Roberto Campos, Pablo A M Casares, M A Martin-Delgado
The efficient resolution of optimization problems is one of the key issues in today's industry. This task relies mainly on classical algorithms that present scalability problems and processing limitations. Quantum computing has emerged to challenge these types of problems. In this paper, we focus on the Metropolis-Hastings quantum algorithm that is based on quantum walks. We use this algorithm to build a quantum software tool called Quantum Metropolis Solver (QMS). We validate QMS with the N-Queen problem to show a potential quantum advantage in an example that can be easily extrapolated to an Artificial Intelligence domain. We carry out different simulations to validate the performance of QMS and its configuration.
Pablo A. M. Casares, Jack S. Baker, Matija Medvidovic et al.
Density functional theory (DFT) stands as a cornerstone method in computational quantum chemistry and materials science due to its remarkable versatility and scalability. Yet, it suffers from limitations in accuracy, particularly when dealing with strongly correlated systems. To address these shortcomings, recent work has begun to explore how machine learning can expand the capabilities of DFT; an endeavor with many open questions and technical challenges. In this work, we present Grad DFT: a fully differentiable JAX-based DFT library, enabling quick prototyping and experimentation with machine learning-enhanced exchange-correlation energy functionals. Grad DFT employs a pioneering parametrization of exchange-correlation functionals constructed using a weighted sum of energy densities, where the weights are determined using neural networks. Moreover, Grad DFT encompasses a comprehensive suite of auxiliary functions, notably featuring a just-in-time compilable and fully differentiable self-consistent iterative procedure. To support training and benchmarking efforts, we additionally compile a curated dataset of experimental dissociation energies of dimers, half of which contain transition metal atoms characterized by strong electronic correlations. The software library is tested against experimental results to study the generalization capabilities of a neural functional across potential energy surfaces and atomic species, as well as the effect of training data noise on the resulting model accuracy.
Predicting the 3D structure of proteins is one of the most important problems in current biochemical research. In this article, we explain how to combine recent deep learning advances with the well known technique of quantum walks applied to a Metropolis algorithm. The result, QFold, is a fully scalable hybrid quantum algorithm that, in contrast to previous quantum approaches, does not require a lattice model simplification and instead relies on the much more realistic assumption of parameterization in terms of torsion angles of the amino acids. We compare it with its classical analog for different annealing schedules and find a polynomial quantum advantage, and implement a minimal realization of the quantum Metropolis in the IBMQ Casablanca quantum system.