Related papers: Quantum Time-Frequency Transforms
We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time…
This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing…
It is impossible to obtain accurate frequencies from time signals of a very short duration. This is a common believe among contemporary physicists. Here I present a practical way of extracting energies to a high precision from very short…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
We construct an efficient quantum algorithm to compute the quantum Schur-Weyl transform for any value of the quantum parameter $q \in [0,\infty]$. Our algorithm is a $q$-deformation of the Bacon-Chuang-Harrow algorithm, in the sense that it…
We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
We investigate the quantum optical response of antireflection temporal coatings, i.e., matching temporal layers that suppress the generation of backward waves in temporal boundaries. Our results reveal that quantum antireflection temporal…
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…
A quantum version of a recent formulation of transition state theory in {\em phase space} is presented. The theory developed provides an algorithm to compute quantum reaction rates and the associated Gamov-Siegert resonances with very high…
This paper constructs the first quantum algorithm for wavelet packet transforms with a "parabolic scaling" tree structure, sometimes called wave atom transforms. Classically, wave atoms are used to construct sparse representations of…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
We present a quantum manipulation of a traveling light pulse using double atomic coherence for two-color stationary light and quantum frequency conversion. The quantum frequency conversion rate of the traveling light achieved by the…
The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…
In this paper we construct directionally sensitive functions that can be viewed as directional time-frequency representations. We call such a sequence a rotational uniform covering frame and by studying rotations of the frame, we derive the…
Extending our previous work on time optimal quantum state evolution, we formulate a variational principle for the time optimal unitary operation, which has direct relevance to quantum computation. We demonstrate our method with three…
In this letter, based on the variational model, we propose a novel time-frequency post-processing technique to approximate the ideal time-frequency representation. Our method has the advantage of modularity, enabling "plug and play",…
An emerging way to deal with high-dimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work…
If several interventions performed on a quantum system are localized in mutually space-like regions, they will be recorded as a sequence of ``quantum jumps'' in one Lorentz frame, and as a different sequence of jumps in another Lorentz…
Bilinear time-frequency representations (TFRs) provide high-resolution time-varying frequency characteristics of nonstationary signals. However, they suffer from crossterms due to the bilinear nature. Existing crossterm-reduced TFRs focus…