This review presents a comprehensive overview of the Unitary Coupled Cluster (UCC) ansatz and related ansätze which are used to solve the electronic structure problem on quantum computers.

We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wave functions. Our approach directly determines system-specific representations of qubit Hamiltonians while fully omitting globally defined basis sets. In this work, we use directly determined pair-natural orbitals on the level of second-order perturbation theory. This results in compact qubit Hamiltonians with high numerical accuracy. We demonstrate initial applications with compact Hamiltonians on up to 22 qubits where conventional representation would for the same systems require 40−100 or more qubits. We further demonstrate reductions in the quantum circuits through the structure of the pair-natural orbitals.

Variational quantum algorithms are currently the most promising class of algorithms for deployment on near-term quantum computers. In contrast to classical algorithms, there are almost no standardized methods in quantum algorithmic development yet, and the field continues to evolve rapidly. As in classical computing, heuristics play a crucial role in the development of new quantum algorithms, resulting in a high demand for flexible and reliable ways to implement, test, and share new ideas. Inspired by this demand, we introduce tequila, a development package for quantum algorithms in python, designed for fast and flexible implementation, prototyping and deployment of novel quantum algorithms in electronic structure and other fields. tequila operates with abstract expectation values which can be combined, transformed, differentiated, and optimized. On evaluation, the abstract data structures are compiled to run on state of the art quantum simulators or interfaces.