Observation of topological Uhlmann phases with superconducting qubits

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.Topological matter: quantum simulation of the Uhlmann phaseA system of entangled qubits is used to simulate a topological insulator, measuring for the first time the topological Uhlmann phase. Observing the Uhlmann phase, which is the generalization of the Berry phase in presence of an environment, requires high level of control over the environmental degrees of freedom, making it unachievable in condensed matter systems. An international team led by Miguel A. Martin-Delgado of the Universidad Computense of Madrid has now shown how to simulate the Uhlmann phase in a system of three entangled qubits. By treating one qubit as system, one as environment and one as probe, the researchers could control the system-environment coupling well enough to detect the temperature-induced topological transition by interferometric means, and compute the topological phase diagram for qubits in the presence of noise.