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The linear canonical transform (LCT) serves as a powerful generalization of the Fourier transform (FT), encapsulating various integral transforms within a unified framework. This versatility has made it a cornerstone in fields such as…

The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…

High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…

Although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications such as communications. In this work, we…

Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert…

We propose a simple drop-in noise-tolerant replacement for the standard finite difference procedure used ubiquitously in blackbox optimization. In our approach, parameter perturbation directions are defined by a family of structured…

The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which…

We propose a novel adaptive kernel based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space…

This paper presents a novel unifying framework of bilinear LSTMs that can represent and utilize the nonlinear interaction of the input features present in sequence datasets for achieving superior performance over a linear LSTM and yet not…

The simulation of chemistry is among the most promising applications of quantum computing. However, most prior work exploring algorithms for block-encoding, time-evolving, and sampling in the eigenbasis of electronic structure Hamiltonians…

The accurate description and robust computational modeling of the nonequilibrium properties of quantum systems remain a challenge in condensed matter physics. In this work, we develop a linear-scale computational simulation technique for…

Using quantum systems to efficiently solve quantum chemistry problems is one of the long-sought applications of near-future quantum technologies. In a recent work, ultra-cold fermionic atoms have been proposed for these purposes by showing…

With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting…

Computational Fluid Dynamics simulations are crucial in industrial applications but require extensive computational resources, particularly for extreme turbulent regimes. While classical digital approaches remain the standard, quantum…

Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for…

Determining the physically accessible unitary dynamics of a quantum system under finite Hamiltonian resources is a central problem in quantum control and Hamiltonian engineering. Dynamical Lie algebras (DLAs) provide the fundamental link…

We provide a new paradigm for quantum simulation that is based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional…

This paper presents a kernel formulation of the recently introduced diff-hash algorithm for the construction of similarity-sensitive hash functions. Our kernel diff-hash algorithm that shows superior performance on the problem of image…

Linear Canonical Transformations (LCTs) are known in signal processing and optics as the generalization of certain useful integral transforms. In quantum theory, they can be identified as the linear transformations which keep invariant the…

Simulating the time evolution of quantum field theories given some Hamiltonian $H$ requires developing algorithms for implementing the unitary operator e^{-iHt}. A variety of techniques exist that accomplish this task, with the most common…