Entanglement from tensor networks on a trapped-ion QCCD quantum computer

The ability to selectively measure, initialize, and reuse qubits during a quantum circuit is a crucial ingredient in scalable (error-corrected) quantum computation. Recently, it has been realized that these tools also enable "holographic" algorithms that map the spatial structure of certain tensor-network states onto the dynamics of a quantum circuit, thereby achieving dramatic resource savings when using a quantum computer to simulate many-body systems with limited entanglement. Here we explore another significant benefit of the holographic approach to quantum simulation: The entanglement structure of an infinite system, specifically the half-chain entanglement spectrum, can be extracted from a data-compressed register of "bond qubits" encoding a matrix-product state. We demonstrate this idea experimentally on a trapped-ion QCCD quantum computer by computing the near-critical entanglement entropy of the transverse-field Ising model directly in the thermodynamic limit, and show that the phase transition becomes very quickly resolved upon expanding the bond qubit register.