Intermediate Temperature Topological Uhlmann Phase Transition on Quantum Computers

The Uhlmann phase is a natural generalization of the Berry phase to mixed quantum states. It reflects a topological indicator known as holonomy of the underlying fiber-bundle. For a typical spin-1/2 system, the Uhlmann phase decrease to zero as temperature is increased. In contrast, a spin-1 system can intermediate temperature topological region with finite Uhlmann phase, which is sandwiched by topologically trivial regions at low and high temperatures. By using two different sets of qubits to serve as the system and ancilla, we design quantum circuits for preparing purified states, generating Uhlmann phase, and measuring the phase using state tomography. We run the circuits on both IBM simulators and their QPU’s to extract the Uhlmann phases of spin-1/2 and spin-1 systems. With the quantized values of the Uhlmann phase, the noise does not wash out the signature from the topological regions. Therefore, we show that the intermediate temperature region survives within a spin-1 system, demonstrating a case where the temperate stabilizes topology.