Measuring Correlation and Entanglement between Molecular Orbitals on a Trapped-Ion Quantum Computer

TL;DR

This paper demonstrates the use of a trapped-ion quantum computer to measure orbital correlation and entanglement in a strongly correlated molecular system, achieving accurate results with noise reduction techniques.

Contribution

It introduces a method to quantify orbital entanglement on a quantum computer, incorporating superselection rules and measurement optimizations for complex molecules.

Findings

Von Neumann entropies match noiseless benchmarks

Orbital entanglement vanishes without opposite-spin open shells

Measurement efficiency is improved through commuting Pauli sets

Abstract

Quantifying correlation and entanglement between molecular orbitals can elucidate the role of quantum effects in strongly correlated reaction processes. However, accurately storing the wavefunction for a classical computation of those quantities can be prohibitive. Here we use the Quantinuum H1-1 trapped-ion quantum computer to calculate von Neumann entropies which quantify the orbital correlation and entanglement in a strongly correlated molecular system relevant to lithium-ion batteries (vinylene carbonate interacting with an O$_2$ molecule). As shown in previous works, fermionic superselection rules decrease correlations and reduce measurement overheads for constructing orbital reduced density matrices. Taking into account superselection rules we further reduce the number of measurements by finding commuting sets of Pauli operators. Using low overhead noise reduction techniques we calculate von Neumann entropies in excellent agreement with noiseless benchmarks, indicating that correlations and entanglement between molecular orbitals can be accurately estimated from a quantum computation. Our results show that the one-orbital entanglement vanishes unless opposite-spin open shell configurations are present in the wavefunction.