Model molecular Hamiltonians

Jin Dai, Xubiao Peng, Antti J. Niemi

We show that topology is a very effective tool, to construct classical Hamiltonian time crystals. For this we numerically analyze a general class of time crystalline Hamiltonians that are designed to model the dynamics of molecular closed strings. We demonstrate how the time crystalline qualities of a closed string are greatly enhanced when the string becomes knotted. The Hamiltonians that we investigate include a generalized Kratky-Porod wormlike chain model in combination with long range Coulomb and Lennard-Jones interactions. Such energy functions are commonplace in coarse grained molecular modeling. Thus we expect that physical realizations of Hamiltonian time crystals can be constructed in terms of knotted ring molecules.

Dmitry S. Golubev, Reza G. Shirazi, Vladimir V. Rybkin +3 more

We propose an approximate mapping of a molecular Hamiltonian to a Hamiltonian of qubits, which allows for high accuracy quantum chemistry calculations of vertical excitation energies of some molecules. The mapping is based on separating of a very small active space of only two orbitals and on modeling the electronic excitations in the remaining orbitals by a set of qubits or, equivalently, by a set of oscillators. This approach is inspired by the Random Phase Approximation (RPA), in which the excitations of electron gas are described by bosonic degrees of freedom. As a result, the Hamiltonian of the molecule is reduced to that of a system-bath model. The "system" part of the Hamiltonian describes the two molecular orbitals -- the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) -- which are populated by two electrons. Two qubits are sufficient to encode the Hamiltonian of such a system. The "bath" consists of oscillators or, equivalently, of two level systems with each of them corresponding to an electron excitation from a doubly occupied orbital below the Fermi level to an empty orbital above the Fermi level. We hope that this mapping can inspire new approaches and algorithms aimed at calculating excitation energies of molecules on near term quantum computers.

Hinne Hettema

Ningyi Lyu, Alessandro Miano, Ioannis Tsioutsios +7 more

We introduce a general method based on the operators of the Dyson-Masleev transformation to map the Hamiltonian of an arbitrary model system into the Hamiltonian of a circuit Quantum Electrodynamics (cQED) processor. Furthermore, we introduce a modular approach to programming a cQED processor with components corresponding to the mapping Hamiltonian. The method is illustrated as applied to quantum dynamics simulations of the Fenna-Matthews-Olson (FMO) complex and the spin-boson model of charge transfer. Beyond applications to molecular Hamiltonians, the mapping provides a general approach to implement any unitary operator in terms of a sequence of unitary transformations corresponding to powers of creation and annihilation operators of a single bosonic mode in a cQED processor.