Strict Frequency Bandwidths from Causal Light Cones Enable Scalable Exact Gradient Evaluation in Quantum Optimization

arXiv:2610.38322v1 Announce Type: new Abstract: Dynamical locality is often regarded as a limitation of shallow quantum circuits, yet we show that it can reduce the number of circuit settings required for exact evaluation of gradients with respect to shared parameters. For layered ansatze generated by commuting local terms, strict Heisenberg light cones confine energy slices obtained by varying one shared layer parameter to finite Fourier bandwidths dictated by local causal geometry. This bandlimit recasts exact gradient evaluation as a local signal recovery problem and, when the relevant frequencies lie on a known frequency lattice, yields an exact multipoint parameter-shift rule based on the discrete sine transform.