Error-Bounded Gradients Through Lossy Quantum State Simulation

Variational quantum algorithms train by evaluating gradients of a cost<psi(theta)|H|psi(theta)> over many optimizer steps, and on a classicalsimulator the memory of the state vector, not its runtime, is the wall thatcaps the trainable circuit size. We show that the adjoint method can computeall parameter gradients while the two carried trajectories are stored in alossily compressed (int16, block-scaled) representation, and we prove ana-priori bound: the error of every gradient component is at most the totalinjected perturbation norm D, linear in a single, runtime-enforced compressionbudget. The bound turns compression precision into a training knob. Weimplement the method as a PennyLane device backed by a from-scratchstate-vector engine and validate it: gradient error is linear in D with abouta 30x margin over the worst case, compressed-gradient VQE converges to withinabout 1e-3 of exact-gradient training (five-seed mean), and a 30-qubit VQEtrains on a free 16 GB cloud GPU where a dense complex64 adjoint runs out ofmemory. The artifact is open and reproducible from a single command.