Exploring complexity and scalability of Near-term Quantum Computing algorithms for Quantum Chemistry

The study of molecular systems is heavily limited by current computing capabilities. As molecular systems grow in complexity exponentially, accurate computation of chemical properties becomes challenging even for small systems. Quantum computing offers many promises in terms of much larger modelling molecular systems than what we can currently do classically. The Variational Quantum Eigensolver (VQE) is one of the main examples of near-term quantum algorithms that are expected to find application in quantum chemistry. However, its scalability is still largely under question. Recently Zhenyu Cai (Oxford) has implemented resource estimates for VQE simulations of the 50-qubit Fermi-Hubbard Model, and discussed the requirement of multi-core NISQ processing to and better error mitigation in the context of near-term quantum hardware. The VQE, relies on classical pre-processing. In particular, we must first compute the second quantised Hamiltonian of the system, which already has a computational cost of O(N^4) for N orbitals. As such it will never replace the most widely used computational quantum chemistry method, Density Functional Theory (DFT) as its cost of solving is O(N^3) not assuming any sparsity (this would bring the cost in either case down). To be computationally relevant, the VQE must first and foremost be able to produce significantly more accurate results than DFT. At the same time, a suitable benchmarking analysis must compare the result and computational cost of VQE to a more accurate Quantum Chemistry method such as Full Configuration Interaction (FCI)/

Rahko is currently leading a project aiming at studying the scalability of the VQE. The start-up is looking for a CASE PhD student to collaborate on furthering this research and conduct a formal study of the feasibility of using near-term quantum computing for quantum chemistry.In particular, the student will be researching the latest literature on Quantum algorithms for quantum chemistry (beyond VQE) and build a methodology for assessing their scalability in comparison to the best practices for the likes of DFT and FCI. As part of this project, the student will define the state-of-the-art methods to implement quantum algorithms and will identify bottlenecks and possible improvements for their scalability throughout the programme stack. The student will be given access to Rahko's quantum development platform, Hyrax , and will gain access to real quantum computers (e.g. AWS Braket, Azure Quantum, IMBQ) and supercomputers through Rahko's and UCL's partnerships.