Simulation of vibrational dynamics using qubits and qudits

TL;DR

This paper explores quantum simulations of molecular vibrational dynamics using various qubit and qudit encodings, demonstrating that qudit encoding yields the most accurate results under certain conditions.

Contribution

It introduces and compares binary, direct, and qudit encodings for vibrational Hamiltonians, highlighting the superior accuracy of qudit encoding in noisy quantum simulations.

Findings

Qudit encoding provides more accurate vibrational dynamics simulations.

The study compares three different quantum encodings for vibrational Hamiltonians.

Noise effects are considered, showing qudit encoding's robustness.

Abstract

We investigate the quantum computing of the vibrational dynamics of CO$_2$ and H$_2$O by constructing the vibrational Hamiltonian in qubit and qudit form by two types of qubit encodings (binary and direct) and a qudit encoding. We simulate the time-dependent vibrational population transfer using the three different encodings, including the effect of noise and find that the qudit encoding leads to the most accurate results both for CO$_2$ and H$_2$O because of the small number of terms in the qudit Hamiltonian as long as the same values of the entangling gate error rates are adopted.