Quantum simulation is one of the most scientifically interesting applications of quantum computers. Prior to the development of a universal quantum computer, near-term quantum simulators may be able to implement the solution of problems that are beyond the capabilities of classical computers. To achieve this ambitious goal, it is paramount to develop algorithms that exploit the strengths of the quantum processor while also making use of classical resources. A notable example of such algorithms is the variational quantum eigensolver (VQE). A crucial aspect of VQEs is the creation of a good variational ansatz, which allows for relatively shallow circuits and a low number of classical optimization parameters. In this talk, I will present ADAPT-VQE, a novel algorithm which realizes such ansatze on quantum computers. Our simulations show that ADAPT-VQE outperforms competing ansatze on all metrics. I will also discuss our work on symmetry-preserving circuits for problems describing physical Hamiltonians, along with some results from the IBM Q superconducting qubit simulators and hardware, where we showed that our ansatze outperform the built-in ones in terms of CNOT count and accuracy.
