Automatic differentiation in quantum chemistry

Abstract

Automatic differentiation (AD) is a well-established tool that allows us to compute exact derivatives of implemented functions with respect to all their parameters. It does so without requiring any extra coding or knowledge of the analytical derivatives. Derivatives of quantum chemistry algorithms are generally very hard to obtain and often cumbersome to implement. AD shows great potential to solve this problem and to facilitate the implementation of gradients in the context of electronic structure methods. In this dissertation, we have applied AD in a broader context and demonstrate that AD tools can compute arbitrary gradients of quantum chemistry methods with respect to any input parameter and any intermediate function. To this end, we have developed the open-source code DiffiQult, a fully differentiable Hartree-Fock (HF) software package. DiffiQult is a python package that uses AD tools using the external libraries JAX and Algopy. As a proof of concept, DiffiQult is an example of an end-to-end differentiable software package of a quantum chemistry algorithm based solely on AD tools. This application has helped us understand the challenges of AD in quantum chemistry. We outline the details, benefits, and caveats of AD for the HF algorithm in this work. We have chosen HF as a starting point since it contains all the functions included in correlated electronic structure methods. In this way, it opens the door for the development of AD for more accurate algorithms. As an application, we describe DiffiQult within the framework of the fully variational HF method, where we use a gradient-based optimization method to compute system-specific basis functions. As a result, the wavefunction can capture more molecular features, and we obtain a set of basis functions for correlated methods in quantum and classical algorithms. This proves that these functions improve variationally energy while keeping a compact representation in correlated methods by interfacing with the quantum chemistry library PySCF, and with Tequila, a platform for rapid development of quantum algorithms. First, we present optimization results of minimal basis sets with respect to all parameters of the molecules H2O, CH4, NH3, HF. Later we include optimization of the potential energy surface of two isomerization mechanisms of diazene and hydrogens chains. Here, we use a minimal optimized basis set to compute FCI when possible with PySCF and VQE energies of hydrogen chains with Tequila. We obtain similar results compared to a bigger basis set with considerably fewer configurations. Also, we show how this approach improves the estimation of the thermodynamic limit in the hydrogen chain at the HF level. Finally, we apply this approach to the optimization of all atomic orbitals of benzene and compute electronic correlations restricting the active space to the 6 π orbitals of benzene using the UpCCGSD ansatz implemented in Tequila.