State-dependent heating induced by measurement in a trapped-ion system

Mid-circuit measurement has recently risen as a key component of quantum information science owing to its extensive applications in error-correction protocols, quantum communication protocols, and measurement-based quantum computing. However, heating caused by fluorescence measurement of trapped ion qubits, which involves stochastic photon recoil, has not been explored so far. Measurement-induced heating could affect gate operations which occur after a mid-circuit measurement and qubit reset cycle. We experimentally observe state-dependent heating during detection by measuring motional state dynamics. We find that the heating rate for the bright state is ~ 2x10^4 quanta per second, which is nearly two orders of magnitude faster than the dark state and ambient heating rates. These observations suggest that recooling schemes may be necessary between a mid-circuit measurement and subsequent gate operations.