Holographic simulation of correlated electrons and thermal states on a trapped-ion quantum processor

We present holographic quantum simulation algorithms to prepare ground- and thermal-states of interacting electron materials as quantum matrix product states (qMPS) or density operators (qMPDO) respectively, requiring far-fewer qubits than the number of orbitals being simulated. We demonstrate both algorithms through numerical simulations and experimental implementations on Honeywell’s H1 trapped-ion quantum processor. First, we adapt a method to compress mean-field fermion states into qMPS form, achieving polynomial reduction of qubit and gate resources compared to recent quantum Hartree-Fock demonstrations, making them ideal for near-term implementations. We show that such mean-field qMPS serve as a useful starting point for variational refinement to build in correlations, and argue that it enables preparation of qMPS with exponentially large bond dimension using polynomial circuit resources. Second, we devise a method for implementing thermal state qMPDO by stochastically sampling over an ensemble of qMPS, which can be optimized variationally. We explore the representational power of thermal state qMPDOs for correlated spin-chains and show that they enable simulation of non-equilibrium thermal transport dynamics from initial states with inhomogeneous temperature.