For a Fistful of Qubits: Computational Quantum Chemistry on Near-Term Quantum Computers

Doctoral thesis, 2023

Quantum computing has been touted as a great new frontier of computation, pushing the limits of what we consider within reach of computation. While not all problems are expected to be efficiently solved by a quantum computer, quantum chemistry is among those where many have speculated on near-term quantum advantage. A leading approach to near-term advantage comes in the form of variational quantum algorithms. In particular, variations of the Variational Quantum Eigensolver (VQE) algorithm form popular choices for chemistry on noisy quantum hardware.

This thesis dives into the topic of near-term quantum computing using variational quantum algorithms, the VQE in particular. Leveraging both classical simulations as well existing quantum computers, challenges of near-term quantum computing are explored. A parameter transfer approach is tested, aimed at helping speedup optimization variational parameters; an error mitigation strategy requiring close to no overhead is developed to reduce errors; and to help gauge the quality of quantum calculations beyond the point of quantum advantage, topologies of electron densities are analyzed. In addition, the application of near-term quantum computers to non-Born--Oppenheimer problems is explored, both for static and dynamic cases. The extension to the non-Born--Oppenheimer, opens for new qubit reduction schemes which are analyzed.

Exploration the limits of near-term quantum hardware and algorithms forms a common thread among the topics investigated. While quantum advantage still remains out of grasp for current generations of quantum computers, hope for near-term advantage remains. By pushing the boundaries, useful quantum computing might come one step closer.