arXiv subjects

Yuan Xu

Publications and source records attributed to Yuan Xu.

At least 127 records · Page 7Linked to original sources

arXiv2021

High-efficiency arbitrary quantum operation on a high-dimensional quantum system

The ability to manipulate quantum systems lies at the heart of the development of quantum technology. The ultimate goal of quantum control is to realize arbitrary quantum operations (AQuOs) for all possible open quantum system dynamics. However, the demanding extra physical resources impose great obstacles. Here, we experimentally demonstrate a universal approach of AQuO on a photonic qudit with minimum physical resource of a two-level ancilla and a $\log_{2}d$-scale circuit depth for a $d$-dimensional system. The AQuO is then applied in quantum trajectory simulation for quantum subspace stabilization and quantum Zeno dynamics, as well as incoherent manipulation and generalized measurements of the qudit. Therefore, the demonstrated AQuO for complete quantum control would play an indispensable role in quantum information science.

quant-ph↗

arXiv2021

The microstructural dependence of ionic transport in bi-continuous nanoporous metal

Ionic transports in nanopores hold the key to unlocking the full potential of bi-continuous nanoporous (NP) metals as advanced electrodes in electrochemical devices. The precise control of the uniform NP metal structures also provides us a unique opportunity to understand how complex structures determine transports at nanoscales. For NP Au from the dealloying of a Ag-Au alloy, we can tune the pore size in the range of 13 nm to 2.4 microns and the porosity between 38% and 69% via isothermal coarsening. For NP Ag from the reduction-induced decomposition of AgCl, we can control additionally its structural hierarchy and pore orientation. We measure the effective ionic conductivities of 1 M NaClO4 through these NP metals as membranes, which range from 7% to 44% of that of a free solution, corresponding to calculated pore tortuosities between 2.7 and 1.3. The tortuosity of NP Au displays weak dependences on both the pore size and the porosity, consistent with the observed self-similarity in the coarsening, except for those of pores < 25 nm, which we consider deviating from the well-coarsened pore geometry. For NP Ag, the low tortuosity of the hierarchical structure can be explained with the Maxwell-Garnett equation and that of the oriented structure underlines the random orientation as the cause of slow transport in other NP metals. At last, we achieve high current densities of CO2 reduction with these two low-tortuosity NP Ags, demonstrating the significance of the structure-transport relationships for designing functional NP metals.

physics.app-ph↗

arXiv2021

Experimental simulation of open quantum system dynamics via Trotterization

Digital quantum simulators provide a diversified tool for solving the evolution of quantum systems with complicated Hamiltonians and hold great potential for a wide range of applications. Although much attention is paid to the unitary evolution of closed quantum systems, dissipation and noise are vital in understanding the dynamics of practical quantum systems. In this work, we experimentally demonstrate a digital simulation of an open quantum system in a controllable Markovian environment with the assistance of a single ancillary qubit. By Trotterizing the quantum Liouvillians, the continuous evolution of an open quantum system is effectively realized, and its application in error mitigation is demonstrated by adjusting the simulated noise intensities. High-order Trotter for open quantum dynamics is also experimentally investigated and shows higher accuracy. Our results represent a significant step towards hardware-efficient simulation of open quantum systems and error mitigation in quantum algorithms in noisy intermediate-scale quantum systems.

quant-ph↗

arXiv2021

Fourier orthogonal series on a paraboloid

We study orthogonal structures and Fourier orthogonal series on the surface of a paraboloid $\mathbb{V}_0^{d+1} = \{(x,t): \|x\| = \sqrt{t}, \, x \in \mathbb{R}^d, \, 0\le t<1\}$. The reproducing kernels of the orthogonal polynomials with respect to $t^β(1-t)^γ$ on $\mathbb{V}_0^{d+1}$ are related to the reproducing kernels of the Jacobi polynomials on the parabolic domain $\{(x_1,x_2): x_1^2 \le x_2 \le 1\}$ in $\mathbb{R}^2$. This connection serves as an essential tool for our study of the Fourier orthogonal series on the surface of the paraboloid, which allow us, in particular, to study the convergence of the Cesàro means on the surface. Analogous results are also established for the solid paraboloid bounded by $\mathbb{V}_0^{d+1}$ and the hyperplane $t=1$.

math.CA↗

arXiv2021

Estimating Phase Aberration from Noisy Radiofrequency Data of a single frame of Synthetic Aperture Ultrasound Image

Phase aberration is one of the main contributors to image degradation in ultrasound imaging. Normalized-Cross-Correlation (NCC) is one of the most extensively studied techniques to estimate the arrival delay error and the aberration profile. \textit{However, the performance of NCC can be compromised when the data have a poor signal-to-noise-ratio.} Here we propose an iterative filtered NCC (f-NCC) method to estimate phase aberration in speckle regions from the noisy radio-frequency data of a single frame of synthetic transmit aperture (STA) image. First, two-dimensional filters were applied in the aperture and temporal domains to suppress noise and off-axis signals in the transmit beamformed data from an arbitrary speckle region. Second, an iterative method that included the phase aberration in both the transmission and receiving process was used to estimate the phase aberration. Third, the estimation were improved by correcting the edge effect with an iterative zero-padding technique. Last, in the experimental study, we proposed and validated a formula to estimate the arrival time error caused by a sound speed error. The results from both the numerical simulations and experimental studies confirm that the proposed filtered NCC method can estimate the phase aberration profile correctly from noisy STA RF data in a speckle region. Image quality in terms of contrast, resolution and image signal-to-noise-ratio was improved. Potential applications of the proposed method to map local speed of samples are also discussed.

physics.med-ph↗

arXiv2021

Approximation and localized polynomial frame on double hyperbolic and conic domains

We study approximation and localized polynomial frames on a bounded double hyperbolic or conic surface and the domain bounded by such a surface and hyperplanes. The main work follows the framework developed recently in \cite{X21} for homogeneous spaces that are assumed to contain highly localized kernels constructed via a family of orthogonal polynomials. The existence of such kernels will be established with the help of closed form formulas for the reproducing kernels. The main results provide a construction of semi-discrete localized tight frame in weighted $L^2$ norm and a characterization of best approximation by polynomials on our domains. Several intermediate results, including the Marcinkiewicz-Zygmund inequalities, positive cubature rules, Christoeffel functions, and Bernstein type inequalities, are shown to hold for doubling weights defined via the intrinsic distance on the domain.

math.CA↗

arXiv2021

Orthogonal polynomials of several variables

Preliminary version of Chapter 2 in the book "Encyclopedia of Special functions: The Askey-Bateman Project, Vol. 2: Multivariate special functions", T. H. Koornwinder and J. V. Stokman (eds.), Cambridge University Press, 2021.

math.CA↗

arXiv2021

Suppressing Coherent Two-Qubit Errors via Dynamical Decoupling

Scalable quantum information processing requires the ability to tune multi-qubit interactions. This makes the precise manipulation of quantum states particularly difficult for multi-qubit interactions because tunability unavoidably introduces sensitivity to fluctuations in the tuned parameters, leading to erroneous multi-qubit gate operations. The performance of quantum algorithms may be severely compromised by coherent multi-qubit errors. It is therefore imperative to understand how these fluctuations affect multi-qubit interactions and, more importantly, to mitigate their influence. In this study, we demonstrate how to implement dynamical-decoupling techniques to suppress the two-qubit analogue of the dephasing on a superconducting quantum device featuring a compact tunable coupler, a trending technology that enables the fast manipulation of qubit--qubit interactions. The pure-dephasing time shows an up to ~14 times enhancement on average when using robust sequences. The results are in good agreement with the noise generated from room-temperature circuits. Our study further reveals the decohering processes associated with tunable couplers and establishes a framework to develop gates and sequences robust against two-qubit errors.

quant-ph↗

arXiv2021

Risk Analysis and Policy Enforcement of Function Interactions in Robot Apps

Robot apps are becoming more automated, complex and diverse. An app usually consists of many functions, interacting with each other and the environment. This allows robots to conduct various tasks. However, it also opens a new door for cyber attacks: adversaries can leverage these interactions to threaten the safety of robot operations. Unfortunately, this issue is rarely explored in past works. We present the first systematic investigation about the function interactions in common robot apps. First, we disclose the potential risks and damages caused by malicious interactions. We introduce a comprehensive graph to model the function interactions in robot apps by analyzing 3,100 packages from the Robot Operating System (ROS) platform. From this graph, we identify and categorize three types of interaction risks. Second, we propose RTron, a novel system to detect and mitigate these risks and protect the operations of robot apps. We introduce security policies for each type of risks, and design coordination nodes to enforce the policies and regulate the interactions. We conduct extensive experiments on 110 robot apps from the ROS platform and two complex apps (Baidu Apollo and Autoware) widely adopted in industry. Evaluation results indicated RTron can correctly identify and mitigate all potential risks with negligible performance cost. To validate the practicality of the risks and solutions, we implement and evaluate RTron on a physical UGV (Turtlebot) with real-word apps and environments.

cs.CR↗

arXiv2021

Laguerre expansions on conic domains

We study the Fourier orthogonal expansions with respect to the Laguerre type weigh functions on the conic surface of revolution and the domain bounded by such a surface. The main results include a closed form formula for the reproducing kernels, which is the kernel of the orthogonal projection operator and a pseudo convolution structure on the conic domain; the latter is shown to be bounded in an appropriate $L^p$ space and used to study mean convergence of the Cesàro means of the Laguerre expansions on conic domains.

math.CA↗

arXiv2021

Phase sensitive Landau-Zener-Stückelberg interference in superconducting quantum circuit

Superconducting circuit quantum electrodynamics (QED) architecture composed of superconducting qubit and resonator is a powerful platform for exploring quantum physics and quantum information processing. By employing techniques developed for superconducting quantum computing, we experimentally investigate phase-sensitive Landau-Zener-Stückelberg (LZS) interference phenomena in a circuit QED. Our experiments cover a large range of LZS transition parameters, and demonstrate the LZS induced Rabi-like oscillation as well as phase-dependent steady-state population.

quant-ph↗

arXiv2020

Hahn polynomials for hypergeometric distribution

Orthogonal polynomials for the multivariate hypergeometric distribution are defined on lattices in polyhedral domains in $\RR^d$. Their structures are studied through a detailed analysis of classical Hahn polynomials with negative integer parameters. Factorization of the Hahn polynomials is explored and used to explain the relation between the index set of orthogonal polynomials and the lattice set in polyhedral domain. In the multivariate case, these constructions lead to nontrivial families of hypergeometric polynomials vanishing on lattice polyhedra. The generating functions and bispectral properties of the orthogonal polynomials are also discussed.

math.CA↗

arXiv2020

High-fidelity, high-scalability two-qubit gate scheme for superconducting qubits

High-quality two-qubit gate operations are crucial for scalable quantum information processing. Often, the gate fidelity is compromised when the system becomes more integrated. Therefore, a low-error-rate, easy-to-scale two-qubit gate scheme is highly desirable. Here, we experimentally demonstrate a new two-qubit gate scheme that exploits fixed-frequency qubits and a tunable coupler in a superconducting quantum circuit. The scheme requires less control lines, reduces crosstalk effect, simplifies calibration procedures, yet produces a controlled-Z gate in 30ns with a high fidelity of 99.5%, derived from the interleaved randomized benchmarking method. Error analysis shows that gate errors are mostly coherence limited. Our demonstration paves the way for large-scale implementation of high-fidelity quantum operations.

quant-ph↗

arXiv2020

Orthogonal polynomials on planar cubic curves

Orthogonal polynomials in two variables on cubic curves are considered, including the case of elliptic curves. For an integral with respect to an appropriate weight function defined on a cubic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. We show that these orthogonal polynomials can be used to approximate functions with cubic and square root singularities, and demonstrate their usage for solving differential equations with singular solutions.

math.NA↗

arXiv2020

Experimental implementation of universal nonadiabatic geometric quantum gates in a superconducting circuit

Using geometric phases to realize noise-resilient quantum computing is an important method to enhance the control fidelity. In this work, we experimentally realize a universal nonadiabatic geometric quantum gate set in a superconducting qubit chain. We characterize the realized single- and two-qubit geometric gates with both quantum process tomography and randomized benchmarking methods. The measured average fidelities for the single-qubit rotation gates and two-qubit controlled-Z gate are 0.9977(1) and 0.977(9), respectively. Besides, we also experimentally demonstrate the noise-resilient feature of the realized single-qubit geometric gates by comparing their performance with the conventional dynamical gates with different types of errors in the control field. Thus, our experiment proves a way to achieve high-fidelity geometric quantum gates for robust quantum computation.

quant-ph↗

arXiv2020

Manipulating complex hybrid entanglement and testing multipartite Bell inequalities in a superconducting circuit

Quantum correlations in observables of multiple systems not only are of fundamental interest, but also play a key role in quantum information processing. As a signature of these correlations, the violation of Bell inequalities has not been demonstrated with multipartite hybrid entanglement involving both continuous and discrete variables. Here we create a five-partite entangled state with three superconducting transmon qubits and two photonic qubits, each encoded in the mesoscopic field of a microwave cavity. We reveal the quantum correlations among these distinct elements by joint Wigner tomography of the two cavity fields conditional on the detection of the qubits and by test of a five-partite Bell inequality. The measured Bell signal is $8.381\pm0.038$, surpassing the bound of 8 for a four-partite entanglement imposed by quantum correlations by 10 standard deviations, demonstrating the genuine five-partite entanglement in a hybrid quantum system.

quant-ph↗

arXiv2020

Intertwining operator associated to symmetric groups and summability on the unit sphere

An integral representation of the intertwining operator for the Dunkl operators associated with symmetric groups is derived for the class of functions of a single component. The expression provides a closed form formula for the reproducing kernels of $h$-harmonics associated with symmetric groups when one of the components is a coordinate vector. The latter allows us to establish a sharp result for the Cesàro summability of $h$-harmonic series on the unit sphere.

math.CA↗

arXiv2020

Demonstration of Controlled-Phase Gates between Two Error-Correctable Photonic Qubits

To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in photonic fields stored in cavities. The gates are realized by dispersively coupling an ancillary superconducting qubit to these cavities and driving it to make a cyclic evolution depending on the joint photonic state of the cavities, which produces a conditional geometric phase. We first realize phase gates for photonic qubits with the logical basis states encoded in two quasiorthogonal coherent states, which have important implications for continuous-variable-based quantum computation. Then we use this geometric method to implement a controlled-phase gate between two binomially encoded logical qubits, which have an error-correctable function.

quant-ph↗