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The Fractional Fourier Transform (FRFT) has been playing a unique and increasingly important role in signal and image processing. In this letter, we investigate the property of frequency shift in two-dimensional FRFT (2D-FRFT) domain. It is…
Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock…
The recent rapid increase in demand for data processing has resulted in the need for novel machine learning concepts and hardware. Physical reservoir computing and an extreme learning machine are novel computing paradigms based on physical…
In this work we study the encoding of smooth, differentiable multivariate functions in quantum registers, using quantum computers or tensor-network representations. We show that a large family of distributions can be encoded as…
A broadband quantum echo effect in a three level $\varLambda$-type system interacting with two laser fields is investigated theoretically. Inspired by the emerging field of nuclear quantum optics which typically deals with very narrow…
Spectroscopy is an indispensable tool in understanding the structures and dynamics of molecular systems. However computational modelling of spectroscopy is challenging due to the exponential scaling of computational complexity with system…
Quantum information processing has been effectively demonstrated on a small number of qubits by nuclear magnetic resonance. An important subroutine in any computing is the readout of the output. ``Spectral implementation'' originally…
Quantum computing exploits the quantum-mechanical nature of matter to exist in multiple possible states simultaneously. This new approach promises to revolutionize the present form of computing. As an approach to quantum computing, we…
The Fourier Transform (FT) is a fundamental tool that permeates modern science and technology. While chemistry undergraduates encounter the FT as early as second year, their courses often only mention it in passing because computers…
New experimental techniques based on non-linear ultrafast spectroscopies have been developed over the last few years, and have been demonstrated to provide powerful probes of quantum dynamics in different types of molecular aggregates,…
This is the first in a series of two papers investigating the effect of electron-phonon coupling in two-dimensional Fourier transformed electronic spectroscopy. We present a series of one- and two-dimensional nonlinear spectroscopic…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic…
We study a dephasing channel with memory, modelled by a multimode environment of oscillators. Focusing on the case of two channel uses, we show that memory effects can enhance the amount of coherent quantum information transmitted down the…
Spectral and temporal mode matching are required for the efficient interaction of photons and quantum memories. In our previous work, we proposed a new route to spectrally compress broadband photons to achieve spectral mode matching with…
Fourier Ptychographic Microscopy (FPM) is a computational technique that achieves a large space-bandwidth product imaging. It addresses the challenge of balancing a large field of view and high resolution by fusing information from multiple…
An optical quantum memory can be broadly defined as a system capable of storing a useful quantum state through interaction with light at optical frequencies. During the last decade, intense research was devoted to their development, mostly…
We report a direct demonstration of quantum-enhanced sensing in the Fourier domain by comparing single- and two-photon interference in a fiber-based interferometer under strictly identical noise conditions. The simultaneous acquisition of…
A new protocol of the optical quantum memory based on the resonant interactions of the multi atomic system with a cavity light mode is proposed. The quantum memory is realized using a controllable inversion of the inhomogeneous broadening…
Quantum Fourier transform is of primary importance in many quantum algorithms. In order to eliminate the destructive effects of decoherence induced by couplings between the quantum system and its environment, we propose a robust scheme for…