On the trainability of variational quantum circuits

Abrupt Transitions in Variational Quantum Circuit Training

Variational quantum algorithms dominate gate-based applications of modern quantum processors.The divide-and-conquer trainability conjecture asserts that a few layers can be trained in sequence to minimize an objective function.Here we prove this conjecture false by considering objective functions that are exponentially close (in the number of qubits) to the identity matrix.A critical layer depth will abruptly train arbitrarily close to the target, thereby minimizing the objective function.These findings shed newlight on the divide-and-conquer trainability of variational quantum circuits and apply to a wide collection of contemporary literature.