Holographic Simulation of Correlated Electrons on a Trapped-Ion Quantum Processor

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 (GMPSs), 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 one-dimensional (1D) 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.