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arXiv:2410.21504

Disentanglement in dephasing channel with machine learning

Qihang Liu, Qiao, Anran, Jung‐Tsung Shen

Published Oct 28, 2024• 0 citations
arXivHTMLPDF

Abstract

Quantum state classification and entanglement quantification are of significant importance in the fundamental research of quantum information science and various quantum applications. Traditional methods, such as quantum state tomography, face exponential measurement demands with increasing numbers of qubits, necessitating more efficient approaches. Recent work has shown promise in using artificial neural networks (ANNs) for quantum state analysis. However, existing ANNs may falter when confronted with states affected by dephasing noise, especially with limited data and computational resources. In this study, we employ a machine-learning approach to investigate the disentanglement process in two-qubit systems in the presence of dephasing noise. Our findings highlight the limitations of general state-trained ANNs in classifying states under dephasing noise. Specialized ANN algorithms, tailored for classifying states and quantifying entanglement in such noisy environments, demonstrate excellent performance using only a subset of tomographic features.

DOI
10.48550/arxiv.2410.21504

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Quantum state classification and entanglement quantification are of significant importance in the fundamental research of quantum information science and various quantum applications. Traditional methods, such as quantum state tomography, face exponential measurement demands with increasing numbers of qubits, necessitating more efficient approaches. Recent work has shown promise in using artificial neural networks (ANNs) for quantum state analysis. However, existing ANNs may falter when confronted with states affected by dephasing noise, especially with limited data and computational resources. In this study, we employ a machine-learning approach to investigate the disentanglement process in two-qubit systems in the presence of dephasing noise. Our findings highlight the limitations of general state-trained ANNs in classifying states under dephasing noise. Specialized ANN algorithms, tailored for classifying states and quantifying entanglement in such noisy environments, demonstrate excellent performance using only a subset of tomographic features.
We address the use of neural networks (NNs) in classifying the environmental parameters of single-qubit dephasing channels. In particular, we investigate the performance of linear perceptrons and of two nonlinear NN architectures. At variance with time-series-based approaches, our goal is to learn a discretized probability distribution over the parameters using tomographic data at just two random instants of time. We consider dephasing channels originating either from classical $1/{f}^{\ensuremath{\alpha}}$ noise or from the interaction with a bath of quantum oscillators. The parameters to be classified are the color $\ensuremath{\alpha}$ of the classical noise or the Ohmicity parameter sss of the quantum environment. In both cases, we find that NNs are able to exactly classify parameters into 16 classes using noiseless data (a linear NN is enough for the color, whereas a single-layer NN is needed for the Ohmicity). In the presence of noisy data (e.g., coming from noisy tomographic measurements), the network is able to classify the color of the $1/{f}^{\ensuremath{\alpha}}$ noise into 16 classes with about 7070%70 accuracy, whereas classification of Ohmicity turns out to be challenging. We also consider a more coarse-grained task and train the network to discriminate between two macroclasses corresponding to $\ensuremath{\alpha}\ensuremath{\lessgtr}1$ and $s\ensuremath{\lessgtr}1$, obtaining up to 9696%96 and 7979%79 accuracy using single-layer NNs.
The paper suggest employing machine learning for resource-efficient classification of quantum correlations in entanglement distribution networks. Specifically, artificial neural networks (ANN) are utilized to classify quantum correlations based on collective measurements conducted in the geometry of entanglement swapping. ANNs are trained to categorize two-qubit quantum states into five mutually exclusive classes depending on the strength of quantum correlations exhibited by the states. The precision and recall of the ANN models are analyzed as functions of the quantum resources consumed, i.e. the number of collective measurements performed.
Quantum entanglement detection is one of the fundamental tasks in quantum information science. Conventional methods for quantum state tomography exhibit limitations in scalability as the number of qubits increases, leading to exponential growth in the number of unknown parameters and required measurements. Consequently, the accuracy enhancement achieved by these methods is constrained. In response to this challenge, we developed a tailored convolutional neural network (CNN) model capable of effectively detecting entanglement in two-qubit quantum states, achieving an accuracy exceeding 97.5%. Notably, even in the presence of noise, this model retains its robust performance, displaying resilience against a tolerable level of noise contamination. Furthermore, the inherent generalization power of CNNs allows our model, which was initially trained on a specific spectrum of quantum states, to extend its applicability to wider states, positioning it as an outstanding tool for the further application of machine learning in the field of quantum computing, opening up new pathways for solving entanglement detection problems in quantum information.
Quantum information technologies provide promising applications in communication and computation, while machine learning has become a powerful technique for extracting meaningful structures in "big data." A crossover between quantum information and machine learning represents a new interdisciplinary area stimulating progress in both fields. Traditionally, a quantum state is characterized by quantum-state tomography, which is a resource-consuming process when scaled up. Here we experimentally demonstrate a machine-learning approach to construct a quantum-state classifier for identifying the separability of quantum states. We show that it is possible to experimentally train an artificial neural network to efficiently learn and classify quantum states, without the need of obtaining the full information of the states. We also show how adding a hidden layer of neurons to the neural network can significantly boost the performance of the state classifier. These results shed new light on how classification of quantum states can be achieved with limited resources, and represent a step towards machine-learning-based applications in quantum information processing.
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Introduction: The scalability of superconducting quantum processors is fundamentally limited by environmental noise and the exponential measurement overhead required for multi-qubit entanglement verification. Methods: In this work, we introduce a hybrid machine learning (ML) framework utilizing convolutional neural networks (CNNs) to simultaneously characterize decoherence channels and verify multipartite entanglement. The model is trained on synthetic noisy syndrome measurement data augmented with empirical SPAM models and applied to a 5-qubit superconducting device, where the neural network acts as a non-linear entanglement witness. Results: sweeps. Furthermore, it successfully verifies genuine multipartite entanglement with a fidelity prediction of 99.1%, while requiring only 12% of the measurement bases demanded by full quantum state tomography (QST). Discussion: Crucially, our methodology bypasses two distinct challenges: it drastically reduces the measurement complexity inherent in multi-qubit entanglement verification, and it inherently filters out state preparation and measurement (SPAM) errors without requiring noise-amplifying matrix inversions. These numerical results demonstrate that ML-assisted protocols provide a highly resource-efficient pathway for the characterization of noisy intermediate-scale quantum (NISQ) devices.