Non-Unitary Quantum Butterfly Effect: Theory and Experiment
We present a generalization of the out of time order correlator (OTOC) for non-unitary systems. For a Haar-random brickwork qudit-circuit, peppered with local, projective measurement, we calculate the infinite-temperature, ensemble-average OTOC. Utilizing transfer matrix machinery, we find that the OTOC asymptotically decays exponentially and that the decay depends on the rate of measurement. In the thermodynamic limit, with sparse measurement, the OTOC approximately exhibits a Gaussian shape. Phenomenologically, this corresponds to the development of a causal scrambling front where unlike the unitary case, the signal decays in the bulk of the causal cone. We develop a Monte Carlo framework to compute the OTOC. We then estimate the OTOC directly via quantum simulation and on Quantinuum's trapped-ion quantum computer. We resolve the unitary and non-unitary OTOC phenomenology despite the presence of hardware noise. Our analytic results characterize how local nonunitary channels affect OTOC decay, providing a quantitative benchmark for the cumulative effects of a broad class of hardware noise on many-body dynamics.