Holographic simulation of correlated electrons on a trapped ion quantum processor

TL;DR

This paper introduces a holographic quantum simulation method that efficiently prepares correlated electronic ground states using fewer qubits, demonstrated on a trapped-ion quantum processor for 1D models like the Fermi-Hubbard chain.

Contribution

The paper presents a novel holographic approach to simulate correlated electrons with reduced qubit and gate resources, advancing quantum simulation efficiency.

Findings

Successfully simulated 1D correlated electron states on a trapped-ion processor.

Accurately captured Mott insulators and Luttinger liquids with fewer parameters.

Demonstrated polynomial resource reduction compared to existing techniques.

Abstract

We develop holographic quantum simulation techniques to prepare correlated electronic ground states in quantum matrix product state (qMPS) form, using far fewer qubits than the number of orbitals represented. Our approach starts with a holographic technique to prepare a compressed approximation to electronic mean-field ground-states, known as fermionic Gaussian matrix product states (GMPS), with a polynomial reduction in qubit- and (in select cases gate-) resources compared to existing techniques. Correlations are then introduced by augmenting the GMPS circuits in a variational technique which we denote GMPS+X. We demonstrate this approach on Quantinuum's System Model H1 trapped-ion quantum processor for 1$d$ models of correlated metal and Mott insulating states. Focusing on the $1d$ Fermi-Hubbard chain as a benchmark, we show that GMPS+X methods faithfully capture the physics of correlated electron states, including Mott insulators and correlated Luttinger liquid metals, using considerably fewer parameters than problem-agnostic variational circuits.