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arXiv:2108.01571 · Physical Review A

Multiclass classification of dephasing channels

Adriano Macarone Palmieri, Federico Bianchi, Matteo G. A. Paris, Claudia Benedetti

Published Nov 10, 2021• 13 citations
arXivHTMLPDF

Abstract

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 $s$ 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 $70%$ 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 $96%$ and $79%$ accuracy using single-layer NNs.

DOI
10.1103/physreva.104.052412

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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.
In this paper, machine learning and artificial neural network models are proposed for quantum noise classification in stochastic quantum dynamics. For this purpose, we train and then validate support vector machine, multi-layer perceptron and recurrent neural network, models with different complexity and accuracy, to solve supervised binary classification problems. By exploiting the quantum random walk formalism, we demonstrate the high efficacy of such tools in classifying noisy quantum dynamics using data sets collected in a single realisation of the quantum system evolution. In addition, we also show that for a successful classification one just needs to measure, in a sequence of discrete time instants, the probabilities that the analysed quantum system is in one of the allowed positions or energy configurations, without any external driving. Thus, neither measurements of quantum coherences nor sequences of control pulses are required. Since in principle the training of the machine learning models can be performed a-priori on synthetic data, our approach is expected to find direct application in a vast number of experimental schemes and also for the noise benchmarking of the already available noisy intermediate-scale quantum devices.
Abstract In this paper machine learning and artificial neural network models are proposed for the classification of external noise sources affecting a given quantum dynamics. For this purpose, we train and then validate support vector machine, multi-layer perceptron and recurrent neural network models with different complexity and accuracy, to solve supervised binary classification problems. As a result, we demonstrate the high efficacy of such tools in classifying noisy quantum dynamics using simulated data sets from different realizations of the quantum system dynamics. In addition, we show that for a successful classification one just needs to measure, in a sequence of discrete time instants, the probabilities that the analysed quantum system is in one of the allowed positions or energy configurations. Albeit the training of machine learning models is here performed on synthetic data, our approach is expected to find application in experimental schemes, as e.g. for the noise benchmarking of noisy intermediate-scale quantum devices.
We investigate the robustness of quantum neural networks (QNNs) trained as binary classifiers against bit flip and depolarizing noise, two channels that emulate a subset of noise present in noisy intermediate-scale quantum (NISQ) devices. The presence of decoherence and other forms of noise poses significant challenges to classification accuracy. To assess the impact of noise on label extraction, and to evaluate the performance and robustness of our models, we trained three different label assignment methods in the presence of various levels of noise. Each QNN model uses 2 qubits to implement a parameterized model and either the qubits of the QNN, or a set of ancilla qubits are used for label extraction. These three different methods project the state of either a single qubit or multiple qubits onto the computational basis. This generates a probability distribution that is post-processed to assign a class label and a class probability. Each QNN is trained using noisy numerical simulation on a dataset with 2 features. Depolarizing noise channels are interleaved with the parameterized gates of the QNN and we include bit flip error prior to extracting the labels. The noise levels for the depolarizing noise and bit flip error are swept over large ranges of values. We deploy QNNs trained at various noise levels on IBM quantum computers- this introduces an additional source of noise due to SWAP gate noise. We observe that the QNNs trained with simulated noise can have good performance on NISQ hardware.
The goal of this work is to define a notion of a “quantum neural network” to classify data, which exploits the low-energy spectrum of a local Hamiltonian. As a concrete application, we build a binary classifier, train it on some actual data and then test its performance on a simple classification task. More specifically, we use Microsoft’s quantum simulator, LIQ[Formula: see text][Formula: see text], to construct local Hamiltonians that can encode trained classifier functions in their ground space, and which can be probed by measuring the overlap with test states corresponding to the data to be classified. To obtain such a classifier Hamiltonian, we further propose a training scheme based on quantum annealing which is completely closed-off to the environment and which does not depend on external measurements until the very end, avoiding unnecessary decoherence during the annealing procedure. For a network of size [Formula: see text], the trained network can be stored as a list of [Formula: see text] coupling strengths. We address the question of which interactions are most suitable for a given classification task, and develop a qubit-saving optimization for the training procedure on a simulated annealing device. Furthermore, a small neural network to classify colors into red versus blue is trained and tested, and benchmarked against the annealing parameters.
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.