How Quantum Circuits Avoid Spurious Local Minima via Homotopy

Researchers have discovered that quantum circuits can become frozen during training, not due to a lack of sensitivity, but because of a misalignment of their frequency content. In two independent experiments with fifty different initializations each, circuits initialized on high-frequency targets collapsed into spurious local minima, remaining locked throughout the run, while circuits that escaped migrated their frequency content. The work demonstrates that standard methods for diagnosing optimization failures miss this, as trapped circuits retain a fully non-degenerate parameter-space QFIM. A frequency-staged homotopy protocol that paces the target frequency tripled the escape rate from these frozen states, increasing it from 6% to 18%, and revealed that Fourier locking is a frequency-alignment problem, and…