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Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
We present $\mathcal{O}(N^2)$ estimators for the small-scale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales,…
Homomorphic encryption (HE) is a privacy-preserving technique that enables computation directly over ciphertext. Unfortunately, a key challenge for HE is that implementations can be impractically slow and have limits on computation that can…
Modeling the energy and forces of atomic systems is a fundamental problem in computational chemistry with the potential to help address many of the world's most pressing problems, including those related to energy scarcity and climate…
Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…
We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve…
The Hilbert transform has been one of the foundational transforms in signal processing, finding it's way into multiple disciplines from cryptography to biomedical sciences. However, there does not exist any quantum analogue for the Hilbert…
This paper introduces a method to preform optical tomography, using 3D radiative transfer as the forward model. We use an iterative approach predicated on the Spherical Harmonics Discrete Ordinates Method (SHDOM) to solve the optimization…
Stochastic variance reduction has proven effective at accelerating first-order algorithms for solving convex finite-sum optimization tasks such as empirical risk minimization. Incorporating second-order information has proven helpful in…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
We propose a framework that automatically transforms non-scalable GNNs into precomputation-based GNNs which are efficient and scalable for large-scale graphs. The advantages of our framework are two-fold; 1) it transforms various…
3D Gaussian splatting (3DGS) has demonstrated impressive 3D reconstruction performance with explicit scene representations. Given the widespread application of 3DGS in 3D reconstruction and generation tasks, there is an urgent need to…
We propose a hybrid quantum-classical algorithm for solving the time-independent Schr\"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes…
Hyper spectral images (HSI) provide rich spectral and spatial information across a series of contiguous spectral bands. However, the accurate processing of the spectral and spatial correlation between the bands requires the use of…
HEALPix (Hierarchical Equal Area isoLatitude Pixelization) is a widely adopted spherical grid system in astrophysics, cosmology, and Earth sciences. Its equal-area, iso-latitude structure makes it particularly well-suited for large-scale…
Ternary Neural Networks (TNNs) have received much attention due to being potentially orders of magnitude faster in inference, as well as more power efficient, than full-precision counterparts. However, 2 bits are required to encode the…
This paper introduces a generalised 3rd-order Spectral Representation Method for the simulation of multi-dimensional stochastic fields with asymmetric non-linearities. The simulated random fields satisfy a prescribed Power Spectrum and…
We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…
We consider an efficient computational framework for speeding up several machine learning algorithms with almost no loss of accuracy. The proposed framework relies on projections via structured matrices that we call Structured Spinners,…
The discovery of fast numerical solvers prompted a clear and rapid shift towards iterative techniques in many applications, especially in computational mechanics, due to the increased necessity for solving very large linear systems. Most…