Intermediate-temperature topological Uhlmann phase on IBM quantum computers

TL;DR

This paper demonstrates the experimental observation of the intermediate-temperature topological Uhlmann phase on IBM quantum computers, highlighting the importance of circuit optimization and hardware upgrades for clear detection.

Contribution

It introduces a quantum circuit for measuring the Uhlmann phase at finite temperature and shows how hardware improvements and optimizations enable its observation on NISQ devices.

Findings

Quantized Uhlmann phase observable with optimized circuits

Hardware upgrades improve signal clarity

Finite-temperature topological phenomena demonstrated on NISQ hardware

Abstract

A spin-1 system can exhibit an intermediate-temperature topological regime with a quantized Uhlmann phase sandwiched by topologically trivial low- and high-temperature regimes. We present a quantum circuit consisting of system and ancilla qubits plus a probe qubit which prepares an initial state corresponding to the purified state of a spin-1 system at finite temperature, evolves the system according to the Uhlmann process, and measures the Uhlmann phase via expectation values of the probe qubit. Although classical simulations suggest the quantized Uhlmann phase is observable on IBM's noisy intermediate-scale quantum (NISQ) computers, an 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 BQSQit, the gate count can be substantially reduced, making the jumps of the Uhlmann phase more visible. A recent hardware upgrade of IBM quantum computers further improves the signals and leads to a clearer demonstration of interesting finite-temperature topological phenomena on NISQ hardware.