Observation of topological Uhlmann phases with superconducting qubits

TL;DR

This paper demonstrates the first experimental measurement of the topological Uhlmann phase in a simulated topological insulator using superconducting qubits, revealing environmental effects and enabling phase diagram mapping.

Contribution

It introduces a novel measurement protocol for the topological Uhlmann phase using entangled qubits and ancilla states on a quantum computer, applicable to complex topological models.

Findings

Successful measurement of the topological Uhlmann phase in a quantum simulator.

Complete phase diagram including environmental effects obtained.

Protocol is extendable to interacting particles and multi-band models.

Abstract

Topological insulators and superconductors at finite temperature can be characterized by the topological Uhlmann phase. However, a direct experimental measurement of this invariant has remained elusive in condensed matter systems. Here, we report a measurement of the topological Uhlmann phase for a topological insulator simulated by a system of entangled qubits in the IBM Quantum Experience platform. By making use of ancilla states, otherwise unobservable phases carrying topological information about the system become accessible, enabling the experimental determination of a complete phase diagram including environmental effects. We employ a state-independent measurement protocol which does not involve prior knowledge of the system state. The proposed measurement scheme is extensible to interacting particles and topological models with a large number of bands.