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Physical Review Research

Adaptive phase estimation through a genetic algorithm

Kartikeya Rambhatla, Simone Evaldo D’Aurelio, Mauro Valeri, Emanuele Polino, Nicolò Spagnolo, Fabio Sciarrino

Published Jul 15, 2020• 30 citations
Publisher

Abstract

Quantum metrology is one of the most relevant applications of quantum information theory to quantum technologies.Here, quantum probes are exploited to overcome classical bounds in the estimation of unknown parameters.In this context, phase estimation, where the unknown parameter is a phase shift between two modes of a quantum system, is a fundamental problem.In practical and realistic applications, it is necessary to devise methods to optimally estimate an unknown phase shift by using a limited number of probes.Here we introduce and experimentally demonstrate a machine learning-based approach for the adaptive estimation of a phase shift in a Mach-Zehnder interferometer, tailored for optimal performances with limited resources.The employed technique is a genetic algorithm used to devise the optimal feedback phases employed during the estimation in an offline fashion.The results show the capability to retrieve the true value of the phase by using few photons, and to reach the sensitivity bounds in such small probe regime.We finally investigate the robustness of the protocol with respect to common experimental errors, showing that the protocol can be adapted to a noisy scenario.Such approach promises to be a useful tool for more complex and general tasks where optimization of feedback parameters is required.

DOI
10.1103/physrevresearch.2.033078

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Quantum metrology is one of the most relevant applications of quantum information theory to quantum technologies.Here, quantum probes are exploited to overcome classical bounds in the estimation of unknown parameters.In this context, phase estimation, where the unknown parameter is a phase shift between two modes of a quantum system, is a fundamental problem.In practical and realistic applications, it is necessary to devise methods to optimally estimate an unknown phase shift by using a limited number of probes.Here we introduce and experimentally demonstrate a machine learning-based approach for the adaptive estimation of a phase shift in a Mach-Zehnder interferometer, tailored for optimal performances with limited resources.The employed technique is a genetic algorithm used to devise the optimal feedback phases employed during the estimation in an offline fashion.The results show the capability to retrieve the true value of the phase by using few photons, and to reach the sensitivity bounds in such small probe regime.We finally investigate the robustness of the protocol with respect to common experimental errors, showing that the protocol can be adapted to a noisy scenario.Such approach promises to be a useful tool for more complex and general tasks where optimization of feedback parameters is required.
Phase estimation represents a significant example to test the application of quantum theory for enhanced measurements of unknown physical parameters. Several recipes have been developed, allowing to define strategies to reach the ultimate bounds in the asymptotic limit of a large number of trials. However, in certain applications it is crucial to reach such bound when only a small number of probes is employed. Here, we discuss an asymptotically optimal, machine learning based, adaptive single-photon phase estimation protocol that allows us to reach the standard quantum limit when a very limited number of photons is employed.
Relevant metrological scenarios involve the simultaneous estimation of multiple parameters. The fundamental ingredient to achieve quantum-enhanced performance is based on the use of appropriately tailored quantum probes. However, reaching the ultimate resolution allowed by physical laws requires nontrivial estimation strategies from both a theoretical and a practical point of view. A crucial tool for this purpose is the application of adaptive learning techniques. Indeed, adaptive strategies provide a flexible approach to obtain optimal parameter-independent performance and optimize convergence to the fundamental bounds with a limited amount of resources. Here, we combine on the same platform quantum-enhanced multiparameter estimation attaining the corresponding quantum limit and adaptive techniques. We demonstrate the simultaneous estimation of three optical phases in a programmable integrated photonic circuit, in the limited-resource regime. The obtained results show the possibility of successfully combining different fundamental methodologies towards transition to quantum sensors applications.
Abstract Quantum phase estimation is a paradigmatic problem in quantum sensing and metrology. Here we show that adaptive methods based on classical machine learning algorithms can be used to enhance the precision of quantum phase estimation when noisy non-entangled qubits are used as sensors. We employ the Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms to this task and we identify the optimal feedback policies which minimize the Holevo variance. We benchmark these schemes with respect to scenarios that include Gaussian and Random Telegraph fluctuations as well as reduced Ramsey-fringe visibility due to decoherence. We discuss their robustness against noise in connection with real experimental setups such as Mach–Zehnder interferometry with optical photons and Ramsey interferometry in trapped ions, superconducting qubits and nitrogen-vacancy (NV) centers in diamond.
Abstract Achieving ultimate bounds in estimation processes is the main objective of quantum metrology. In this context, several problems require measurement of multiple parameters by employing only a limited amount of resources. To this end, adaptive protocols, exploiting additional control parameters, provide a tool to optimize the performance of a quantum sensor to work in such limited data regime. Finding the optimal strategies to tune the control parameters during the estimation process is a non-trivial problem, and machine learning techniques are a natural solution to address such task. Here, we investigate and implement experimentally an adaptive Bayesian multiparameter estimation technique tailored to reach optimal performances with very limited data. We employ a compact and flexible integrated photonic circuit, fabricated by femtosecond laser writing, which allows to implement different strategies with high degree of control. The obtained results show that adaptive strategies can become a viable approach for realistic sensors working with a limited amount of resources.
Phase estimation has applications from quantum imaging to gravitational-wave detection. In areas such as biological-system sampling or quantum metrology, it is crucial to optimally acquire information from a very limited number of probes. To address this need, the authors describe and experimentally verify a machine-learning method for optimal adaptive single-photon phase estimation based on a small number of trials. This approach could be used to optimize quantum metrology protocols, and can be extended to general multiparameter scenarios.
One of the most immediate practical applications of quantum information processing is performing precise quantum measurements. Quantum measurement schemes employing adaptive feedback are most effective, since accumulated information from measurements is exploited to maximize the information gain in subsequent measurements. Yet devising such feedback policies is complicated and often involves clever guesswork. Here we present an automated method, based on machine learning, to generate adaptive feedback measurement policies. We apply our technique to adaptive quantum phase measurement, which is important for applications such as atomic clocks and gravitational wave detection. Our algorithm autonomously learns to perform phase estimation based on experimental trial runs, which can be either simulated or performed using a real world experiment.