The multi-level and multi-dimensional quantum wavelet packet transforms

© 2018, The Author(s). The classical wavelet packet transform has been widely applied in the information processing field. It implies that the quantum wavelet packet transform (QWPT) can play an important role in quantum information processing. In this paper, we design quantum circuits of a generalized tensor product (GTP) and a perfect shuffle permutation (PSP). Next, we propose multi-level and multi-dimensional (1D, 2D and 3D) QWPTs, including a Haar QWPT (HQWPT), a D4 QWPT (DQWPT) based on the periodization extension and their inverse transforms for the first time, and prove the correctness based on the GTP and PSP. Furthermore, we analyze the quantum costs and the time complexities of our proposed QWPTs and obtain precise results. The time complexities of HQWPTs is at most 6 on 2n elements, which illustrates high-efficiency of the proposed QWPTs. Simulation experiments demonstrate that the proposed QWPTs are correct and effective

An improved model-free adaptive integral sliding mode control for a class of nonlinear discrete-time systems

For a class of uncertain single-input single-output (SISO) nonlinear discrete-time systems, an improved model-free adaptive integral sliding mode control (MFA-ISMC) algorithm is proposed based on a disturbance observer. The pseudo-partial derivative (PPD) estimation algorithm used to describe the system dynamics is modified and the stability of the closed-loop system is guaranteed. It is shown that the corresponding closed-loop system performance is improved and the effectiveness of the proposed method is demonstrated by a simulation example

Degradation mechanism of tris(2-chloroethyl) phosphate (TCEP) as an emerging contaminant in advanced oxidation processes: a DFT modelling approach

As a typical toxic organophosphate and emerging contaminant, tris(2-chloroethyl) phosphate (TCEP) is resistant to conventional water treatment processes. Studies on advanced oxidation processes (AOPs) to degrade TCEP have received increasing attention, but the detailed mechanism is not yet fully understood. This study investigated the mechanistic details of TCEP degradation promoted by ·OH using the density functional theory (DFT) method. Our results demonstrated that in the initial step, energy barriers of the hydrogen abstraction pathways were no more than 7 kcal/mol. Cleavage of the P-O or C-Cl bond was verified to be possible to occur, whilst the C-O or C-C cleavage had to overcome an energy barrier above 50 kcal/mol, which was too high for mild experimental conditions. The bond dissociation energy (BDE) combined with the distortion/interaction energy (DIE) analysis disclosed origin of the various reactivities of each site of TCEP. The systematic calculations on the transformation of products generated in the initial step showed remarkable exothermic property. The systematic calculations on the transformation of products generated in the initial step showed remarkable exothermic property. The novel information at molecular level provides insight on how these products are generated and offers valuable theoretical guidance to help develop more effective AOPs to degrade TCEP or other emerging environmental contaminant

Supervised learning for robust quantum control in composite-pulse systems

In this work, we develop a supervised learning model for implementing robust quantum control in composite-pulse systems, where the training parameters can be either phases, detunings, or Rabi frequencies. This model exhibits great resistance to all kinds of systematic errors, including single, multiple, and time-varying errors. We propose a modified gradient descent algorithm for adapting the training of phase parameters, and show that different sampling methods result in different robust performances. In particular, there is a trade-off between high fidelity and robustness for a given number of training parameters, and both can be simultaneously enhanced by increasing the number of training parameters (pulses). For its applications, we demonstrate that the current model can be used for achieving high-fidelity arbitrary superposition states and universal quantum gates in a robust manner. This work provides a highly efficient learning model for fault-tolerant quantum computation by training various physical parameters.Comment: 19 pages, comments welcome

A genuine maximally seven-qubit entangled state

Contrary to A.Borras et al.'s [1] conjecture, a genuine maximally seven-qubit entangled state is presented. We find a seven-qubit state whose marginal density matrices for subsystems of 1,2- qubits are all completely mixed and for subsystems of 3-qubits is almost completely mixed

Photoconductivity of biased graphene

Graphene is a promising candidate for optoelectronic applications such as photodetectors, terahertz imagers, and plasmonic devices. The origin of photoresponse in graphene junctions has been studied extensively and is attributed to either thermoelectric or photovoltaic effects. In addition, hot carrier transport and carrier multiplication are thought to play an important role. Here we report the intrinsic photoresponse in biased but otherwise homogeneous graphene. In this classic photoconductivity experiment, the thermoelectric effects are insignificant. Instead, the photovoltaic and a photo-induced bolometric effect dominate the photoresponse due to hot photocarrier generation and subsequent lattice heating through electron-phonon cooling channels respectively. The measured photocurrent displays polarity reversal as it alternates between these two mechanisms in a backgate voltage sweep. Our analysis yields elevated electron and phonon temperatures, with the former an order higher than the latter, confirming that hot electrons drive the photovoltaic response of homogeneous graphene near the Dirac point