Quantum Signal Processing - A New Single-Qubit Approach to Quantum Algorithms
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. Quantum signal processing, and its generalization to the quantum singular value transform, are now known to provide exponential improvements for quantum matrix arithmetic.