Spin polarized nematic order, quantum valley Hall states, and field tunable topological transitions in twisted multilayer graphene systems

We theoretically study the correlated insulator states, quantum anomalous Hall (QAH) states, and field-induced topological transitions between different correlated states in twisted multilayer graphene systems. Taking twisted bilayer-monolayer graphene and twisted double-bilayer graphene as examples, we show that both systems stay in spin polarized, $C_{3z}$-broken insulator states with zero Chern number at 1/2 filling of the flat bands under finite displacement fields. In some cases these spin polarized, nematic insulator states are in the quantum valley Hall phase by virtue of the nontrivial band topology of the systems. The spin polarized insulator state is quasi-degenerate with the valley polarized state when only the dominant intra-valley Coulomb interactions are included. Such quasi-degeneracy can be split by atomic on-site interactions such that the spin polarized, nematic state become the unique ground state. Such a scenario applies to various twisted multilayer graphene systems at 1/2 filling, thus can be considered as a universal mechanism. Moreover, under vertical magnetic fields, the giant orbital Zeeman splittings in twisited multilayer graphene systems compete with the atomic Hubbard interactions, which can drive transitions from spin polarized zero-Chern-number states to valley-polarized QAH states with small onset magnetic fields.Comment: 5+17 page

Quantum Algorithms for Identifying Hidden Strings with Applications to Matroid Problems

In this paper, we explore quantum speedups for the problem, inspired by matroid theory, of identifying a pair of $n$-bit binary strings that are promised to have the same number of 1s and differ in exactly two bits, by using the max inner product oracle and the sub-set oracle. More specifically, given two string $s, s'\in\{0, 1\}^n$ satisfying the above constraints, for any $x\in\{0, 1\}^n$ the max inner product oracle $O_{max}(x)$ returns the max value between $s\cdot x$ and $s'\cdot x$, and the sub-set oracle $O_{sub}(x)$ indicates whether the index set of the 1s in $x$ is a subset of that in $s$ or $s'$. We present a quantum algorithm consuming $O(1)$ queries to the max inner product oracle for identifying the pair $\{s, s'\}$, and prove that any classical algorithm requires $\Omega(n/\log_{2}n)$ queries. Also, we present a quantum algorithm consuming $\frac{n}{2}+O(\sqrt{n})$ queries to the subset oracle, and prove that any classical algorithm requires at least $n+\Omega(1)$ queries. Therefore, quantum speedups are revealed in the two oracle models. Furthermore, the above results are applied to the problem in matroid theory of finding all the bases of a 2-bases matroid, where a matroid is called $k$-bases if it has $k$ bases

DART: Distribution Aware Retinal Transform for Event-based Cameras

We introduce a generic visual descriptor, termed as distribution aware retinal transform (DART), that encodes the structural context using log-polar grids for event cameras. The DART descriptor is applied to four different problems, namely object classification, tracking, detection and feature matching: (1) The DART features are directly employed as local descriptors in a bag-of-features classification framework and testing is carried out on four standard event-based object datasets (N-MNIST, MNIST-DVS, CIFAR10-DVS, NCaltech-101). (2) Extending the classification system, tracking is demonstrated using two key novelties: (i) For overcoming the low-sample problem for the one-shot learning of a binary classifier, statistical bootstrapping is leveraged with online learning; (ii) To achieve tracker robustness, the scale and rotation equivariance property of the DART descriptors is exploited for the one-shot learning. (3) To solve the long-term object tracking problem, an object detector is designed using the principle of cluster majority voting. The detection scheme is then combined with the tracker to result in a high intersection-over-union score with augmented ground truth annotations on the publicly available event camera dataset. (4) Finally, the event context encoded by DART greatly simplifies the feature correspondence problem, especially for spatio-temporal slices far apart in time, which has not been explicitly tackled in the event-based vision domain.Comment: 12 pages, revision submitted to TPAMI in Nov 201

Characterization, synthesis, and optimization of quantum circuits over multiple-control Z\textit{Z}-rotation gates: A systematic study

We conduct a systematic study of quantum circuits composed of multiple-control $Z$-rotation (MCZR) gates as primitives, since they are widely-used components in quantum algorithms and also have attracted much experimental interest in recent years. Herein, we establish a circuit-polynomial correspondence to characterize the functionality of quantum circuits over the MCZR gate set with continuous parameters. An analytic method for exactly synthesizing such quantum circuit to implement any given diagonal unitary matrix with an optimal gate count is proposed, which also enables the circuit depth optimal for specific cases with pairs of complementary gates. Furthermore, we present a gate-exchange strategy together with a flexible iterative algorithm for effectively optimizing the depth of any MCZR circuit, which can also be applied to quantum circuits over any other commuting gate set. Besides the theoretical analysis, the practical performances of our circuit synthesis and optimization techniques are further evaluated by numerical experiments on two typical examples in quantum computing, including diagonal Hermitian operators and Quantum Approximate Optimization Algorithm (QAOA) circuits with tens of qubits, which can demonstrate a reduction in circuit depth by 33.40\% and 15.55\% on average over relevant prior works, respectively. Therefore, our methods and results provide a pathway for implementing quantum circuits and algorithms on recently developed devices.Comment: Comments are welcom

Delay characterization in FPGA-based reconfigurable systems

Runtime reconfigurable architectures accelerate the operation of a standard processor core by hardware accelerators implemented in Field Programmable Gate Arrays (FPGAs). Partial runtime reconfiguration allows the hardware accelerators to efficiently adapt to different computational tasks dynamically. Nowadays, the FPGAs from major vendors, such as Xilinx and Altera, support this feature, including the Xilinx Virtex-5 FPGA family which is the implementation platform of this work. Manufactured at 28 nm scaled technological node or lower, concerns rise about the impact of aging-related failure mechanisms on the modern generations of FPGAs. To detect degradation in the reconfigurable gate arrays, dedicated on- and offline test methods must be employed in the field. Design for dependability requires that the degradation is detected and localized, so that the degraded logic elements will not be used as a first choice in the reconfiguration. This thesis presents the development and the evaluation of a delay characterization method for FPGA CLBs which comprise most of the FPGA logic elements. The purpose of FPGA delay characterization method in this work is to detect and localize the delay variance. This delay variance information may be used for achieving a speed optimized reconfiguration for a FPGA-based runtime system. Different delay characterization methods have been studied in this thesis for determining a suitable method to be implemented in the partial reconfigurable system. The delay characterization is performed in a part of area in the FPGA before a module is placed in this area to avoid the degraded portion. This thesis uses low level hardware description language to generate the fine-grained measurement units which can cover the target area. VHDL is used to generate the test wrapper, control circuit, and the circuit for communicating between the FPGA and the workstation. Several measurement techniques are used to evaluate the accuracy of the delay characterization method. Additionally, this thesis evaluates the temperature influence on the delay characterization. The results show that this delay characterization method can compare the speed of logic elements in the partial runtime reconfiguration area with high accuracy. The degradation can be detected and localized. The results also show that this method can be adapted to different size and location, fitting in the partial runtime reconfigurable design. Twelve configurations are required to have a full coverage of all the CLBs in the area under test

Mechanism Design of a Compact 4-DOF Robotic Needle Guide for MRI-Guided Prostate Intervention

In the past several MRI compatible robotic needle guide devices for targeted prostate biopsy have been developed. The large and complex structure have been identified as the major limitations of those devices. Such limitations, in addition to complex steps for device to image registration have prevented widespread implementation of MRI-guided prostate biopsy despite the advantages of MRI compared to TRUS. We have designed a compact MRI-guided robotic intervention with the capability to have angulated insertion to avoid damage to any anatomical feature along the needle path. The system consists of a novel mechanism driven Robotic Needle Guide (RNG). The RNG is a 4-DOF robotic needle manipulator mounted on a Gross Positioning Module (GPM), which is locked on the MRI table. The RNG consists of four parallel stacked disks with an engraved profile path. The rotary motion and positioning of the discs at an angle aids in guiding the biopsy needle. Once a clinician selects a target for needle insertion, the intervention provides possible insertion angles. Then, the most suitable angle is selected by the clinician based on the safest trajectory. The selected target and insertion angle are then computed as control parameters of RNG i.e. the discs are then rotated to the required angle. Insertion is followed by quick confirmation scans to ascertain needle position at all times

The Complex Function Method Roadway Section Design of the Soft Coal Seam

As for the sophisticated advanced support technique of vertical wall semicircle arch roadway in the three-soft coal seam, a design of flat top U-shape roadway section was put forward. Based on the complex function method, the surrounding rock displacement and stress distribution laws both of vertical wall semicircle arch roadway and of flat top U-shape roadway were obtained. The results showed that the displacement distribution laws in the edge of roadway surrounding rock were similar between the two different roadways and the area of plasticity proportion of flat top U-shape roadway approximately equals that of vertical wall semicircle arch roadway. Based on finite element method, the bearing behaviors of the U-type steel support under the interaction of surrounding rock in vertical wall semicircle arch roadway and flat top U-shape roadway were analyzed. The results showed that, from a mechanics perspective, U-type steel support can fulfill the requirement of surrounding rock supporting in flat top U-shape roadway and vertical wall semicircle arch roadway. The field measurement of mining roadway surrounding rock displacement in Zouzhuang coal mine working face 3204 verified the accuracy of theoretical analysis and numerical simulation