Classical simulation of amplitude-damped bucket-brigade quantum random access memories via predictable branch evolution
Classical simulation of quantum random access memory (QRAM) under noise can be accelerated dramatically by branch pruning: noise histories are sampled as trajectory ensembles, and good branches, whose routing paths avoid every sampled fault, need not be evolved because their final states are analytically predictable. Under amplitude damping this predictability is not automatic, because the no-jump operator $K_0$ acts on every branch at every time slice. Here we give a complete account of damping-channel predictability in bucket-brigade QRAM simulation, for both qutrit and qubit encodings. For the qutrit encoding, $K_0$ is diagonal in the node basis, and the wait state $|W\rangle$ is its fixed point, so a good branch follows the noiseless orbit up to a scalar attenuation. In the qubit encoding, phase-kickback memory fetching between two Hadamard walls makes $K_0$ no longer diagonal, yet the resulting structure is exactly solvable in closed form. Conditional on no jump, the in-branch infidelity of a good branch is second order in the damping rate $γ$, with coherent leakage $\sim n^2γ^2/4$ per data qubit, and the closed form captures it without approximation. We also revise the pruning criterion for the qubit encoding. The resulting algorithm evolves only the bad branches plus one reference branch and shares every other cost with the full evolution it replaces. It is validated by end-to-end benchmarks with pruned-over-full speedups up to $285\times$ and by trajectory-level tests confirming every closed form to machine precision.