Algorithms for Quantum Chemistry on a Digital Quantum Computer

Quantum chemistry problem is one of the attractive targets for demonstrating the quantum advantage of quantum computing technology. Having strongly correlated systems as the main target, I would like to discuss what new classical computing techniques need to be developed to help quantum computing algorithms solve the electronic structure problem. Encoding the electronic Hamiltonian in the second quantized form on a quantum computer is not a trivial problem, and its efficiency can become a bottleneck for the entire quantum solution. Dealing with this Hamiltonian can be facilitated by partitioning it into a sum of fragments diagonalizable using rotations from either small Lie groups or the Clifford group. These fragments are convenient for performing various algebraic manipulations required in circuit compiling and quantum measurement. I will illustrate how the Hamiltonian partitioning can be used to improve the performance of several quantum algorithms for quantum chemistry (e.g. Variational Quantum Eigensolver and Quantum Phase Estimation).

Artur Izmaylov

Associate Professor of Chemistry, University of Toroanto on October 11, 2024 at 10:15 AM in EB2 1231
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Prof. Izmaylov is a Full Professor at the Departments of Chemistry and Physical and Environmental Sciences of the University of Toronto. He received his PhD from Rice University in 2009, where he developed several novel methods of density functional theory for accurate description of electronic properties of solids. He implemented them in the famous Gaussian software, which was noted in the 1998 Nobel Prize in chemistry and is widely used by the scientific community. Publications on the density functionals that he worked on have been already cited over 6000 times. After a joint postdoctoral appointment at Yale University and Gaussian Inc., in 2012 he joined the University of Toronto.

The main efforts of his group in the period of 2012-2018 were directed toward providing fundamental insights into the ways the geometric phase affects molecular dynamics and discovering new simulation methods that enable capturing these important effects. This work was recognized by multiple highly competitive awards and fellowships: Sloan Fellowship (USA, 2015), Ontario Early Researcher Award (Canada, 2017), Tom Ziegler Award (Canadian Society for Chemistry, 2019), and Journal of Physical Chemistry Lectureship Award (ACS, 2019).

Since 2017, Prof. Izmaylov has started developing quantum computational algorithms for solving quantum many-body problems challenging for classical algorithms. Among these problems are 1) finding electronic states and their properties for strongly correlated molecules and solids, 2) predicting dynamics and vibrational spectra of molecules with high anharmonicity and non-adiabaticity, and 3) modelling non-equilibrium stationary state of open quantum systems. Main achievements of his research program for near-term quantum algorithms are efficient techniques for the state preparation (Qubit Coupled Cluster theory) and quantum measurements. These developments were recognized by the Google Quantum Research Award (2019) and several industry partnership grants. Current efforts of his group focus on developments for error-corrected quantum algorithms and quantum inspired techniques for classical computing.