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arXiv:1801.07508 · Physical Review A

Experimentally detecting a quantum change point via the Bayesian inference

Shang Yu, Chang-Jiang Huang, Jian‐Shun Tang, Zhian Jia, Yi-Tao Wang, Zhi‐Jin Ke, Wei Liu, Xiao Liu, Zong‐Quan Zhou, Ze-Di Cheng, Jin‐Shi Xu, Yu-Chun Wu, Yuanyuan Zhao, Guo‐Yong Xiang, Chuan‐Feng Li, Guang‐Can Guo, Gael Sentís, R. Muñoz-Tapia

Published Oct 15, 2018• 5 citations
arXivHTMLPDF

Abstract

Detecting a change point is a crucial task in statistics that has been recently extended to the quantum realm. A source state generator that emits a series of single photons in a default state suffers an alteration at some point and starts to emit photons in a mutated state. The problem consists in identifying the point where the change took place. In this Rapid Communication, we build a pseudo-on-demand single-photon source to prepare the photon sequences, and consider a learning agent that applies Bayesian inference on experimental data to solve this problem. This learning machine adjusts the measurement over each photon according to the past experimental results and finds the change position in an online fashion. Our results show that the local-detection success probability can be largely improved by using such a machine-learning technique. This protocol provides a tool for improvement in many applications where a sequence of identical quantum states is required.

DOI
10.1103/physreva.98.040301

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Detecting a change point is a crucial task in statistics that has been recently extended to the quantum realm. A source state generator that emits a series of single photons in a default state suffers an alteration at some point and starts to emit photons in a mutated state. The problem consists in identifying the point where the change took place. In this Rapid Communication, we build a pseudo-on-demand single-photon source to prepare the photon sequences, and consider a learning agent that applies Bayesian inference on experimental data to solve this problem. This learning machine adjusts the measurement over each photon according to the past experimental results and finds the change position in an online fashion. Our results show that the local-detection success probability can be largely improved by using such a machine-learning technique. This protocol provides a tool for improvement in many applications where a sequence of identical quantum states is required.
Sudden changes are ubiquitous in nature. Identifying them is crucial for a number of applications in biology, medicine, and social sciences. Here we take the problem of detecting sudden changes to the quantum domain. We consider a source that emits quantum particles in a default state, until a point where a mutation occurs that causes the source to switch to another state. The problem is then to find out where the change occurred. We determine the maximum probability of correctly identifying the change point, allowing for collective measurements on the whole sequence of particles emitted by the source. Then, we devise online strategies where the particles are measured individually and an answer is provided as soon as a new particle is received. We show that these online strategies substantially underperform the optimal quantum measurement, indicating that quantum sudden changes, although happening locally, are better detected globally.
The detection of change points is a pivotal task in statistical analysis. In the quantum realm, it is a new primitive where one aims at identifying the point where a source that supposedly prepares a sequence of particles in identical quantum states starts preparing a mutated one. We obtain the optimal procedure to identify the change point with certainty-naturally at the price of having a certain probability of getting an inconclusive answer. We obtain the analytical form of the optimal probability of successful identification for any length of the particle sequence. We show that the conditional success probabilities of identifying each possible change point show an unexpected oscillatory behavior. We also discuss local (online) protocols and compare them with the optimal procedure.
We consider online detection strategies for identifying a change point in a stream of quantum particles allegedly prepared in identical states. We show that the identification of the change point can be done without error via sequential local measurements while attaining the optimal performance bound set by quantum mechanics. In this way, we establish the task of exactly identifying a quantum change point as an instance where local protocols are as powerful as global ones. The optimal online detection strategy requires only one bit of memory between subsequent measurements, and it is amenable to experimental realization with current technology.
Quantum sensors offer significant advantages over classical devices in spatial resolution and sensitivity, enabling transformative applications across materials science, healthcare, and beyond. Their practical performance, however, is often constrained by unmodelled effects, including noise, imperfect state preparation, and non-ideal control fields. In this work, we report the first experimental implementation of a graybox modelling strategy for a solid-state open quantum system. The graybox framework integrates a physics-based system model with a data-driven description of experimental imperfections, achieving higher fidelity than purely analytical (whitebox) approaches while requiring fewer training resources than fully deep-learning blackbox models. We experimentally validate the method on the task of estimating a static magnetic field using a single-spin quantum sensor, performing Bayesian inference with a graybox model trained on prior experimental data. Using roughly 10,000 training datapoints, the graybox model yields several orders of magnitude improvement in mean squared error over the corresponding physics-only model, as well as significant improvement over a blackbox model with comparable size. These results are broadly applicable to a wide range of quantum sensing platforms, not limited to single-spin systems, and are particularly valuable for real-time adaptive protocols, where model inaccuracies can otherwise lead to suboptimal control and degraded performance.
Quantum-enhanced Bayesian inference offers a paradigm shift in the field of machine learning, addressing the fundamental limitations of classical Bayesian methods – namely, computational complexity and scalability – when dealing with high-dimensional data. This paper presents a novel quantum-enhanced Bayesian inference algorithm designed to drastically reduce these challenges. We explore the use of quantum annealing and quantum approximate optimization algorithms to efficiently navigate the complex search space of model parameters, leading to significantly improved accuracy and reduced computational costs. This work demonstrates the potential of quantum computing to revolutionize machine learning, particularly within domains characterized by high data complexity and demanding performance requirements. The core mechanism focuses on leveraging quantum phenomena – superposition and entanglement – to accelerate the exploration of parameter space and improve the convergence of inference algorithms. The investigation includes a detailed analysis of the algorithm's performance compared to classical methods, highlighting the benefits of quantum acceleration in specific machine learning tasks.
Quantum Bayesian Inference (QBI) presents a novel approach to statistical machine learning, utilizing the principles of quantum mechanics to enhance the accuracy and robustness of models, particularly when dealing with high-dimensional data and complex Bayesian frameworks. This paper introduces a quantum algorithm designed to efficiently estimate the posterior distribution of parameters in a Bayesian model through the application of quantum superposition and entanglement, aiming to overcome the limitations of classical methods. We explore the potential of this paradigm shift to deliver exponential speedups in inference tasks, offering a compelling path towards more accurate and reliable statistical machine learning algorithms.