Algebraic techniques for quantum chemistry on a quantum computer

Quantum chemistry problem is one of the attractive targets for demonstrating quantum advantage of quantum computing technology. Quantum computing algorithms for solving this problem require algebraic operations with the electronic Hamiltonian. Dealing with this Hamiltonian in the second quantized form 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. In this talk, I will illustrate how the Hamiltonian partitioning can be used to improve performance of the Variational Quantum Eigensolver and Quantum Phase Estimation algorithms.