arXiv subjects

Guofeng Zhang

Publications and source records attributed to Guofeng Zhang.

At least 199 records · Page 11Linked to original sources

arXiv2020

Quantum tensor singular value decomposition with applications to recommendation systems

In this paper, we present a quantum singular value decomposition algorithm for third-order tensors inspired by the classical algorithm of tensor singular value decomposition (t-svd) and then extend it to order-$p$ tensors. It can be proved that the quantum version of the t-svd for a third-order tensor $\mathcal{A} \in \mathbb{R}^{N\times N \times N}$ achieves the complexity of $\mathcal{O}(N{\rm polylog}(N))$, an exponential speedup compared with its classical counterpart. As an application, we propose a quantum algorithm for recommendation systems which incorporates the contextual situation of users to the personalized recommendation. We provide recommendations varying with contexts by measuring the output quantum state corresponding to an approximation of this user's preferences. This algorithm runs in expected time $\mathcal{O}(N{\rm polylog}(N){\rm poly}(k)),$ if every frontal slice of the preference tensor has a good rank-$k$ approximation. At last, we provide a quantum algorithm for tensor completion based on a different truncation method which is tested to have a good performance in dynamic video completion.

quant-ph↗

arXiv2019

All-optical reversible manipulation of exciton and trion emissions in monolayer WS2

Monolayer transition metal dichalcogenides (TMDs) are direct gap semiconductors emerging promising applications in diverse optoelectronic devices. To improve performance, recent investigations have been systematically focused on the tuning of their optical properties. However, an all-optical approach with the reversible feature is still a challenge. Here we demonstrate the tunability of the photoluminescence (PL) properties of monolayer WS2 via laser irradiation. The modulation of PL intensity, as well as the conversion between neutral exciton and charged trion have been readily and reversibly achieved by using different laser power densities. We attribute the reversible manipulation to the laser-assisted adsorption and desorption of gas molecules, which will deplete or release free electrons from the surface of WS2 and thus modify its PL properties. This all-optical manipulation, with advantages of reversibility, quantitative control, and high spatial resolution, suggests promising applications of TMDs monolayers in optoelectronic and nanophotonic applications, such as optical data storage, micropatterning, and display.

cond-mat.mtrl-sci↗

arXiv2019

Depth Completion from Sparse LiDAR Data with Depth-Normal Constraints

Depth completion aims to recover dense depth maps from sparse depth measurements. It is of increasing importance for autonomous driving and draws increasing attention from the vision community. Most of existing methods directly train a network to learn a mapping from sparse depth inputs to dense depth maps, which has difficulties in utilizing the 3D geometric constraints and handling the practical sensor noises. In this paper, to regularize the depth completion and improve the robustness against noise, we propose a unified CNN framework that 1) models the geometric constraints between depth and surface normal in a diffusion module and 2) predicts the confidence of sparse LiDAR measurements to mitigate the impact of noise. Specifically, our encoder-decoder backbone predicts surface normals, coarse depth and confidence of LiDAR inputs simultaneously, which are subsequently inputted into our diffusion refinement module to obtain the final completion results. Extensive experiments on KITTI depth completion dataset and NYU-Depth-V2 dataset demonstrate that our method achieves state-of-the-art performance. Further ablation study and analysis give more insights into the proposed method and demonstrate the generalization capability and stability of our model.

cs.CV↗

arXiv2019

On the response of a two-level system to two-photon inputs

The purpose of this paper is to study the interaction between a two-level system and two continuous-mode photons. Two scenarios are investigated: Case 1, how a two-level system changes the pulse shapes of two input photons propagating in a single input channel; and Case 2, how a two-level system responds to two counter-propagating photons. By means of a transfer function approach, the steady-state output field states for both cases are derived analytically. In Example 1, a two-photon input state of Gaussian pulse shape is used to excite a two-level atom. The simulation demonstrates that in the time domain the atom tends to stretch out the two photons. Moreover, the striking difference between the joint probability distribution of the output two-photon state and that of the input two-photon state occurs exactly under the setting when the two-level atom is most efficiently excited. In Example 2, a two-photon input state of rising exponential pulse shape is used to excite a two-level atom. Strong anti-correlation of the output two-photon state is observed, which is absent in Example 1 for the Gaussian pulse shape. Such difference indicates that different pulse shapes give rise to drastically different frequency entanglement of the output two-photon state. Example 3 is used to illustrate Case 2, where two counter-propagating single photons of rising exponential pulse shapes are input to a two-level atom. The frequency-dependent Hong-Ou-Mandel (HOM) interference phenomenon is observed. The simulation results base on the analytic forms of output two-photon states are consistent with those based on quantum master or filter equations [43,11]. Similar physical phenomena have been observed in physical settings such as cavity opto-mechanical systems and Keer nonlinear cavities.

quant-ph↗

arXiv2019

An Improved Quantum Projection Filter

This work extends the previous quantum projection filtering scheme in [Gao Q., Zhang G., & Petersen I. R. (2019). An exponential quantum projection filter for open quantum systems. \emph{Automatica}, 99, 59-68.], by adding an optimality analysis result. A reformulation of the quantum projection filter is derived by minimizing the truncated Stratonovich stochastic Taylor expansion of the difference between the true quantum trajectory and its approximation on a lower-dimensional submanifold through quantum information geometric techniques. Simulation results for a qubit example demonstrate better approximation performance for the new quantum projection filter.

quant-ph↗

arXiv2019

Structural Decomposition for Quantum Two-level Systems

An input-output model of a two-level quantum system in the Heisenberg picture is of bilinear form with constant system matrices, which allows the introduction of the concepts of controllability and observability in analogy with those of quantum linear systems. By means of the notions of controllability and observability, coordinate transformations, which are rotation matrices, can be constructed explicitly that transform an input-output model to a new one. The new input-output model enables us to investigate many interesting properties of the two-level quantum system, such as steady-state solutions to the Lindblad master equation, quantum decoherence-free (DF) subspaces, quantum non-demolition (QND) variables, and the realization of quantum back-action evading (BAE) measurements. The physical system in (Wang, J. \& Wiseman, H. M. (2001), Feedback-stabilization of an arbitrary pure state of a two-level atom, Physical Review A 64(6), 063810) is re-studied to illustrate the results presented in this paper.

quant-ph↗

arXiv2019

Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement

The purpose of this paper is to study the problem of computing unitary eigenvalues (U-eigenvalues) of non-symmetric complex tensors. By means of symmetric embedding of complex tensors, the relationship between U-eigenpairs of a non-symmetric complex tensor and unitary symmetric eigenpairs (US-eigenpairs) of its symmetric embedding tensor is established. An algorithm (Algorithm \ref{algo:1}) is given to compute the U-eigenvalues of non-symmetric complex tensors by means of symmetric embedding. Another algorithm, Algorithm \ref{algo:2}, is proposed to directly compute the U-eigenvalues of non-symmetric complex tensors, without the aid of symmetric embedding. Finally, a tensor version of the well-known Gauss-Seidel method is developed. Efficiency of these three algorithms are compared by means of various numerical examples. These algorithms are applied to compute the geometric measure of entanglement of quantum multipartite non-symmetric pure states.

quant-ph↗

arXiv2019

Structural characterization of linear quantum systems with application to back-action evading measurement

The purpose of this paper is to study the structure of quantum linear systems in terms of their Kalman canonical form, which was proposed in a recent paper \cite{ZGPG18}. The spectral structure of quantum linear systems is explored, which indicates that a quantum linear system is both controllable and observable provided that it is Hurwitz stable. A new parameterization method for quantum linear systems is proposed. This parameterization is designed for the Kalman canonical form directly. Consequently, the parameters involved are in a blockwise form in correspondence with the blockwise structure of the Kalman canonical form. This parameter structure can be used to simplify various quantum control design problems. For example, necessary and sufficient conditions for the realization of quantum back-action evading (BAE) measurements are given in terms of these new parameters. Due to their blockwise nature, a small number of parameters are required for realizing quantum BAE measurements.

quant-ph↗

arXiv2019

Quantum filtering for a two-level atom driven by two counter-propagating photons

The purpose of this paper is to propose quantum filters for a two-level atom driven by two continuous-mode counter-propagating photons and under continuous measurements. Two scenarios of multiple measurements, 1) homodyne detection plus photodetection, and 2) two homodyne detections, are discussed. Filtering equations for both cases are derived explicitly. As demonstration, the two input photons with rising exponential and Gaussian pulse shapes are used to excite a two-level atom under two homodyne detection measurements. Simulations reveal scaling relations between atom-photon coupling and photonic pulse shape for maximum atomic excitation.

quant-ph↗

arXiv2019

Angle-based Shape Determination Theory of Planar Graphs with Application to Formation Stabilization

This paper presents an angle-based approach for distributed formation shape stabilization of multi-agent systems in the plane. We develop an angle rigidity theory to study whether a planar framework can be determined by angles between segments uniquely up to translations, rotations, scalings and reflections. The proposed angle rigidity theory is applied to the formation stabilization problem, where multiple single-integrator modeled agents cooperatively achieve an angle-constrained formation. During the formation process, the global coordinate system is unknown for each agent and wireless communications between agents are not required. Moreover, by utilizing the advantage of high degrees of freedom, we propose a distributed control law for agents to stabilize a target formation shape with desired orientation and scale. Simulation examples are performed for illustrating effectiveness of the proposed control strategies.

eess.SY↗

arXiv2018

Energy cost for controlling complex networks

The controllability of complex networks has received much attention recently, which tells whether we can steer a system from an initial state to any final state within finite time with admissible external inputs. In order to accomplish the control in practice at the minimum cost, we must study how much control energy is needed to reach the desired final state. At a given control distance between the initial and final states, existing results present the scaling behavior of lower bounds of the minimum energy in terms of the control time analytically. However, to reach an arbitrary final state at a given control distance, the minimum energy is actually dominated by the upper bound, whose analytic expression still remains elusive. Here we theoretically show the scaling behavior of the upper bound of the minimum energy in terms of the time required to achieve control. Apart from validating the analytical results with numerical simulations, our findings are feasible to the scenario with any number of nodes that receive inputs directly and any types of networks. Moreover, more precise analytical results for the lower bound of the minimum energy are derived in the proposed framework. Our results pave the way to implement realistic control over various complex networks with the minimum control cost.

math.OC↗

arXiv2018

Representation and Network Synthesis for a Class of Mixed Quantum-Classical Linear Stochastic Systems

The purpose of this paper is to present a network realization theory for a class of mixed quantum-classical linear stochastic systems. Two forms, the standard form and the general form, of this class of linear mixed quantum-classical systems are proposed. Necessary and sufficient conditions for their physical realizability are derived. Based on these physical realizability conditions, a network synthesis theory for this class of linear mixed quantum-classical systems is developed, which clearly exhibits the quantum component, the classical component, and their interface. An example is used to illustrate the theory presented in this paper.

quant-ph↗

arXiv2018

An Exponential Quantum Projection Filter for Open Quantum Systems

An approximate exponential quantum projection filtering scheme is developed for a class of open quantum systems described by Hudson- Parthasarathy quantum stochastic differential equations, aiming to reduce the computational burden associated with online calculation of the quantum filter. By using a differential geometric approach, the quantum trajectory is constrained in a finite-dimensional differentiable manifold consisting of an unnormalized exponential family of quantum density operators, and an exponential quantum projection filter is then formulated as a number of stochastic differential equations satisfied by the finite-dimensional coordinate system of this manifold. A convenient design of the differentiable manifold is also presented through reduction of the local approximation errors, which yields a simplification of the quantum projection filter equations. It is shown that the computational cost can be significantly reduced by using the quantum projection filter instead of the quantum filter. It is also shown that when the quantum projection filtering approach is applied to a class of open quantum systems that asymptotically converge to a pure state, the input-to-state stability of the corresponding exponential quantum projection filter can be established. Simulation results from an atomic ensemble system example are provided to illustrate the performance of the projection filtering scheme. It is expected that the proposed approach can be used in developing more efficient quantum control methods.

math-ph↗

arXiv2018

Weak Rigidity Theory and its Application to Multi-agent Formation Stabilization

This paper introduces the notion of weak rigidity to characterize a framework by pairwise inner products of inter-agent displacements. Compared to distance-based rigidity, weak rigidity requires fewer constrained edges in the graph to determine a geometric shape in an arbitrarily dimensional space. A necessary and sufficient graphical condition for infinitesimal weak rigidity of planar frameworks is derived. As an application of the proposed weak rigidity theory, a gradient based control law and a non-gradient based control law are designed for a group of single-integrator modeled agents to stabilize a desired formation shape, respectively. Using the gradient control law, we prove that an infinitesimally weakly rigid formation is locally exponentially stable. In particular, if the number of agents is one greater than the dimension of the space, a minimally infinitesimally weakly rigid formation is almost globally asymptotically stable. In the literature of rigid formation, the sensing graph is always required to be rigid. Using the non-gradient control law based on weak rigidity theory, the sensing graph is unnecessary to be rigid for local exponential stability of the formation. A numerical simulation is performed for illustrating effectiveness of our main results.

eess.SY↗

arXiv2018

Single-photon quantum filtering with multiple measurements

The single-photon quantum filtering problems have been investigated recently with applications in quantum computing. In practice, the detector responds with a quantum efficiency of less than unity since there exists some mode mismatch between the detector and the system, and the single-photon signal may be corrupted by quantum white noise. Consequently, quantum filters based on multiple measurements are designed in this paper to improve the estimation performance. More specifically, the filtering equations for a two-level quantum system driven by a single-photon input state and under multiple measurements are presented in this paper. Four scenarios, 1) two diffusive measurements with Q-P quadrature form, 2) two diffusive measurements with Q-Q quadrature form, 3) diffusive plus Poissonian measurements, and 4) two Poissonian measurements, are considered. It is natural to compare the filtering results, i.e., measuring single channel or both channels, which one is better? By the simulation where we use a single photon to excite an atom, it seems that multiple measurements enable us to excite the atom with higher probability than only measuring single channel. In addition, measurement back-action phenomenon is revealed by the simulation results.

quant-ph↗

arXiv2017

Regularly Decomposable Tensors and Classical Spin States

A spin-$j$ state can be represented by a symmetric tensor of order $N=2j$ and dimension $4$. Here, $j$ can be a positive integer, which corresponds to a boson; $j$ can also be a positive half-integer, which corresponds to a fermion. In this paper, we introduce regularly decomposable tensors and show that a spin-$j$ state is classical if and only if its representing tensor is a regularly decomposable tensor. In the even-order case, a regularly decomposable tensor is a completely decomposable tensor but not vice versa; a completely decomposable tensors is a sum-of-squares (SOS) tensor but not vice versa; an SOS tensor is a positive semi-definite (PSD) tensor but not vice versa. In the odd-order case, the first row tensor of a regularly decomposable tensor is regularly decomposable and its other row tensors are induced by the regular decomposition of its first row tensor. We also show that complete decomposability and regular decomposability are invariant under orthogonal transformations, and that the completely decomposable tensor cone and the regularly decomposable tensor cone are closed convex cones. Furthermore, in the even-order case, the completely decomposable tensor cone and the PSD tensor cone are dual to each other. The Hadamard product of two completely decomposable tensors is still a completely decomposable tensor. Since one may apply the positive semi-definite programming algorithm to detect whether a symmetric tensor is an SOS tensor or not, this gives a checkable necessary condition for classicality of a spin-$j$ state. Further research issues on regularly decomposable tensors are also raised.

quant-ph↗

arXiv2017

Robust Keyframe-based Dense SLAM with an RGB-D Camera

In this paper, we present RKD-SLAM, a robust keyframe-based dense SLAM approach for an RGB-D camera that can robustly handle fast motion and dense loop closure, and run without time limitation in a moderate size scene. It not only can be used to scan high-quality 3D models, but also can satisfy the demand of VR and AR applications. First, we combine color and depth information to construct a very fast keyframe-based tracking method on a CPU, which can work robustly in challenging cases (e.g.~fast camera motion and complex loops). For reducing accumulation error, we also introduce a very efficient incremental bundle adjustment (BA) algorithm, which can greatly save unnecessary computation and perform local and global BA in a unified optimization framework. An efficient keyframe-based depth representation and fusion method is proposed to generate and timely update the dense 3D surface with online correction according to the refined camera poses of keyframes through BA. The experimental results and comparisons on a variety of challenging datasets and TUM RGB-D benchmark demonstrate the effectiveness of the proposed system.

cs.CV↗

arXiv2017

How entangled can a multi-party system possibly be?

The geometric measure of entanglement of a pure quantum state is defined to be its distance to the space of product (seperable) states. Given an $n$-partite system composed of subsystems of dimensions $d_1,\ldots, d_n$, an upper bound for maximally allowable entanglement is derived in terms of geometric measure of entanglement. This upper bound is characterized exclusively by the dimensions $d_1,\ldots, d_n$ of composite subsystems. Numerous examples demonstrate that the upper bound appears to be reasonably tight.

quant-ph↗