Variational quantum sensing

Sensing strategies that leverage quantum correlations, such as entanglement, can reach precisions beyond the fundamental limits of classical techniques, and are broadly relevant, e.g., in optical and atomic interferometry. However, constraints imposed in near-term quantum devices, such as noise processes, limited number of qubits, and limited sampling rates, motivate the need for quantum sensing protocols that are adaptive to device capabilities. In recent years, learning techniques have found wide-spread application in quantum technologies; through variational quantum algorithms and classical machine-learning techniques trained on data from quantum devices. In this work, towards protocol adaptivity, we frame each step of a quantum sensing protocol as a variational learning problem. First, the maximum achievable precision, bounded by the Cramér–Rao bound, is optimized by tuning the parameters of the probe state preparation and detection. Next, a classical neural network is trained on simulated, single shot data from the optimized device and used to efficiently estimate the unknown parameter. Using this approach, we design sensing protocols that mitigate the effects of noisy state preparation, and reach precisions that surpass the standard quantum limit. Our framework provides a promising avenue for designing entanglement-enhanced sensing protocols with realistic, near-term quantum devices.