arXiv subjects

Yuan Xu

Publications and source records attributed to Yuan Xu.

At least 109 records · Page 6Linked to original sources

arXiv2023

Sharp Bernstein inequalities on simplex

We prove several new families of Bernstein inequalities of two types on the simplex. The first type consists of inequalities in $L^2$ norm for the Jacobi weight, some of which are sharp, and they are established via the spectral operator that has orthogonal polynomials as eigenfunctions. The second type consists of inequalities in $L^p$ norm for doubling weight on the simplex. The first type is not necessarily a special case of the second type when $d \ge 3$.

math.CA↗

arXiv2023

PND-Net: Physics based Non-local Dual-domain Network for Metal Artifact Reduction

Metal artifacts caused by the presence of metallic implants tremendously degrade the reconstructed computed tomography (CT) image quality, affecting clinical diagnosis or reducing the accuracy of organ delineation and dose calculation in radiotherapy. Recently, deep learning methods in sinogram and image domains have been rapidly applied on metal artifact reduction (MAR) task. The supervised dual-domain methods perform well on synthesized data, while unsupervised methods with unpaired data are more generalized on clinical data. However, most existing methods intend to restore the corrupted sinogram within metal trace, which essentially remove beam hardening artifacts but ignore other components of metal artifacts, such as scatter, non-linear partial volume effect and noise. In this paper, we mathematically derive a physical property of metal artifacts which is verified via Monte Carlo (MC) simulation and propose a novel physics based non-local dual-domain network (PND-Net) for MAR in CT imaging. Specifically, we design a novel non-local sinogram decomposition network (NSD-Net) to acquire the weighted artifact component, and an image restoration network (IR-Net) is proposed to reduce the residual and secondary artifacts in the image domain. To facilitate the generalization and robustness of our method on clinical CT images, we employ a trainable fusion network (F-Net) in the artifact synthesis path to achieve unpaired learning. Furthermore, we design an internal consistency loss to ensure the integrity of anatomical structures in the image domain, and introduce the linear interpolation sinogram as prior knowledge to guide sinogram decomposition. Extensive experiments on simulation and clinical data demonstrate that our method outperforms the state-of-the-art MAR methods.

physics.med-ph↗

arXiv2023

Beating the break-even point with a discrete-variable-encoded logical qubit

Quantum error correction (QEC) aims to protect logical qubits from noises by utilizing the redundancy of a large Hilbert space, where an error, once it occurs, can be detected and corrected in real time. In most QEC codes, a logical qubit is encoded in some discrete variables, e.g., photon numbers. Such encoding schemes make the codewords orthogonal, so that the encoded quantum information can be unambiguously extracted after processing. Based on such discrete-variable encodings, repetitive QEC demonstrations have been reported on various platforms, but there the lifetime of the encoded logical qubit is still shorter than that of the best available physical qubit in the entire system, which represents a break-even point that needs to be surpassed for any QEC code to be of practical use. Here we demonstrate a QEC procedure with a logical qubit encoded in photon-number states of a microwave cavity, dispersively coupled to an ancilla superconducting qubit. By applying a pulse featuring a tailored frequency comb to the ancilla, we can repetitively extract the error syndrome with high fidelity and perform error correction with feedback control accordingly, thereby exceeding the break-even point by about 16% lifetime enhancement. Our work illustrates the potential of the hardware-efficient discrete-variable QEC codes towards a reliable quantum information processor.

quant-ph↗

arXiv2023

Continued fractions and orthogonal polynomials in several variables

We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition for the characterization is the commutativity of the multiplication operators on finite polynomial subspaces modulo an ideal. Moreover, starting from the orthogonal polynomials or the three-term recurrence, our method constructs a sequence of moment sequences that provides an approximation of the maximal order for recovering the moment sequence that defines the orthogonality.

math.CA↗

arXiv2023

Interaction-induced topological pumping in a solid-state quantum system

As the basis for generating multi-particle quantum correlations, inter-particle interaction plays a crucial role in collective quantum phenomena, quantum phase transitions, and quantum information processing. It can profoundly alter the band structure of quantum many-body systems and give rise to exotic topological phenomena. Conventional topological pumping, which has been well demonstrated in driven linear or noninteracting systems, may break down in the presence of strong interaction. However, the interplay between band topology and interaction could also induce emergent topological pumping of interacting particles, but its experimental realization has proven challenging. Here we demonstrate interaction-induced topological pumping in a solid-state quantum system comprising an array of 36 superconducting qubits. With strong interaction inherent in the qubits and site-resolved controllability of the lattice potential and hopping strength, we realize the topological Thouless pumping of single and two bounded particles. Beyond these topological phenomena with linear or noninteracting counterparts, we also observe topologically resonant tunneling and asymmetric edge-state transport of interacting particles. Our work creates a paradigm for multi-particle topological effects, and provides a new pathway to the study of exotic topological phenomena, many-body quantum transport, and quantum information transfer.

quant-ph↗

arXiv2023

SoK: Rethinking Sensor Spoofing Attacks against Robotic Vehicles from a Systematic View

Robotic Vehicles (RVs) have gained great popularity over the past few years. Meanwhile, they are also demonstrated to be vulnerable to sensor spoofing attacks. Although a wealth of research works have presented various attacks, some key questions remain unanswered: are these existing works complete enough to cover all the sensor spoofing threats? If not, how many attacks are not explored, and how difficult is it to realize them? This paper answers the above questions by comprehensively systematizing the knowledge of sensor spoofing attacks against RVs. Our contributions are threefold. (1) We identify seven common attack paths in an RV system pipeline. We categorize and assess existing spoofing attacks from the perspectives of spoofer property, operation, victim characteristic and attack goal. Based on this systematization, we identify 4 interesting insights about spoofing attack designs. (2) We propose a novel action flow model to systematically describe robotic function executions and unexplored sensor spoofing threats. With this model, we successfully discover 103 spoofing attack vectors, 26 of which have been verified by prior works, while 77 attacks are never considered. (3) We design two novel attack methodologies to verify the feasibility of newly discovered spoofing attack vectors.

cs.CR↗

arXiv2023

Low-loss interconnects for modular superconducting quantum processors

Scaling is now a key challenge in superconducting quantum computing. One solution is to build modular systems in which smaller-scale quantum modules are individually constructed and calibrated, and then assembled into a larger architecture. This, however, requires the development of suitable interconnects. Here, we report low-loss interconnects based on pure aluminium coaxial cables and on-chip impedance transformers featuring quality factors up to $8.1 \times 10^5$, which is comparable to the performance of our transmon qubits fabricated on single-crystal sapphire substrate. We use these interconnects to link five quantum modules with inter-module quantum state transfer and Bell state fidelities up to 99\%. To benchmark the overall performance of the processor, we create maximally-entangled, multi-qubit Greenberger-Horne-Zeilinger (GHZ) states. The generated inter-module four-qubit GHZ state exhibits 92.0\% fidelity. We also entangle up to 12 qubits in a GHZ state with $55.8 \pm 1.8\%$ fidelity, which is above the genuine multipartite entanglement threshold of 1/2. These results represent a viable modular approach for large-scale superconducting quantum processors.

quant-ph↗

arXiv2022

Orthogonal polynomials on a class of planar algebraic curves

We construct bivariate orthogonal polynomials (OPs) on algebraic curves of the form $y^m = ϕ(x)$ in $\mathbb{R}^2$ where $m = 1, 2$ and $ϕ$ is a polynomial of arbitrary degree $d$, in terms of univariate semiclassical OPs. We compute connection coeffeicients that relate the bivariate OPs to a polynomial basis that is itself orthogonal and whose span contains the OPs as a subspace. The connection matrix is shown to be banded and the connection coefficients and Jacobi matrices for OPs of degree $0, \ldots, N$ are computed via the Lanczos algorithm in $O(Nd^4)$ operations.

math.NA↗

arXiv2022

Monomial and Rodrigues orthogonal polynomials on the cone

We study two families of orthogonal polynomials with respect to the weight function $w(t)(t^2-\|x\|^2)^{μ-\frac12}$, $μ> -\frac 12$, on the cone $\{(x,t): \|x\| \le t, \, x \in \mathbb{R}^d, t >0\}$ in $\mathbb{R}^{d+1}$. The first family consists of monomial polynomials $\mathsf{V}_{\mathbf{k},n}(x,t) = t^{n-|\mathbf{k}|} x^\mathbf{k} + \cdots$ for $\mathbf{k} \in \mathbb{N}_0^d$ with $|\mathbf{k}| \le n$, which has the least $L^2$ norm among all polynomials of the form $t^{n-|\mathbf{k}|} x^\mathbf{k} + \mathsf{P}$ with $°\mathsf{P} \le n-1$, and we will provide an explicit construction for $\mathsf{V}_{\mathbf{k},n}$. The second family consists of orthogonal polynomials defined by the Rodrigues type formulas when $w$ is either the Laguerre weight or the Jacobi weight, which satisfies a generating function in both cases. The two families of polynomials are partially biorthogonal.

math.CA↗

arXiv2022

Optimal charging of a superconducting quantum battery

Quantum batteries are miniature energy storage devices and play a very important role in quantum thermodynamics. In recent years, quantum batteries have been extensively studied, but limited in theoretical level. Here we report the experimental realization of a quantum battery based on superconducting qubits. Our model explores dark and bright states to achieve stable and powerful charging processes, respectively. Our scheme makes use of the quantum adiabatic brachistochrone, which allows us to speed up the {battery ergotropy injection. Due to the inherent interaction of the system with its surrounding, the battery exhibits a self-discharge, which is shown to be described by a supercapacitor-like self-discharging mechanism. Our results paves the way for proposals of new superconducting circuits able to store extractable work for further usage.

quant-ph↗

arXiv2022

$\ell^1$-summability and Fourier series of B-splines with respect to their knots

We study the $\ell^1$-summability of functions in the $d$-dimensional torus $\mathbb{T}^d$ and so-called $\ell^1$-invariant functions. Those are functions on the torus whose Fourier coefficients depend only on the $\ell^1$-norm of their indices. Such functions are characterized as divided differences that have $\cos θ_1,\ldots,\cosθ_d$ as knots for $(θ_1\,\ldots, θ_d) \in \mathbb{T}^d$. It leads us to consider the $d$-dimensional Fourier series of univariate B-splines with respect to its knots, which turns out to enjoy a simple bi-orthogonality that can be used to obtain an orthogonal series of the B-spline function.

math.CA↗

arXiv2022

Scalable Method for Eliminating Residual $ZZ$ Interaction between Superconducting Qubits

Unwanted $ZZ$ interaction is a quantum-mechanical crosstalk phenomenon which correlates qubit dynamics and is ubiquitous in superconducting qubit systems. It adversely affects the quality of quantum operations and can be detrimental in scalable quantum information processing. Here we propose and experimentally demonstrate a practically extensible approach for complete cancellation of residual $ZZ$ interaction between fixed-frequency transmon qubits, which are known for long coherence and simple control. We apply to the intermediate coupler that connects the qubits a weak microwave drive at a properly chosen frequency in order to noninvasively induce an ac Stark shift for $ZZ$ cancellation. We verify the cancellation performance by measuring vanishing two-qubit entangling phases and $ZZ$ correlations. In addition, we implement a randomized benchmarking experiment to extract the idling gate fidelity which shows good agreement with the coherence limit, demonstrating the effectiveness of $ZZ$ cancellation. Our method allows independent addressability of each qubit-qubit connection, and is applicable to both nontunable and tunable couplers, promising better compatibility with future large-scale quantum processors.

quant-ph↗

arXiv2022

Leaky-wave metasurfaces for integrated photonics

Metasurfaces have been rapidly advancing our command over the many degrees of freedom of light within compact, lightweight devices. However, so far, they have mostly been limited to manipulating light in free space. Grating couplers provide the opportunity of bridging far-field optical radiation and in-plane guided waves, and thus have become fundamental building blocks in photonic integrated circuits. However, their operation and degree of light control is much more limited than metasurfaces. Metasurfaces integrated on top of guided wave photonic systems have been explored to control the scattering of light off-chip with enhanced functionalities - namely, point-by-point manipulation of amplitude, phase or polarization. However, these efforts have so far been limited to controlling one or two optical degrees of freedom at best, and to device configurations much more complex compared to conventional grating couplers. Here, we introduce leaky-wave metasurfaces, which are based on symmetry-broken photonic crystal slabs that support quasi-bound states in the continuum. This platform has a compact form factor equivalent to the one of conventional grating couplers, but it provides full command over amplitude, phase and polarization (four optical degrees of freedom) across large apertures. We present experimental demonstrations of various functionalities for operation at wavelengths near 1.55 microns based on leaky-wave metasurfaces, including devices for phase and amplitude control at a fixed polarization state, and devices controlling all four optical degrees of freedom. Our results merge the fields of guided and free-space optics under the umbrella of metasurfaces, exploiting the hybrid nature of quasi-bound states in the continuum, for opportunities to advance in disruptive ways imaging, communications, augmented reality, quantum optics, LIDAR and integrated photonic systems.

physics.optics↗

arXiv2022

Bernstein inequality on conic domains and triangle

We establish weighted Bernstein inequalities in $L^p$ space for the doubling weight on the conic surface $\mathbb{V}_0^{d+1} = \{(x,t): \|x\| = t, x \in \mathbb{R}^d, t\in [0,1]\}$ as well as on the solid cone bounded by the conic surface and the hyperplane $t =1$, which becomes a triangle on the plane when $d=1$. While the inequalities for the derivatives in the $t$ variable behave as expected, there are inequalities for the derivatives in the $x$ variables that are stronger than what one may have expected. As an example, on the triangle $\{(x_1,x_2): x_1 \ge 0, \, x_2 \ge 0,\, x_1+x_2 \le 1\}$, the usual Bernstein inequality for the derivative $\partial_1$ states that $\|ϕ_1 \partial_1 f\|_{p,w} \le c n \|f\|_{p,w}$ with $ϕ_1(x_1,x_2):= x_1(1-x_1-x_2)$, whereas our new result gives $$\| (1-x_2)^{-1/2} ϕ_1 \partial_1 f\|_{p,w} \le c n \|f\|_{p,w}.$$ The new inequality is stronger and points out a phenomenon unobserved hitherto for polygonal domains.

math.CA↗

arXiv2021

Scalable algorithm simplification using quantum AND logic

Implementing quantum algorithms on realistic hardware requires translating high-level global operations into sequences of native elementary gates, a process known as quantum compiling. Physical limitations, such as constraints in connectivity and gate alphabets, often result in unacceptable implementation costs. To enable successful near-term applications, it is crucial to optimize compilation by exploiting the potential capabilities of existing hardware. Here, we implement a resource-efficient construction for a quantum version of AND logic that can reduce the cost, enabling the execution of key quantum circuits. On a high-scalability superconducting quantum processor, we demonstrate low-depth synthesis of high-fidelity generalized Toffoli gates with up to 8 qubits and Grover's search algorithm in a search space of up to 64 entries; both are the largest such implementations in scale to date. Our experimental demonstration illustrates a scalable implementation of simplifying quantum algorithms, paving the way for larger, more meaningful quantum applications on noisy devices.

quant-ph↗

arXiv2021

Superrobust Geometric Control of a Superconducting Circuit

Geometric phases accompanying adiabatic quantum evolutions can be used to construct robust quantum control for quantum information processing due to their noise-resilient feature. A significant development along this line is to construct geometric gates using nonadiabatic quantum evolutions to reduce errors due to decoherence. However, it has been shown that nonadiabatic geometric gates are not necessarily more robust than dynamical ones, in contrast to an intuitive expectation. Here we experimentally investigate this issue for the case of nonadiabatic holonomic quantum computation~(NHQC) and show that conventional NHQC schemes cannot guarantee the expected robustness due to a cross coupling to the states outside the computational space. We implement a different set of constraints for gate construction in order to suppress such cross coupling to achieve an enhanced robustness. Using a superconducting quantum circuit, we demonstrate high-fidelity holonomic gates whose infidelity against quasi-static transverse errors can be suppressed up to the fourth order, instead of the second order in conventional NHQC and dynamical gates. In addition, we explicitly measure the accumulated dynamical phase due to the above mentioned cross coupling and verify that it is indeed much reduced in our NHQC scheme. We further demonstrate a protocol for constructing two-qubit NHQC gates also with an enhanced robustness.

quant-ph↗

arXiv2021

Maximal functions and multiplier theorem for Fourier orthogonal series

Under the assumption that orthogonal polynomials of several variables admit an addition formula, we can define a convolution structure and use it to study the Fourier orthogonal expansions on a homogeneous space. We define a maximal function via the convolution structure induced by the addition formula and use it to establish a Marcinkiewicz multiplier theorem. For the homogeneous space defined by a family of weight functions on conic domains, we show that the maximal function is bounded by the Hardy-Littlewood maximal function so that the multiplier theorem holds on conic domains.

math.CA↗

arXiv2021

Approximation and localized polynomial frame on conic domains

Highly localized kernels constructed by orthogonal polynomials have been fundamental in recent development of approximation and computational analysis on the unit sphere, unit ball and several other regular domains. In this work we first study homogeneous spaces that are assumed to contain highly localized kernels and establish a framework for approximation and localized tight frame in such spaces, which extends recent works on bounded regular domains. We then show that the framework is applicable to homogeneous spaces defined on bounded conic domains, which consists of conic surfaces and the solid domains bounded by such surfaces and hyperplanes. 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 conic domains. The latter is achieved by using a $K$-functional, defined via the differential operator that has orthogonal polynomials as eigenfunctions, as well as a modulus of smoothness defined via a multiplier operator that is equivalent to the $K$-functional. Several intermediate results are of interest in their own right, including the Marcinkiewicz-Zygmund inequalities, positive cubature rules, Christoeffel functions, and several Bernstein type inequalities. Moreover, although the highly localizable kernels hold only for special families of weight functions on each domain, many intermediate results are shown to hold for doubling weights defined via the intrinsic distance on the domain.

math.CA↗