Methods for simulating chemistry using quantum computers

Electronic structure calculations are routinely used by researchers in chemistry, materials science, physics and engineering to model and predict molecular properties and processes from the well-established laws of quantum mechanics. They play a central role in computational quantum chemistry and are crucial for the discovery and rational design of new chemicals and materials such as catalysts, drugs, optoelectronic devices, and other functional molecular assemblies. However, they suffer from a practical difficulty: finding the exact solution to a quantum many-particle problem requires computational resources which scale exponentially with the size of the simulated system. This is a consequence of the exponential scaling of the space of possible solutions as a function of the number of degrees of freedom that are used in the simulation, which is proportional to the size of the simulated system. Hence, when performed on a conventional computer, quantum simulations of chemistry are constrained to very small molecules or require strong approximations which severely limit the accuracy of simulations.
Quantum computers could perform certain computational tasks much faster than conventional ("classical") computers. In particular, they could circumvent the curse of dimensionality which limits the accuracy of quantum simulation on classical machines. Consequently, quantum simulation is widely believed to be one of the most promising applications of quantum computers.
Currently available quantum devices can create and control quantum states with increasing complexity, despite being imperfect and limited in size. Due to the recent emergence of noisy, intermediate-scale quantum (NISQ) devices, much research is being devoted towards finding quantum algorithms which can exploit such near-term machines to achieve a significant speed-up when simulating chemical systems of interest (a prospect often termed "quantum advantage"). However, research on quantum algorithms involves techniques suited for both NISQ as well as long-term, fault tolerant quantum computers.
This DPhil project will aim to investigate methods for efficiently simulating chemical systems using quantum computers. In particular, new approaches will be developed for finding accurate and efficient mappings which encode electronic molecular systems into states of qubits, as well as algorithms which can exploit the unique power of quantum computers to solve for the eigenstates of electronic Hamiltonians. Such developments could enable a fundamental leap forward in electronic structure calculations and unlock the possibility of accurate computational quantum-mechanical modeling of complex molecular systems.
The project falls within the EPSRC Quantum Technologies research area.
The DPhil student will be co-supervised by Prof. David Tew (Department of Chemistry, University of Oxford) and Prof. Simon Benjamin (Department of Materials, University of Oxford). The work will be theoretical but will involve a collaboration with the Quantum Photonics group of Prof. Anthony Laing, University of Bristol, where quantum algorithms will be tested on real quantum devices developed in the group.