Quantum metrology is an important application of emerging quantum technologies. We explore whether a hybrid system of quantum sensors and quantum circuits can surpass the classical limit of sensing. In particular, we use a circuit learning approach to search for encoder and decoder circuits that scalably improve sensitivity under given application and noise characteristics. Our approach uses a variational algorithm that can learn a quantum sensing circuit based on platform-specific control capacity, noise, and signal distribution. The quantum circuit is composed of an encoder which prepares the optimal sensing state and a decoder which gives an output distribution containing information of the signal. We optimize the full circuit to maximize the Signal-to-Noise Ratio (SNR). Furthermore, this learning algorithm can be run on real hardware scalably by using the parameter-shift rule which enables gradient evaluation on noisy quantum circuits, avoiding the exponential cost of quantum system simulation. We demonstrate a 1.69x SNR improvement over the classical limit on a 5-qubit IBM quantum computer. More notably, our algorithm overcomes the plateauing (or even decreasing) performance of existing entanglement-based protocols with increased system sizes.
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