相关论文: Classical and Quantum Ensembles via Multiresolutio…
We introduce new representations to formulate quantum mechanics on noncommutative phase space, in which both coordinate-coordinate and momentum-momentum are noncommutative. These representations explicitly display entanglement properties…
We introduce a variational quantum computing approach for quantum state reconstruction within a discretized logical framework, using experimental measurement data as input. By mapping the reconstruction cost function onto an Ising model,…
The metaplectic covariance for all forms of the Weyl-Wigner-Groenewold-Moyal quantization is established with different realizations of the inhomogeneous symplectic algebra. Beyond that, in its most general form $W_{\infty}$ -covariance of…
A high order wavelet integral collocation method (WICM) is developed for general nonlinear boundary value problems in physics. This method is established based on Coiflet approximation of multiple integrals of interval bounded functions…
We develop a general framework for studying relative weight representations for certain pairs consisting of an associative algebra and a commutative subalgebra. Using these tools we describe projective and simple weight modules for quantum…
Model quantization can reduce the model size and computational latency, it has become an essential technique for the deployment of deep neural networks on resourceconstrained hardware (e.g., mobile phones and embedded devices). The existing…
The resource theory of coherence addresses the extent to which quantum properties are present in a given quantum system. While coherence has been extensively studied for individual quantum states, measures of coherence for ensembles of…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
Machine-learning models based on a point-cloud representation of a physical object are ubiquitous in scientific applications and particularly well-suited to the atomic-scale description of molecules and materials. Among the many different…
Some general remarks about integral transform approaches to response functions are made. Their advantage for calculating cross sections at energies in the continuum is stressed. In particular we discuss the class of kernels that allow…
We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies…
The nondecimated or translation-invariant wavelet transform (NDWT) is a central tool in classical multiscale signal analysis, valued for its stability, redundancy, and shift invariance. This paper develops two complementary quantum…
The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It is first applied to an oscillator coupled to an equilibrium…
In this work, we present straightforward and concrete computations of the unitary irreducible representations of the Euclidean motion group $M(2)$ employing the methods of deformation quantization. Deformation quantization is a quantization…
Quantum engineering now allows to design and construct multi-qubit states in a range of physical systems. These states are typically quite complex in nature, with disparate, but relevant properties that include both single and multi-qubit…
Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…
We present a general M-estimation framework for inference on the wavelet variance. This framework generalizes the results on the scale-wise properties of the standard estimator and extends them to deliver the joint asymptotic properties of…
Unbounded potentials are always utilized to strictly confine quantum dynamics and generate bound or stationary states due to the existence of quantum tunneling. However, the existed accurate Wigner solvers are often designed for either…
Wavelet theory has been well studied in recent decades. Due to their appealing features such as sparse multiscale representation and fast algorithms, wavelets have enjoyed many tremendous successes in the areas of signal/image processing…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…