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It is well known that the number of particles should be scaled up to enable industrial scale simulation. The calculations are more computationally intensive when the motion of the surrounding fluid is considered. Besides the advances in…
Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large…
A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as…
Computational modeling of cellular systems, where reactants are governed by biochemical equations and physical representations, requires extensive classical computing resources. These limitations significantly constrain the system size and…
Predictive simulation of surface chemistry is of paramount importance for progress in fields from catalysis to electrochemistry and clean energy generation. Ab-initio quantum many-body methods should be offering deep insights into these…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
Accurate prediction of bond dissociation energies (BDEs) underpins mechanistic insight and the rational design of molecules and materials. We present a systematic, reproducible benchmark comparing quantum and classical machine learning…
Quantum computing presents a promising alternative to classical computational methods for modeling strongly correlated materials with partially filled d orbitals. In this study, we perform a comprehensive quantum resource estimation using…
Modeling and simulating the protein folding process overall remains a grand challenge in computational biology. We systematically investigate end-to-end quantum algorithms for simulating various protein dynamics with effects, such as…
Dynamical response functions are fundamental quantities to describe the excited-state properties in quantum many-body systems. Quantum algorithms have been proposed to evaluate these quantities by means of quantum phase estimation (QPE),…
Quantum phase classification is a fundamental problem in quantum many-body physics, traditionally approached using order parameters or quantum machine learning techniques such as quantum convolutional neural networks (QCNNs). However, these…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
The brain interprets ambiguous sensory information faster and more reliably than modern computers, using neurons that are slower and less reliable than logic gates. But Bayesian inference, which underpins many computational models of…
Modern problems in high-performance computing, ranging from training and inferencing deep learning models in computer vision and language models to simulating complex physical systems with nonlinearly-coupled equations, require exponential…
With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an…
Simulating the full dynamics of a quantum field theory over a wide range of energies requires exceptionally large quantum computing resources. Yet for many observables in particle physics, perturbative techniques are sufficient to…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
Unwanted interaction between a quantum system and its fluctuating environment leads to decoherence and is the primary obstacle to establishing a scalable quantum information processing architecture. Strategies such as environmental and…