From quantum computation to quantum signal processing: the power of a single qubit

Quantum computers are celebrated for their ability to rapidly solve certain computational problems, while quantum metrology offers increased sensitivity, beyond standard shot-noise limits. A common denominator is the lowly two-level quantum system, oft explored, but never fully appreciated. Drawing on techniques from classical signal processing, we theoretically predict, and experimentally demonstrate with a trapped ion, how composite gates on a single qubit allows Heisenberg-limited imaging. We also show how such "quantum signal processing" gives rise to unexpected computational power, providing a novel algorithm for simulation of physical Hamiltonians which saturates optimality bounds.​