Flexible resources for quantummetrology

Quantummetrology offers a quadratic advantage over classical approaches to parameter estimation problems by utilising entanglement and nonclassicality. However, the hurdle of actually implementing the necessary quantumprobe states andmeasurements, which vary drastically for different metrological scenarios, is usually not taken into account.We show that for awide range of tasks in metrology, 2D cluster states (a particular family of states useful formeasurement-based quantum computation) can serve asflexible resources that allow one to efficiently prepare any required state for sensing, and perform appropriate (entangled)measurements using only single qubit operations. Crucially, the overhead in the number of qubits is less than quadratic, thus preserving the quantum scaling advantage. This is ensured by using a compression to a logarithmically sized space that contains all relevant information for sensing.We specifically demonstrate howourmethod can be used to obtain optimal scaling for phase and frequency estimation in local estimation problems, as well as for the Bayesian equivalents withGaussian priors of varyingwidths. Furthermore, we show that in the paradigmatic case of local phase estimation 1D cluster states are sufficient for optimal state preparation andmeasurement.