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 $4^n$ memory cost. Their bottleneck is estimator variance: resolving one expectation value can demand thousands of trajectories. Recent tensor-network work shows that \emph{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 \emph{GPU dense-statevector} trajectory engine and validate them against the exact density matrix (ideal-circuit fidelity $1-2.2\times10^{-16}$; $1/\sqrt{N}$ convergence; all unravelings unbiased to trace distance $<0.01$). On a single consumer GPU, projector unraveling reaches a target standard error with $20.8\times$ fewer trajectories than Qiskit-Aer's \texttt{batched\_shots\_gpu} at $n=10$, a factor that holds at $19$--$26\times$ across $n=8$--$20$. A regime map places analog sampling optimal at weak noise and projector at strong noise, crossing near $\gamma t\approx0.35$. We further report a systems finding: Qiskit-Aer applies noise at the \emph{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.