Abstract: One promising near-term application of quantum computers is the simulation of correlated quantum systems. The matrix product state not only gives a compressed representation of many states of interest but also enables further algorithms which can save quantum resources to exploit near-term quantum computers and gain possible advantages on classically hard simulations. We demonstrate "holographic" quantum simulation techniques for simulating correlated electron models in quantum matrix product state (qMPS) form, using far fewer qubits than the number of orbitals being simulated.