A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules

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 the fundamental scattering $S$-matrix by inverting the Hamiltonian matrix expressed in the basis of square-integrable functions. The computational bottleneck of the classical algorithm -- symmetric matrix inversion -- is addressed here using the variational quantum linear solver (VQLS), a recently developed noisy intermediate-scale quantum (NISQ) algorithm for solving systems of linear equations. We apply our algorithm to single and multichannel quantum scattering problems, obtaining accurate vibrational relaxation probabilities in collinear atom-molecule collisions. We also show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules. Our results demonstrate that it is possible to calculate scattering cross sections and rates for complex molecular collisions on NISQ quantum processors, opening up the possibility of scalable digital quantum computation of gas-phase bimolecular collisions and reactions of relevance to astrochemistry and ultracold chemistry.Comment: 8 pages,6 figure

Physics-Informed Neural Networks for an optimal counterdiabatic quantum computation

We introduce a novel methodology that leverages the strength of Physics-Informed Neural Networks (PINNs) to address the counterdiabatic (CD) protocol in the optimization of quantum circuits comprised of systems with $N_{Q}$ qubits. The primary objective is to utilize physics-inspired deep learning techniques to accurately solve the time evolution of the different physical observables within the quantum system. To accomplish this objective, we embed the necessary physical information into an underlying neural network to effectively tackle the problem. In particular, we impose the hermiticity condition on all physical observables and make use of the principle of least action, guaranteeing the acquisition of the most appropriate counterdiabatic terms based on the underlying physics. The proposed approach offers a dependable alternative to address the CD driving problem, free from the constraints typically encountered in previous methodologies relying on classical numerical approximations. Our method provides a general framework to obtain optimal results from the physical observables relevant to the problem, including the external parameterization in time known as scheduling function, the gauge potential or operator involving the non-adiabatic terms, as well as the temporal evolution of the energy levels of the system, among others. The main applications of this methodology have been the $\mathrm{H_{2}}$ and $\mathrm{LiH}$ molecules, represented by a 2-qubit and 4-qubit systems employing the STO-3G basis. The presented results demonstrate the successful derivation of a desirable decomposition for the non-adiabatic terms, achieved through a linear combination utilizing Pauli operators. This attribute confers significant advantages to its practical implementation within quantum computing algorithms.Comment: 28 pages, 10 figures, 1 algorithm, 1 tabl

Educación ambiental y sociedad. Saberes locales para el desarrollo y la sustentabilidad

EL LIBRO PERMITE REFLEXIONAR SOBRE LA IMPORTANCIA DE FOMENTAL LA EDUCACIÓN AMBIENTAL PARA RESOLVER LA PROBLEMÁTICA AMBIENTALEL LIBRO PRESENTA DIFERENTES TRABAJOS QUE ESTUDIAN EL TEMA D ELA SUSTENTABILIDAD, ENFATIZANDO LA IMPORTANCIA DE LA EDUCACIÓN AMBIENTAL Y LA TRANSDISCIPLINANINGUN