Quantum hardware calculations of periodic systems with partition-measurement symmetry verification: simplified models of hydrogen chain and iron crystals

TL;DR

This paper demonstrates quantum hardware calculations of periodic solid-state systems, using noise mitigation and symmetry verification techniques, successfully approximating energies for hydrogen chains and iron crystals with limited quantum resources.

Contribution

It introduces a novel noise mitigation method called partition-measurement symmetry verification for quantum calculations of crystalline materials on real hardware.

Findings

Quantum hardware calculations agree with simulations within ~5 kJ/mol.

The techniques are applicable to more complex systems as hardware improves.

Successful calculation of energies for simple iron models and hydrogen chains.

Abstract

Running quantum algorithms on real hardware is essential for understanding their strengths and limitations, especially in the noisy intermediate scale quantum (NISQ) era. Herein we focus on the practical aspect of quantum computational calculations of solid-state crystalline materials based on theory developed in our group by using real quantum hardware with a novel noise mitigation technique referred to as partition-measurement symmetry verification, which performs post-selection of shot counts based on $Z_{2}$ and $U_{1}$ symmetry verification. We select two periodic systems with different level of complexity for these calculations. One of them is the distorted hydrogen chain as an example of very simple systems, and the other one is iron crystal in the BCC and FCC phases as it is considered to be inaccessible by using classical computational wavefunction methods. The ground state energies are evaluated based on the translational quantum subspace expansion (TransQSE) method for the hydrogen chain, and periodic boundary condition adapted VQE for our iron models. By applying these techniques for the simplest 2 qubit iron model systems, the correlation energies obtained by the hardware calculations agree with those of the state-vector simulations within $\sim$5 kJ/mol. Although the quantum computational resources used for those experiments are still limited, the techniques applied to obtain our simplified models will be applicable in essentially the same manner to more complicated cases as quantum hardware matures.