Advantages and Limitations in Quantum Computing Enhanced Sensing

Quantum metrology is one of the most promising applications of quantum technology and aims to address a basic science question: what are the fundamental limits on our capability to learn about the physical world? One such result is the well-known Heisenberg limit, the highest sensitivity achievable in learning the parameters of a time-independent Hamiltonian. In this work, we characterize another sensing task: detecting a weak AC signal at unknown frequency within a broad band. We present a lower bound, set by quantum mechanics, on the time to achieve this task. The lower bound is saturated, up to logarithmic corrections, by our new algorithm, in which sensors are controlled by a quantum computer. Our approach is quadratically faster than existing protocols, in which sensors are controlled by a classical computer. The key idea is to obtain a Grover speed-up by constructing a robust digital oracle out of the unknown signal, using techniques such as superadiabaticity and quantum signal processing. These results both improve our understanding of the limits of quantum metrology and introduce the new paradigm of quantum computing enhanced sensing.