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*Monday 1st March 2021, 12:10-13:40 GMT*

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*Monday 1st March 2021, 14:10-15:10 GMT – Q&A at 20:45-21:25 GMT*

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*Monday 1st March 2021, 16:30-17:15 GMT*

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*Monday 1st March 2021, 20:00-20:45 GMT*

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*Wednesday 3rd March 2021, 12:00-12:45 GMT*

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.

**Contributed Talks**

**Leonardo Banchi **(University of Florence, Italy)**Quantum-enhanced barcode decoding and pattern recognition***Monday 1st March 2021, 17:15-17:40 GMT*

We show that the use of quantum entangled sources, combined with suitable measurements and data processing, greatly outperforms classical coherent-state strategies for the tasks of barcode data decoding and classification of black and white patterns. We then numerically investigate the use of quantum enhanced statistical classifiers, in which quantum sensors are used in conjunction with machine learning image classification methods, proving definitive advantage for handwritten digit classification in the low loss regime.**Tools**: *statistical learning theory*

**David Wise** (University College London, UK)**A neural network based approach to efficient inference of the qubit noise environment***Monday 1st March 2021, 17:40-18:05 GMT*

Accurate inference of the spectrum of noise experienced by a qubit can yield key information about that qubit’s environment. Extraction of this noise spectrum is challenging, however, requiring either mathematical approximation with limited accuracy or taxing experimental processes. We investigate how deep learning can be applied to this problem and show accuracy comparable to resource intensive state-of-the-art experimental techniques, using only simple Hahn echo coherence decay measurements.**Tools**: *Neural networks, including LSTMs and convolutional auto encoders*

**Durga B R Dasari** (University of Stuttgart, Germany)**Environment induced non-classical measurement statistics of a quantum sensor***Monday 1st March 2021, 19:30-19:55 GMT*

Repeated measurements of a quantum system gradually collapse an unknown, and arbitrary sized bath coupled to it, to a state with very low fluctuation noise. Such a projected quantum bath leads to an unusual extension of the spin coherence time of the quantum system coupled to it. We confirm this both experimentally and theoretically. Further, the measurement basis is used as a learning parameter to find optimal measurement trajectories using reinforcement learning.**Tools**: *Reinforcement Learning*

**Kyunghoon Jung** (Seoul National University, Korea)**Deep Learning Enhanced Individual Nuclear-Spin Detection in Diamond***Wednesday 3rd March 2021, 12:45-13:!0 GMT*

The detection of nuclear spins using individual electron spins has enabled diverse opportunities in quantum sensing and quantum information processing. To image more complex samples and to realize larger-scale quantum processors, however, computerized methods that efficiently and automatically characterize spin systems are required. Here, we introduce analysis procedures via deep learning models for automatic identification of nuclear spins using the electron spin of single nitrogen-vacancy (NV) centers in diamond as a sensor.**Tools**: *Image Recognition through Supervised Learning*

**Lukas J Fiderer** (University of Nottingham, UK)**Smart Quantum Sensors: Neural-Network Heuristics for Adaptive Bayesian Quantum Estimation***Wednesday 3rd March 2021, 13:30-13:55 GMT*

The paradigm of smart quantum sensors is introduced. We show that neural networks can play the role of a “brain” in the sensor. More precisely, based on a Bayesian approach to metrology, we use reinforcement learning to train neural networks to become fast and strong experiment-design heuristics. Neural-network heuristics are shown to outperform established heuristics for the technologically important example of frequency estimation of a qubit that suffers from dephasing.**Tools**: *Reinforcement learning (trust region policy optimization) and an evolutionary strategy (cross-entropy method)*

**Kirill Streltsov** (University of Ulm, Germany)**Efficient Sensing for Experiments with Limited Prior Knowledge and Total Sensing Time***Wednesday 3rd March 2021, 13:55-14:20 GMT*

We present a Bayesian adaptive sensing scheme that is designed for experiments where the prior distribution of the unknown parameter is broad and the total time available for sensing limited. Our protocol addresses these constraints by adapting the parameters of each measurement such that the maximal amount of information is gained. We show that this approach enables efficient state estimation of levitated mesoscopic particles and, when combined with a feedback mechanism, leads to ground state cooling. **Tools**: *Bayesian inference*

**Johannes Jakob Meyer** (Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Germany)

**Improving Quantum Sensing with Variational Methods**

*Friday 5th March 2021, 14:45-15:10 GMT*

Quantum advantages in sensing arise from a complex interplay between the probe state, the sensing interaction and the performed measurements. On near-term devices, noise and device limitations have to be taken into account during the design of optimal sensing protocols. I will show how variational methods can be used to overcome this challenge and outline their implementation on near-term quantum computers and sensing devices.

**Tools**:

*variational quantum algorithms, gradient descent, quantum autodifferentiation, pennylane*

**Matteo Rosati ** (Universitat Autonoma de Barcelona, Spain)

**Real-time calibration of coherent-state receivers: learning by trial and error**

*Friday 5th March 2021, 15:10-15:35 GMT*

We introduce self-calibrating quantum devices based on reinforcement learning agents, discovering near-optimal setups for state discrimination. The entire experiment is a black box: at each repetition the agents choose a setup and a guessing rule, then receive a binary stochastic information about the chosen strategy’s value. Still, they perform near-optimally both in real-time guessing and calibration, efficiently using the number of repetitions without fully estimating the value of each strategy.

**Tools**:

*Q-Learning, multi-armed bandits, Thomson sampling, upper confidence bound, dynamic programming, lattice regression*