Quantum Zeno approach for molecular energies with maximum commuting initialHamiltonians

TL;DR

This paper introduces a quantum Zeno approach combined with adiabatic and simulated-annealing techniques to compute molecular ground and excited states, addressing degeneracy issues with a maximum commuting Hamiltonian.

Contribution

It presents a novel quantum Zeno method that improves ground and excited state calculations by mitigating degeneracy problems in adiabatic quantum algorithms.

Findings

The Zeno method effectively reduces degeneracy issues.

Accurate computation of low-lying excited states.

Enhanced robustness of quantum adiabatic processes.

Abstract

We propose to use a quantum adiabatic and simulated-annealing framework to compute theground state of small molecules. The initial Hamiltonian of our algorithms is taken to be themaximum commuting Hamiltonian that consists of a maximal set of commuting terms in the fullHamiltonian of molecules in the Pauli basis. We consider two variants. In the first method, weperform the adiabatic evolution on the obtained time- or path-dependent Hamiltonian with theinitial state as the ground state of the maximum commuting Hamiltonian. However, this methoddoes suffer from the usual problems of adiabatic quantum computation due to degeneracy andenergy-level crossings along the Hamiltonian path. This problem is mitigated by a Zeno method,i.e., via a series of eigenstate projections used in the quantum simulated annealing, with the path-dependent Hamiltonian augmented by a sum of Pauli X terms, whose contribution vanishes at thebeginning and the end of the path. In addition to the ground state, the low lying excited states canbe obtained using this quantum Zeno approach with equal accuracy to that of the ground state.