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

TL;DR

This paper demonstrates how tensor network states can be efficiently mapped onto a trapped-ion quantum computer to extract entanglement properties of many-body systems, enabling resource-efficient quantum simulations.

Contribution

It introduces a method to encode the entanglement spectrum of an infinite system into a small quantum register and experimentally verifies this on a trapped-ion quantum computer.

Findings

Successfully extracted the half-chain entanglement spectrum.

Measured the entanglement entropy near a critical point.

Showed phase transition resolution improves with larger bond-qubit registers.

Abstract

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 using a quantum computer to simulate many-body systems with limited entanglement. We experimentally demonstrate a significant benefit of this approach to quantum simulation: In addition to all correlation functions, 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 a trapped-ion QCCD quantum computer equipped with selective mid-circuit 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.