On the Phase Transition of Corrupted Sensing

In \cite{FOY2014}, a sharp phase transition has been numerically observed when a constrained convex procedure is used to solve the corrupted sensing problem. In this paper, we present a theoretical analysis for this phenomenon. Specifically, we establish the threshold below which this convex procedure fails to recover signal and corruption with high probability. Together with the work in \cite{FOY2014}, we prove that a sharp phase transition occurs around the sum of the squares of spherical Gaussian widths of two tangent cones. Numerical experiments are provided to demonstrate the correctness and sharpness of our results.Comment: To appear in Proceedings of IEEE International Symposium on Information Theory 201

Banking reforms, performance and risk in China

We investigate the impact of the banking reform started from 2005 on ownership structures in China on commercial banks’ profitability, efficiency and risk over the period 2000–2012, providing comprehensive evidence on the impact of banking reform in China. We find that banks on average tend to have higher profitability, lower risk and lower efficiency after the reforms, and the results are robust with our difference-in-difference approach. Our results also show that the Big 5 state-owned banks (SOCB) underperform banks with other types of ownership when risk is measured by non-performing loans (NPLs) over the entire study period but tend to have fewer NPLs than other banks during the post-reform period. Our results provide some supporting evidence on the ongoing banking reforms in China, suggesting that attracting strategic foreign investors and listing SOCBs on stock exchanges appear to be effective ways to help SOCBs deal with the problem of NPLs and manage their risk

Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms

Nonadiabatic geometric quantum computation (NGQC) has been developed to realize fast and robust geometric gate. However, the conventional NGQC is that all of the gates are performed with exactly the sameamount of time, whether the geometric rotation angle is large or small, due to the limitation of cyclic condition. Here, we propose an unconventional scheme, called nonadiabatic noncyclic geometric quantum computation(NNGQC), that arbitrary single- and two-qubit geometric gate can be constructed via noncyclic non-Abeliangeometric phase. Consequently, this scheme makes it possible to accelerate the implemented geometric gatesagainst the effects from the environmental decoherence. Furthermore, this extensible scheme can be applied invarious quantum platforms, such as superconducting qubit and Rydberg atoms. Specifically, for single-qubit gate,we make simulations with practical parameters in neutral atom system to show the robustness of NNGQC and also compare with NGQC using the recent experimental parameters to show that the NNGQC can significantly suppress the decoherence error. In addition, we also demonstrate that nontrivial two-qubit geometric gate can berealized via unconventional Rydberg blockade regime within current experimental technologies. Therefore, ourscheme provides a promising way for fast and robust neutral-atom-based quantum computation.Comment: 6 pages, 6 figures. Published visio