相关论文: Optimal Evaluation of Generalized Euler Angles wit…

Many energy-based control strategies for mechanical systems require the choice of a Coriolis factorization satisfying a skew-symmetry property. This paper (a) explores if and when a control designer has flexibility in this choice, (b)…

The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the…

[...] In this thesis, we are interested in generalizing factor graphs and the relevant methods toward describing quantum systems. Two generalizations of classical graphical models are investigated, namely double-edge factor graphs (DeFGs)…

We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values $(x,y)$ to $(x,x \oplus y)$) is universal in the sense that all unitary operations on arbitrarily many…

This paper proposes a new factor rotation for the context of functional principal components analysis. This rotation seeks to re-represent a functional subspace in terms of directions of decreasing smoothness as represented by a generalized…

For each $n=1,2,\dots$, let $\mathsf{GL}(n,\mathbb{Z})\ltimes \mathbb{Z}^n$ be the affine group over the integers. For every point $x=(x_1,\dots,x_n) \in \mathbb{R}^n$ let $\mathrm{orb}(x)=\{\gamma(x)\in \mathbb{R}^n\mid\gamma\in…

In the prequel to this paper, we proved that for a $SU(2,\mathbb C)$ valued loop having the critical degree of smoothness (one half of a derivative in the $L^2$ Sobolev sense), the following statements are equivalent: (1) the Toeplitz and…

In high-energy processes which are sensitive to small transverse momenta, individual contributions from collinear and soft momentum regions are not separately well-defined in dimensional regularization. A simple possibility to solve this…

Outliers contaminating data sets are a challenge to statistical estimators. Even a small fraction of outlying observations can heavily influence most classical statistical methods. In this paper we propose generalized spherical principal…

Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…

The generating functions for the gauge theory observables are often represented in terms of the unitary matrix integrals. In this work, the perturbative and non-perturbative aspects of the generic multi-critical unitary matrix models are…

We give several criteria for a ring to be a UFD including generalizations of some criteria due to P. Samuel. These criteria are applied to construct, for any field k, (1) a Z-graded non-noetherian rational UFD of dimension three over k, and…

Following the works by Lin et al. (Circuits Syst. Signal Process. 20(6): 601-618, 2001) and Liu et al. (Circuits Syst. Signal Process. 30(3): 553-566, 2011), we investigate how to factorize a class of multivariate polynomial matrices. The…

Controlled operations allow for the entanglement of quantum registers. In particular, a controlled-$U$ gate allows an operation, $U$, to be applied to the target register and entangle the results to certain values in the control register.…

Quantum circuit model is the most popular paradigm for implementing complex quantum computation. Based on Cartan decomposition, we show that $2(N-1)$ generalized controlled-$X$ (GCX) gates, $6$ single-qubit rotations about the $y$- and…

The entanglement entropy for a quantum critical system across a boundary with a corner exhibits a sub-leading logarithmic scaling term with a scale-invariant coefficient. Using a Numerical Linked Cluster Expansion, we calculate this…

Although only two quantum states of a physical system are often used to encode quantum information in the form of qubits, many levels can in principle be used to obtain qudits and increase the information capacity of the system. To take…

Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…

A generalized exponential matrix based on the construction of kernel operators for generalized summability is defined and analyzing its main properties, generalizing the classical exponential matrix and fractional exponential matrix. This…

In this note, we show how to provide sharp control on the least singular value of a certain translated linearization matrix arising in the study of the local universality of products of independent random matrices. This problem was first…