Measurement of Intermediate-temperature topological Uhlmann phase on IBM quantum computers

A spin-1 (three-level) system can exhibit an intermediate-temperature topological regime with a quantized Uhlmann phase sandwiched by topologically trivial low- and high-temperature regimes. In this regime, a sharp, quantized change in the Uhlmann phase can be seen and is associated with a Topological Quantum Phase Transition (TQPT). We present a quantum circuit for realizing the spin-1 Uhlmann phase on IBM’s current-day noisy intermediate-scale quantum (NISQ) computers. Although classical simulations suggest the quantized Uhlmann phase is observable on NISQ computers, a naive implementation of the circuit without any optimization exceeds the gate count for the error budget and results in unresolved signals. Through a series of optimization with Qiskit and BQSKit, the gate count can be substantially reduced, making the jumps of the Uhlmann phase more visible. On the latest generation of IBM quantum computers, further improvement of the fidelity of the gates and devices leads to a clearer demonstration of interesting finite-temperature topological phenomena on NISQ hardware.