Entanglement from Tensor Networks on a Trapped-Ion Quantum Computer

The ability to selectively measure, initialize, and reuse qubits during a quantum circuit enables a mapping of the spatial structure of certain tensor-network states onto the dynamics of quantum circuits, thereby achieving dramatic resource savings when simulating quantum systems with limited entanglement. We experimentally demonstrate a significant benefit of this approach to quantum simulation: the entanglement structure of an infinite system-specifically the half-chain entanglement spectrum-is conveniently encoded within a small register of "bond qubits" and can be extracted with relative ease. Using Honeywell's model H0 quantum computer equipped with selective midcircuit measurement and reset, we quantitatively determine the near-critical entanglement entropy of a correlated spin chain directly in the thermodynamic limit and show that its phase transition becomes quickly resolved upon expanding the bond-qubit register.