Electronic Structure Methods

Electronic Structure Methods

Electronic structure

Our research addresses the following two specific challenges a) the development of computer code for easy prototyping of new ideas in the field, and b) the development of compact wave functions for classical quantum chemistry and quantum computer simulation of molecules.

As the first area of research, we are developing the open-source DiffiQult package. DiffiQult is a code that employs modern automatic differentiation techniques allowing rapid development of new ideas without the tedious manual implementation of derivatives. We developed the code and applied it for the optimization of the centers and exponents of Gaussian basis functions for small molecules. The implementation excels where there are “difficult” or time-consuming derivatives to code, which can take, in our own experience, two to three person-years. Currently we're implementing the next generation of this code including interface to post Hartree-Fock methods and higher angular momentum basis functions.

The second area of research is the development of compact wave functions for the simulation of quantum chemistry on quantum computers, a very rapidly-growing field that we have actively helped to pioneer, since 2005. In particular, we can reduce the size of the basis sets with our DiffiQult software package. DiffiQult can generate custom basis functions for particular molecules at given geometries that then can be correlated on a quantum computer using the Variational Quantum Eigensolver (VQE) algorithm pioneered by the group. In order to do so, DiffiQult can be combined with Tequila which is also developed in the group and  allows the rapid development of new quantum algorithms in the same spirit.  Another approach that our group has explored is reducing the number of configurations by the NOMAGIC algorithm. NOMAGIC uses the basis-pursuit method stemming from the field of compressed sensing to obtain short non-orthogonal configuration interaction descriptions of correlated molecules by greedy selection. These ansatzes could bring more power to near-term quantum computing molecular calculations by shifting part of the computation to classical preprocessing and feeding a highly optimized initial wave function to the quantum computer.


Tequila is an open-source development tool for the rapid implementation of new ideas for quantum algorithms. It operates on abstract data structures allowing the formulation, combination, automatic differentiation and optimization of generalized objectives.

Tequila can execute the underlying quantum expectation values on state of the art simulators as well as on real quantum computers by communicating with their python interfaces. The high level of abstraction and generalized principles within Tequila allow fast implementation from blackboard to functional code as well as adaptation, modification and extension of existing algorithms for new research ideas.

The group uses Tequila to develop and test new ideas for quantum algorithms in electronic-structure, quantum-optics and quantum machine learning.

The code is open-source and freely available. It can be obtained from the group’s github page where we also provided tutorial notebooks.