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Tomography of quantum detectors using neural networks

Hailan Ma, Shuixin Xiao, Daoyi Dong, Ian R. Petersen

Published Jan 1, 2023• 3 citations
Publisher

Abstract

Quantum detector tomography is a fundamental technique for calibrating quantum devices and thus lay foundations for quantum information processing tasks. In this work, we propose a quantum detector tomography method that employs deep neural networks to reconstruct quantum detectors from a set of probe states with high efficiency. Numerical results demonstrate that the proposed method exhibits a significant potential to estimate phase-insensitive detectors.

DOI
10.1016/j.ifacol.2023.10.088

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Quantum state tomography is defined as a process of reconstructing the density matrix of a quantum state and is an important task for various emerging quantum technologies. In this work, we propose a general quantum state tomography framework that employs deep neural networks to reconstruct quantum states from a set of measurements with high efficiency. In particular, we apply it to two cases, including few measurement copies and incomplete measurement. Numerical results demonstrate that the proposed method exhibits a significant potential to achieve high fidelity for quantum state tomography when measurement resources are limited.
Abstract Quantum state tomography is a crucial technique for characterizing the state of a quantum system, which is essential for many applications in quantum technologies. In recent years, there has been growing interest in leveraging neural networks to enhance the efficiency and accuracy of quantum state tomography. However, versatile methods that are broadly applicable across diverse reconstruction scenarios remain relatively underexplored. In this paper, we present two neural network-based approaches for both pure and mixed quantum state tomography: Restricted Feature Based Neural Network and Mixed States Neural Network, evaluate its effectiveness in comparison to existing neural network-based methods. We demonstrate that our proposed methods can achieve state-of-the-art results in reconstructing mixed quantum states from experimental data. Our work highlights the potential of neural networks in facilitating the development of quantum technologies. Source code is publicly available at https://github.com/luutn2002/uni-qst
We revisit quantum tomography in an informationally incomplete scenario and propose improved state reconstruction methods using deep neural networks. In the first approach, the trained network predicts an optimal linear or quadratic reconstructor with coefficients depending only on the collection of (already taken) measurement operators. This effectively refines the undercomplete tomographic reconstructor based on pseudoinverse operation. The second, based on an LSTM recurrent network performs state reconstruction sequentially. It can also optimize the measurement sequence, which suggests a no-free-lunch theorem for tomography: by narrowing the state space, we gain the possibility of more efficient tomography by learning the optimal sequence of measurements. Numerical experiments for a 2-qubit system show that both methods outperform standard maximum likelihood estimation and also scale to larger 3- and 4-qubit systems. Our results demonstrate that neural networks can effectively learn the underlying geometry of multi-qubit states and use it for their reconstruction.
Abstract Quantum compressed sensing is a fundamental technique for tomographic reconstruction of low-rank density matrices in informationally incomplete scenarios. However, when the available measurement data is insufficient, standard compressed sensing, like other algorithmic estimators such as maximum-likelihood, can yield imprecise or noisy estimates. To mitigate this, we propose a deep neural network-based post-processing to enhance the initial reconstruction. By treating the compressed sensing-estimated quantum state as a noisy input, the network performs a supervised denoising task. After the network is applied, a projection onto the space of feasible density matrices is performed to obtain an improved final state estimation. We demonstrate the effectiveness of our method through numerical experiments. Additionally, we explore iterative application of the inference process to further enhance performance, and we analyze the network’s generalization ability by testing its performance on states and noise models not seen during training.
Quantum state tomography (QST) is a fundamental technique in quantum information science, used to characterize the density matrix of an unknown quantum state. However, traditional QST methods are often computationally intensive, requiring a large number of measurements and sophisticated data analysis techniques. This paper proposes a novel approach utilizing self-organizing neural networks (SONNs) for direct quantum state reconstruction. The core idea is to train a SONN to learn the mapping between experimental measurement data and the corresponding density matrix, thereby bypassing the need for precise control over the quantum system and significantly reducing the computational burden. We detail the architecture of the SONN, the training process, and demonstrate the potential of this method to achieve accurate state reconstruction with fewer measurements. The proposed method offers a promising path towards more efficient and scalable QST, particularly for complex quantum systems.