Variance-Reduced Trajectory Unravelings for GPU Noisy Quantum-Circuit Simulation: Characterization and a Qiskit-Aer Integration Gap

Monte-Carlo trajectory (quantum-jump) methods are the practical route to simulating noisy quantum circuits once the exact density-matrix method is precluded by its 4ⁿ memory cost. Their bottleneck is estimator variance: resolving one expectation value can demand thousands of trajectories. Recent tensor-network work shows that variance-reduced unravelings - projector and analog sampling - sharply cut this variance, but only on CPU matrix-product-state backends, with no path into production tooling. We implement both unravelings on a GPU dense-statevector trajectory engine and validate them against the exact density matrix ideal-circuit fidelity $1-2.2times10^-16$; $1/sqrt{N}$ convergence; all unravelings unbiased to trace distance $<0.01$. On a single consumer GPU, projector unraveling reaches a target standard error with 20.8times fewer trajectories than Qiskit-Aer's \texttt{batched_shots_gpu} at n=10, a factor that holds at 19--26times across n=8--20. A regime map places analog sampling optimal at weak noise and projector at strong noise, crossing near γtapprox0.35. We further report a systems finding: Qiskit-Aer applies noise at the channel level and reconstructs a canonical Kraus decomposition at apply time, discarding any user-supplied unraveling, so variance-reduced unravelings cannot be delivered through its public API. Because Aer's Born-rule collapse machinery already exists, we specify a minimal change that would unlock the technique in production.