Entanglement from Tensor Networks on a Trapped-Ion Quantum Computer.

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Quantum Computing

Background:

• Simulating quantum systems with limited entanglement is computationally intensive.
• Tensor-network states often possess spatial structures that are challenging to represent efficiently.
• Quantum circuits offer a potential avenue for simulating these complex systems.

Purpose of the Study:

• To demonstrate resource savings in quantum simulation by mapping tensor-network states to quantum circuits.
• To experimentally extract the entanglement structure of infinite systems using a novel quantum circuit approach.
• To quantitatively determine entanglement entropy and phase transitions in correlated spin chains.

Main Methods:

• Utilizing selective midcircuit measurement and reset of qubits in a quantum circuit.
• Encoding the entanglement structure of an infinite system into a small register of 'bond qubits'.
• Employing Honeywell's model H0 quantum computer for experimental demonstration.

Main Results:

• Achieved dramatic resource savings in quantum simulation by mapping spatial structures to circuit dynamics.
• Successfully encoded and extracted the half-chain entanglement spectrum of an infinite system.
• Quantitatively determined near-critical entanglement entropy of a correlated spin chain in the thermodynamic limit.

Conclusions:

• Selective qubit operations in quantum circuits enable efficient simulation of tensor-network states.
• The 'bond qubit' approach provides a powerful tool for extracting entanglement properties of extended quantum systems.
• This method facilitates the resolution of phase transitions in the thermodynamic limit.