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The European Physical Journal Plus

Investigating reconstruction of quantum state distributions with neural networks

Huikang Huang, Haozhen Situ

Published Feb 1, 2021• 2 citations
Publisher
DOI
10.1140/epjp/s13360-021-01206-4

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Abstract Quantum noise is currently limiting efficient quantum information processing and computation, impacting on the fidelity and reliability of quantum states. In this work, we consider the tasks of reconstructing and classifying quantum states corrupted by the action of an unknown noisy channel using classical feed-forward neural networks. By framing reconstruction as a regression problem, we show how such an approach can be used to recover with fidelities exceeding 99% the noiseless density matrices of quantum states of up to three qubits undergoing noisy evolution, and we test its performance with both single-qubit (bit-flip, phase-flip, depolarizing, and amplitude damping) and two-qubit quantum channels (correlated amplitude damping). Furthermore, a critical aspect of our investigation involves also a comprehensive comparison between mean squared error and infidelity as loss functions. Our findings reveal that these two metrics yield comparable results in the context of state reconstruction. Moreover, we also consider the task of distinguishing between different quantum noisy channels, and show how a neural network-based classifier is able to solve such a classification problem with perfect accuracy.
we advance non-Markovian quantum process tomography through a novel neural network-based approach, effectively transforming experimental data into a process tensor represented by the Choi state. Our investigations validate that neural networks excel in reconstructing process tensors with superior precision and robustness against noise, particularly under the challenges of undersampling. The neural network model we present not only outstrips traditional linear inversion methods in computational efficiency and accuracy but also showcases remarkable generalization across varying environments. This study fully leverages causality constraints to reduce the number of parameters in process tensor prediction, significantly enhancing the training and data efficiency of neural networks in quantum process tomography. This work marks progress in quantum computing, leveraging the strengths of neural networks to robustly characterize and identify quantum processes, thereby broadening the horizons for practical quantum process tomography applications.
Quantum photonic circuits began growing in research interest due to the long coherence times of photonic qubits, allowing for potential long-range quantum communication. To miniaturize these photonic circuits, much research has been done into integrating these systems into a chip-architecture, commonly known as an integrated photonic circuit. Due to the collapse postulate of quantum mechanics, information encoded into photons must be extracted from measurement distributions, formally known as quantum state tomography. This thesis examines the use of neural networks in quantum state tomography, compared to the commonly used maximum likelihood estimation method in a two-qubit system, in the presence of errors typically found in integrated photonic circuits. It is shown in simulation, that by altering the training of a neural network to incorporate errors, the state reconstruction infidelity can be greatly decreased and far surpass the maximum likelihood estimation. Networks are also shown with low bit-precisions, allowing for the potential future use of ultra-fast optical processors to create the neural network. From this work, it can be concluded that neural networks are able to not only complete the task of quantum state tomography, but are able to withstand errors and create more faithful reconstructions for the outputs of integrated quantum photonic circuits.