Question-1: **How can a quantum sensor optimally extract information about its environment?**

Tutorial

**Tutorials**

**Alex Retzker **(The Hebrew University of Jerusalem – Israel)

Quantum sensing with nitrogen-vacancy centres in diamond

In this talk I will review the various methods and applications of NV centers in diamond with respect to quantum sensing and discuss the potential benefits of utilizing Machine Learning methods for frequency estimation

**Chris Ferrie **(University of Technology, Sydney – Australia)

Parameter estimation, the quantum way: theory and application of quantum estimation

Parameter estimation is a fundamental task in metrology, the science of measurement. The ultimate limits of precision in this task are determined by physics, and the ultimate theory of physics is quantum. In this tutorial, I will review the task of parameter estimation from both a classical and quantum perspective, demonstrating the first identified “quantum advantage”. More recently results, including the application of machine learning to the problem will also be touched upon.

**Invited Talks**

**Christian Degen **(Department of Physics, ETH Zurich – Switzerland)

Parallel detection and spatial mapping of large nuclear spin clusters

Quantum nodes consisting of a central electronic spin surrounded by a number of ancillary nuclear spins are important building blocks in solid-state quantum architectures, especially in quantum networks and quantum simulators. In this talk, we address the question of how to precisely characterize and calibrate such an electronic-nuclear quantum node. We introduce a concept for an efficient, parallel mapping of coupling constants based on weak quantum measurements. We demonstrate our protocol by detecting clusters of up to 25 carbon-13 nuclei using the central electronic spin of a nitrogen-vacancy center in diamond. We further show that the three-dimensional locations of the carbon nuclei can be mapped with high precision using maximum likelihood estimation. We give an outlook on exploiting this capability for the imaging of atomic structures of molecules and proteins

**Luca Pezze’ **(NO-CNR and LENS, Florence – Italy)

Neural-network-enhanced parameter estimation exploiting classification and regression

Quantum parameter estimation is currently an extremely active area of research, which has both fascinating implications for fundamental science and applications in state-of-the art sensors. In this talk we explore machine learning technique for parameter estimation tasks. In particular, we follow two (conceptually) different paths for parameter estimation: classification and regression. Classification naturally performs Bayesian inference, with the prior knowledge determined by the distribution of the calibration data. In this case, the output of the network is a Bayesian posterior distribution, which is centred at the true (unknown) parameter value with an uncertainty given by the inverse Fisher information, representing the ultimate sensitivity limit for the given apparatus. Regression on the other hand, does not provide confidence intervals, merely a direct estimate of the parameter.

In this case we argue that regression naturally performs frequentist inference and explore conditions under which the model is unbiased and efficient, saturating the ultimate Cramer-Rao bound. We show that quantum noise limits how finely the parameter space can be sampled, which affects the ability of the model to generalise well to unseen data. Finally, we present results of a recent optical experiment showing neural-network-enhanced Bayesian parameter estimation using weak measurement techniques.

**Tim Taminiau **(QuTech, Delft – the Netherlands)

Atomic-scale imaging of nuclear spins with a quantum sensor

Optically active defect spins provide a promising platform for quantum sensing, quantum simulation, quantum computing and quantum networks. A compelling approach is to use a single electron spin to detect, image and control multiple electron and nuclear spins in its environment. This can lead both to the atomic-scale magnetic imaging of complex spin samples, as well as the realisation of large multi-qubit quantum registers for quantum information processing.

In this talk, I will discuss the question of how we can use a single-spin quantum sensor to characterise its microscopic spin environment. I will discuss recent results that demonstrate various experimental techniques to detect, image and control individual spins. This includes the atomic-scale imaging of large nuclear spin clusters, detecting and controlling individual electron spins, and the application of machine learning methods towards the efficient imaging and characterisation of complex spin systems.