Distinguishing Synthetic Unravelings on Quantum Computers

Distinct monitoring or intervention schemes can generate different conditioned stochastic quantum trajectories while sharing the same unconditional (ensemble-averaged) dynamics. This is the essence of unravelings of a given Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation: trajectory-ensemble averages of quantities linear in the conditional state are determined by the unconditional density matrix, whereas nonlinear averages can depend on the unraveling. A paradigmatic example is resonance fluorescence, where direct photodetection and homodyne or heterodyne detection define inequivalent unravelings of the same GKSL dynamics. In earlier work, we showed that nonlinear trajectory averages can distinguish such unravelings, but observing the effect in that setting requires demanding experimental precision. Here we translate the same idea to a digital setting by introducing synthetic unravelings implemented as quantum circuits acting on one and two qubits. We design a projective-measurement unraveling and a random-unitary “kick” unraveling that share the same ensemble-averaged evolution while yielding different nonlinear conditional state statistics. Using IBM Quantum superconducting qubit hardware, we show that trajectory variance and ensemble-averaged von Neumann entropy distinguish the unravelings, while the unconditional state and all ensemble averages linear in the state remain identical. Our results show that quantum trajectories encode information about measurement backaction beyond the unconditional dynamics.