Auditing Claimed Speedups of Learned Surrogates for Variational Quantum Optimization

A growing line of work accelerates variational quantum algorithms by learning a classical surrogate of the optimization trajectory and rolling it forward, so that quantum measurements are replaced by classical inference. We observe that the two headline results in this line—a $30\times$ physics-informed speedup and a $>200\times$ Koopman speedup in an over-parameterised regime—are both measured against small-step gradient-descent reference trajectories, at $\eta =10^{-2}$ and $\eta =5\times 10^{-6}$. We show this makes the reported quantity uninformative: for quadratics the reference needs $\Theta (1/\eta )$ iterations in the worst case, so a ratio against a fixed step diverges as $\eta \to 0$. We also show that a rule predicting the next iterate from the step index and the parameter vector alone cannot represent the transition law of an optimizer with internal state, which covers one of the two families we audit. Running both released implementations unmodified through one counter that charges energy and gradient evaluations at their true circuit cost, Adam is more query-efficient in both families; for the physics-informed surrogate it also reaches accuracies the surrogate never attains, at $8$, $20$ and $40$ qubits, on two Hamiltonians, and under finite sampling. On ibm_kawasaki we verify our sampling model to within $7\%$ and find a device error that, at the configurations tested, is two orders of magnitude larger than the accuracy at which those ratios are defined. Asked of ourselves, the same sensitivity analysis shows our ordering holds over a $25\times$ range of step size—and reverses below it, at exactly the reference value the audited work uses.