Tomografia de estados quânticos assistida por aprendizado de máquina: um estudo de caso usando redes generativas adversárias condicionais.

Silvio Jonas da Silva Júnior

Published May 29, 2024• 0 citations

Abstract

In the present work, we present a study on Generative Neural Networks applied to the problem of Quantum State Tomography (QST). Our objective was to gain understanding of the use of various Neural Networks and obtain insights on how to apply them to the QST problem, in order to select an approach with promising application. To achieve this, we investigated various networks and explored two cases: Restricted Boltzmann Machines (RBMs) and Conditional Generative Adversarial Networks (cGANs); RBM was chosen for being a pioneer in the context of QST, while cGAN was selected due to its broad successful applicability in various problems, and having been the subject of a recent study in the field, representing, so far, the only application of this type of network to the QST problem. Our case study involved simulations of a 4-qubit quantum state and real data from an experiment with highly entangled 8-qubits. For the first case, we used a well-known Python package (QuCumber, employing an RBM), and also adapted an existing network (a cGAN) to our specific state, achieving successful reconstruction with relatively low training and processing time. However, in the second case, when applying the cGAN to the 8-qubit data, we did not succeed in the reconstruction, possibly due to the limited expressiveness of the network for this scenario or the high processing time required to train it, since we relied only on a CPU and limited computational resources. In our study, we discuss the relevance of these networks to the QST problem and speculate on the next interesting steps at the intersection between Quantum Information Theory and Machine Learning.

Related papers

Quantum State Tomography with Conditional Generative Adversarial Networks

Shahnawaz Ahmed, Carlos Sánchez Muñoz, Franco Nori +1 more

Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two dueling neural networks, a generator and a discriminator, learn multimodal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity, using orders of magnitude fewer iterative steps, and less data, than both accelerated projected-gradient-based and iterative maximum-likelihood estimation. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pretrained on similar quantum states.

arXiv:2008.03240Physical Review LettersSep 27, 2021165 citations

Classification and reconstruction of optical quantum states with deep neural networks

Shahnawaz Ahmed, Carlos Sánchez Muñoz, Franco Nori +1 more

We apply deep-neural-network-based techniques to quantum state classification and reconstruction. Our methods demonstrate high classification accuracies and reconstruction fidelities, even in the presence of noise and with little data. Using optical quantum states as examples, we first demonstrate how convolutional neural networks (CNNs) can successfully classify several types of states distorted by, e.g., additive Gaussian noise or photon loss. We further show that a CNN trained on noisy inputs can learn to identify the most important regions in the data, which potentially can reduce the cost of tomography by guiding adaptive data collection. Secondly, we demonstrate reconstruction of quantum-state density matrices using neural networks that incorporate quantum-physics knowledge. The knowledge is implemented as custom neural-network layers that convert outputs from standard feed-forward neural networks to valid descriptions of quantum states. Any standard feed-forward neural-network architecture can be adapted for quantum state tomography (QST) with our method. We present further demonstrations of our proposed QST technique with conditional generative adversarial networks (QST-CGAN) [Ahmed et al., Phys. Rev. Lett. 127, 140502 (2021)]. We motivate our choice of a learnable loss function within an adversarial framework by demonstrating that the QST-CGAN outperforms, across a range of scenarios, generative networks trained with standard loss functions. For pure states with additive or convolutional Gaussian noise, the QST-CGAN is able to adapt to the noise and reconstruct the underlying state. The QST-CGAN reconstructs states using up to two orders of magnitude fewer iterative steps than iterative and accelerated projected-gradient-based maximum-likelihood estimation (MLE) methods. We also demonstrate that the QST-CGAN can reconstruct both pure and mixed states from two orders of magnitude fewer randomly chosen data points than these MLE methods. Our paper opens possibilities to use state-of-the-art deep-learning methods for quantum state classification and reconstruction under various types of noise.

arXiv:2012.02185Physical Review ResearchSep 27, 202196 citations

Machine Learning Assisted Quantum State Tomography

Murali Krishna Kurmapu

Quantum state tomography (QST) can be posed as an optimization problem, where the goal is to find the quantum state ρ that makes the observed data more likely. Obtaining the complete description of a quantum state is crucial for many quantum informational and computing tasks, and various approaches have been proposed to solve this fundamental problem. This thesis aims at presenting two models based on feedforward neural network architecture for QST. The first model is based on a multi-layer perceptron network, while the second one is based on autoregressive neural networks. We show that the perceptron model demonstrates less overfit compared to the standard iterative maximum likelihood model, however, the number of parameters in the network increases exponentially with respect to the system size. In contrast to the perceptron model, we show that the autoregressive model scales efficiently since the number of parameters grows polynomially instead of exponentially, making it suitable for QST of many-qubit systems. For the perceptron model, we presented a reconstruction of an engineered 4-qubit W state and an arbitrary optical superposition of up to 2 photons. On the other hand, using the autoregressive model, we performed QST of a 20-qubit engineered quantum state of trapped ions observed in an experiment. To the best of our knowledge, our results are the first of its kind in performing QST of complex and highly entangled out-of-equilibrium states produced by dynamics of an Ising-type Hamiltonian, engineered via laser fields on 1D trapped ion systems

Sep 8, 20200 citations

Quantum Generative Adversarial Networks (QGANs) for Data Augmentation

Jincheng Zhang

This paper investigates the application of Quantum Generative Adversarial Networks (QGANs) to data augmentation for machine learning. Traditional Generative Adversarial Networks (GANs) rely on classical neural networks, while this research explores leveraging quantum circuits as generators within a QGAN architecture. The core idea is to train a quantum generator to produce synthetic data samples, supplementing existing datasets with novel instances. The discriminator remains a classical neural network, tasked with distinguishing between real and generated data. We present a theoretical framework for this approach, outlining the mathematical formulation and key components. Specifically, we introduce the notation (x, s_1, s_2, ..., s_K) to represent data samples, generator states, and relevant parameters. The objective function for the QGAN is defined as minimizing the Jensen-Shannon divergence between the real and generated data distributions. The effectiveness of this approach is discussed, highlighting potential advantages and challenges. This work contributes to the emerging field of quantum machine learning and offers a novel strategy for improving the performance of machine learning models, particularly in scenarios with limited training data.

Aug 31, 20260 citations

Efficient quantum state tomography with mode-assisted training

Yuanhang Zhang, Massimiliano Di Ventra

Neural networks (NNs) representing quantum states are typically trained using Markov chain Monte Carlo based methods. However, unless specifically designed, such samplers only consist of local moves, making the slow-mixing problem prominent even for extremely simple quantum states. Here, we propose to use mode-assisted training that provides global information via the modes of the NN distribution. Applied to quantum state tomography using restricted Boltzmann machines, this method improves the quality of reconstructed quantum states by orders of magnitude. The method is applicable to other types of NNs and may efficiently tackle problems previously unmanageable.

arXiv:2112.14866Physical Review AOct 17, 20223 citations

Quantum state tomography of multi-qubit systems — a comparative study

Chengwei Pan, Jiaoyang Zhang, Shuang Cong +1 more

Multi-qubit state tomography is a key problem in quantum information technology, which has been studied extensively. In this work, we focus on multi-qubit state tomography based on neural network estimators and typical conventional estimation approaches. For multi-qubit pure states, fully connected neural networks and restricted Boltzmann machine networks are designed, respectively, to carry out state tomography of 2-qubit (low-dimensional) systems and 5-qubit (high-dimensional) systems. Comparisons are made with maximum likelihood estimation and least squares estimation, where performance indicators are selected as reconstruction accuracy, time cost and the number of parameters. Simulation results indicate that intelligent approaches have significant advantages over conventional approaches for state tomography of low-dimensional systems; for high-dimensional systems, however, the conventional approach is still dominant when the measurement is complete, while the restricted Boltzmann machine network can achieve higher reconstruction accuracy when the measurement is incomplete.

International Journal of Quantum InformationAug 24, 20222 citations