Winding-Number Measurements in a Noisy Quantum Simulation

We demonstrate a shallow-circuit approach to topological measurements in an extended transverse-field Ising chain by measuring the transverse magnetization and finite-grid winding number with 16 and 32 qubits on the Tianyan-176 superconducting processor. Independent momentum pairs are prepared in parallel, and single-qubit Z components and two-qubit XX correlations give both observables without an inverse fermionic Fourier transformation. Although the measured magnetization deviates from the ideal result, 99.1% of the individual winding-number measurements reproduce the ideal finite-grid value. The few incorrect results occur near phase transitions, where pseudospins at neighboring points of the finite momentum grid become nearly antiparallel and small errors can change the winding number by one. Noise simulations show that increasing the number of shots reduces finite-shot errors but does not correct noise-induced changes in the mean pseudospin directions.