PhD Defense Jakob Günther

Title: Quantum algorithms for molecular electronic structure

Abstract: 

The behaviour of electrons lies at the heart of the formation of molecules, giving rise to complex chemical processes and structures up to the biomolecular scale. Studying this behaviour from first principles comes with several advantages: it allows for very accurate predictions, it is a universal approach for all molecular systems and, importantly, it results in a better understanding of chemical mechanisms. However, solving the underlying quantum many-body problem is notoriously difficult for classical computers, and an efficient, system-agnostic method is lacking. Quantum computing is a new paradigm that is naturally suited to numerically study complex quantum systems. In this thesis we describe how quantum computers can be used to solve molecular electronic structure problems. To lower the quantum resource requirements for computing electronic ground state energies, we introduce new methods and improve existing quantum algorithms.
 In the first part of the thesis, we combine deterministic and randomized product formulas to reduce the cost of phase estimation, and we find that Hamiltonians describing electrons in molecules are particularly well suited for such an approach. Further algorithmic improvements include a novel analysis of the phase estimation signal, an optimized Hamiltonian representation, more efficient gate compilation and tighter Trotter error estimation. We find that resource estimates on chemical benchmark systems are significantly lower than previous estimates based on product formulas.
 In the second part, a large-scale classical simulation of the partially randomized algorithm is performed on a fragment of a biologically relevant ligand, showing that algorithmic errors are orders of magnitude lower than rigorous error bounds suggest.
 In the final part of this thesis, we improve upon the chemical model by introducing a method that goes beyond the ubiquitously used ‘active-space’ approximation. The method includes contributions to the ground state energy from virtual orbitals up to second order in perturbation theory. A key insight is that no additional qubits are needed to represent the virtual orbitals. Moreover, for a fixed active space numerical results suggest that the asymptotic total runtime scales sublinearly with the number of virtual orbitals

Thesis for download (pdf)

Advisor: Professor, Matthias Christandl, MATH, University of Copenhagen

Assessment committee:

Chair, Associate Prof. Daniel Stilck Franca, MATH, University of Copenhagen 

Professor, Toby Cubitt, University College London