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Benchmarking quantum tomography completeness and fidelity with machine learning

Yong-Siah, Teo, Shin, Seongwood, Hyunseok Jeong, Yosep Kim, Yoon-Ho Kim, G. I. Struchalin, E. V. Kovlakov, Stanislav S. Straupe, S. P. Kulik, Gerd Leuchs, Sánchez Soto, Luis Lorenzo

Published Oct 14, 2021• 19 citations
OpenAlex

Abstract

We train convolutional neural networks to predict whether or not a set of measurements is informationally complete to uniquely reconstruct any given quantum state with no prior information. In addition, we perform fidelity benchmarking based on this measurement set without explicitly carrying out state tomography. The networks are trained to recognize the fidelity and a reliable measure for informational completeness. By gradually accumulating measurements and data, these trained convolutional networks can efficiently establish a compressive quantum-state characterization scheme by accelerating runtime computation and greatly reducing systematic drifts in experiments. We confirm the potential of this machine-learning approach by presenting experimental results for both spatial-mode and multiphoton systems of large dimensions. These predictions are further shown to improve when the networks are trained with additional bootstrapped training sets from real experimental data. Using a realistic beam-profile displacement error model for Hermite-Gaussian sources, we further demonstrate numerically that the orders-of-magnitude reduction in certification time with trained networks greatly increases the computation yield of a large-scale quantum processor using these sources, before state fidelity deteriorates significantly.

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We train convolutional neural networks to predict whether or not a set of measurements is informationally complete to uniquely reconstruct any given quantum state with no prior information. In addition, we perform fidelity benchmarking based on this measurement set without explicitly carrying out state tomography. The networks are trained to recognize the fidelity and a reliable measure for informational completeness. By gradually accumulating measurements and data, these trained convolutional networks can efficiently establish a compressive quantum-state characterization scheme by accelerating runtime computation and greatly reducing systematic drifts in experiments. We confirm the potential of this machine-learning approach by presenting experimental results for both spatial-mode and multiphoton systems of large dimensions. These predictions are further shown to improve when the networks are trained with additional bootstrapped training sets from real experimental data. Using a realistic beam-profile displacement error model for Hermite-Gaussian sources, we further demonstrate numerically that the orders-of-magnitude reduction in certification time with trained networks greatly increases the computation yield of a large-scale quantum processor using these sources, before state fidelity deteriorates significantly.
We train convolutional neural networks to predict whether or not a set of measurements is informationally complete to uniquely reconstruct any given quantum state with no prior information. In addition, we perform fidelity benchmarking based on this measurement set without explicitly carrying out state tomography. The networks are trained to recognize the fidelity and a reliable measure for informational completeness. By gradually accumulating measurements and data, these trained convolutional networks can efficiently establish a compressive quantum-state characterization scheme by accelerating runtime computation and greatly reducing systematic drifts in experiments. We confirm the potential of this machine-learning approach by presenting experimental results for both spatial-mode and multiphoton systems of large dimensions. These predictions are further shown to improve when the networks are trained with additional bootstrapped training sets from real experimental data. Using a realistic beam-profile displacement error model for Hermite–Gaussian sources, we further demonstrate numerically that the orders-of-magnitude reduction in certification time with trained networks greatly increases the computation yield of a large-scale quantum processor using these sources, before state fidelity deteriorates significantly.
Abstract Modern day quantum simulators can prepare a wide variety of quantum states but the accurate estimation of observables from tomographic measurement data often poses a challenge. We tackle this problem by developing a quantum state tomography scheme which relies on approximating the probability distribution over the outcomes of an informationally complete measurement in a variational manifold represented by a convolutional neural network. We show an excellent representability of prototypical ground- and steady states with this ansatz using a number of variational parameters that scales polynomially in system size. This compressed representation allows us to reconstruct states with high classical fidelities outperforming standard methods such as maximum likelihood estimation. Furthermore, it achieves a reduction of the estimation error of observables by up to an order of magnitude compared to their direct estimation from experimental data.
Modern day simulators can prepare a wide variety of states but extracting observables from the resulting quantum data often poses a challenge. We tackle this problem by developing a state tomography scheme which relies on approximating the probability distribution over the outcomes of an informationally complete measurement in a variational manifold represented by a convolutional neural network. We show an excellent representability of prototypical ground- and steady states with this ansatz using a number of variational parameters that scales polynomially in system size. This compressed representation allows us to reconstruct states with high classical fidelities outperforming standard methods such as maximum likelihood estimation. Furthermore, it achieves a reduction of the root mean square errors of observables by up to an order of magnitude compared to their direct estimation from experimental data.
Abstract We build a general quantum state tomography framework that makes use of machine learning techniques to reconstruct quantum states from a given set of coincidence measurements. For a wide range of pure and mixed input states we demonstrate via simulations that our method produces functionally equivalent reconstructed states to that of traditional methods with the added benefit that expensive computations are front-loaded with our system. Further, by training our system with measurement results that include simulated noise sources we are able to demonstrate a significantly enhanced average fidelity when compared to typical reconstruction methods. These enhancements in average fidelity are also shown to persist when we consider state reconstruction from partial tomography data where several measurements are missing. We anticipate that the present results combining the fields of machine intelligence and quantum state estimation will greatly improve and speed up tomography-based quantum experiments.
We present a supervised machine learning-based method using convolutional neural networks to estimate the covariance matrix of Gaussian quantum states in the presence of thermal noise. Unlike computationally intensive density matrix reconstructions, our machine learning-based method allows for the reconstruction of impure squeezed vacuum states using sparse measurements of quadrature sequences based on a model employing a two-component state mixed together from thermal and squeezed thermal states. The method achieves high fidelity and precision, notably also at high squeezing levels, while offering an effective characterization of physical quantities and accurately estimating the covariance matrix. We benchmark our machine against experimental data of single-mode squeezed vacuum states, demonstrating its accuracy and capability to quantify experimental degradation to squeezing and purity. We experimentally verify that our covariance matrix estimation exhibits robustness to state degradation induced by thermal state admixtures. We provide a method for lightweight, compact, and complete representation of lab-generated Gaussian states and lay the foundation for extending real-time quantum state tomography for thermal multi-component Gaussian states to multi-mode systems.
We study the performance of efficient quantum state tomography methods based on neural-network quantum states using measured data from a two-photon experiment. Machine-learning-inspired variational methods provide a promising route towards scalable state characterization for quantum simulators. While the power of these methods has been demonstrated on synthetic data, applications to real experimental data remain scarce. We benchmark and compare several such approaches by applying them to measured data from an experiment producing two-qubit entangled states. We find that in the presence of experimental imperfections and noise, confining the variational manifold to physical states, i.e., to positive semidefinite density matrices, greatly improves the quality of the reconstructed states but renders the learning procedure more demanding. Including additional, possibly unjustified, constraints, such as assuming pure states, facilitates learning, but also biases the estimator.