Observing a Topological Transition in Weak-Measurement-Induced Geometric Phases*

Quantum measurements induce backaction on quantum states resulting in measurement induced dynamics. A sequence of weak measurements can consequently realize a cyclic motion for the qubit state in Hilbert space and thus induce a geometric phase. As the measurement strength is varied between weak and strong regimes, we expect a topological transition corresponding to a change in the Chern number of the surface tracked by the qubit’s cyclic motion. To experimentally measure this transition, we employ quantum non-demolition measurement of a superconducting transmon circuit in the strong dispersive regime. This transition is revealed as a quantized jump in the averaged geometric phase when tuning the strength for the measurement sequence, giving new insights into how weak measurements are a powerful tool for quantum control.