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At the intersection of quantum computing and machine learning, quantum machine learning (QML) is poised to revolutionize artificial intelligence. However, the vulnerability of the current generation of quantum computers to noise and…
Adaptive ansatz construction has emerged as a powerful technique for reducing circuit depth and improving optimization efficiency in variational quantum eigensolvers. However, existing adaptive methods, including ADAPT-VQE, rely solely on…
We present a theoretical and numerical scheme that enables quantifying hydrogen ingress in metals for arbitrary environments and defect geometries. This is achieved by explicitly resolving the electrochemical behaviour of the electrolyte,…
In recent years, molecular representation learning has emerged as a key area of focus in various chemical tasks. However, many existing models fail to fully consider the geometric information of molecular structures, resulting in less…
Network geometry, characterized by nodes with associated latent variables, is a fundamental feature of real-world networks. Still, when only the network edges are given, it may be difficult to assess whether the network contains an…
This paper proposes a machine learning (ML) method to predict stable molecular geometries from their chemical composition. The method is useful for generating molecular conformations which may serve as initial geometries for saving time…
In this educational paper, we will discuss calculations on the hydrogen molecule both on classical and quantum computers. In the former case, we will discuss the calculation of molecular integrals that can then be used to calculate…
We present the first demonstration of an end-to-end pipeline with quantum error correction (QEC) for a quantum computation of the electronic structure of molecular systems. We calculate the ground-state energy of molecular hydrogen, using…
Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of…
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…
The geometric measure of entanglement is the distance or angle between an entangled target state and the nearest unentangled state. Often one considers the geometric measure of entanglement for highly symmetric entangled states because it…
We revisit the representation of generalized quantum observables by establishing a geometric picture in terms of their positive operator-valued measures (POVMs). This leads to a clear geometric interpretation of Born's rule by introducing…
Geometric phases play a crucial role in diverse fields. In chemistry they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wavefunction experiences quantum-mechanical…
Formal methods for verification of programs are extended to testing of programs. Their combination is intended to lead to benefits in reliable program development, testing, and evolution. Our geometric theory of testing is intended to serve…
Machine learning (ML) outperforms traditional approaches in many molecular design tasks. ML models usually predict molecular properties from a 2D chemical graph or a single 3D structure, but neither of these representations accounts for the…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
A key challenge in machine learning is to explain how learning dynamics select among the many solutions that achieve identical loss values in overparameterized models - a phenomenon known as implicit bias. Controlling this bias provides a…
As science and engineering have become increasingly data-driven, the role of optimization has expanded to touch almost every stage of the data analysis pipeline, from signal and data acquisition to modeling and prediction. The optimization…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Exact calculation of electronic properties of molecules is a fundamental step for intelligent and rational compounds and materials design. The intrinsically graph-like and non-vectorial nature of molecular data generates a unique and…