Initialization-controlled fault sensitivity and force-balance plateaus in noisy variational quantum optimization
We study deep variational circuits for a periodic Heisenberg chain under local gate depolarization, at depths where noiseless training is coherently exact. Full-width initializations reach low coherent error faster than circuits with confined transverse generators, but incur a larger noise shift and need an order of magnitude more updates for noisy convergence. In many-body-localization-inspired initialization, bounding the initial transverse generator amplitudes keeps the operator support localized and suffices for low-fragility optimization, so longitudinal disorder and Floquet layer repetition are unnecessary. The fault-erasure fraction, the mean fraction of coherent energy removed per fault, sets the effective visibility through a parameter-free exponential model. Full-width circuits start with delocalized operator support, and once coherent energy builds up, each fault erases nearly all of it. Initially, their noise-induced gradient almost uniformly attenuates the coherent gradient, so coherent descent proceeds at the noiseless rate. They then stall on a high-noise force-balance plateau, where finite coherent and noise-induced gradients cancel to first order. At late times all initializations reach the same fault-erasure fraction and noisy-error band, but operator support contracts more slowly, at a rate set by the plateau residence time.