device genuinely speed up certain algorithms, even when the problem size is much larger than M? Here we answer this question to the affirmative. We present a hybrid quantum-classical algorithm to solve 3SAT problems involving n>>M variables that significantly speeds up its fully classical counterpart. This question may be relevant in view of the current quest to build small quantum computers.