U(1)-symmetric recurrent neural networks for quantum state reconstruction

Morawetz, Stewart; Vlugt, Isaac J. S. De; Carrasquilla, Juan; Melko, Roger G.

doi:10.1103/physreva.104.012401

Cited by 25 publications

(6 citation statements)

References 33 publications

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“…more possible reference bases in the first step. Our active learning scheme can furthermore be generalized to state representations other than the restricted Boltzmann machines considered here, such as variational autoencoders [21], recurrent [22] and convolutional neural networks [23], generative adversarial networks [24], and transformer architectures [25].…”

Section: Discussionmentioning

confidence: 99%

“…Here, we use the implementation of RBM quantum state tomography by Beach et al [20] in the form of a python package called QuCumber. However, the idea of our AL scheme is independent of the specific implementation of the RBMs and can in principle be applied in combination with any other quantum state tomography scheme, such as other neural network architectures [21][22][23][24][25] as well as matrix-product state based state reconstruction [26,27]. Here, the target many-body quantum state is represented in terms of an artificial neu-ral network (RBM) wave function…”

Section: Restricted Boltzmann Machinesmentioning

confidence: 99%

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Adaptive Quantum State Tomography with Active Learning

Lange¹,

Kebrič²,

Buser³

et al. 2022

Preprint

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Recently, tremendous progress has been made in the field of quantum science and technologies: different platforms for quantum simulation as well as quantum computing, ranging from superconducting qubits to neutral atoms, are starting to reach unprecedentedly large systems. In order to benchmark these systems and gain physical insights, the need for efficient tools to characterize quantum states arises. The exponential growth of the Hilbert space with system size renders a full reconstruction of the quantum state prohibitively demanding in terms of the number of necessary measurements. Here we propose and implement an efficient scheme for quantum state tomography using active learning. Based on a few initial measurements, the active learning protocol proposes the next measurement basis, designed to yield the maximum information gain. For a fixed total number of measurements and basis configurations, our algorithm maximizes the information one can obtain about the quantum state under consideration. We apply the active learning quantum state tomography scheme to reconstruct different multi-qubit states with varying degree of entanglement as well as to ground states of a kinetically constrained spin chain. In all cases, we obtain a significantly improved reconstruction as compared to a reconstruction based on the exact same number of measurements, but with randomly chosen basis configurations. Our scheme is highly relevant to gain physical insights in quantum many-body systems as well as for the characterization of quantum devices, and paves the way for benchmarking and probing large quantum systems.

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Section: Discussionmentioning

confidence: 99%

Section: Restricted Boltzmann Machinesmentioning

confidence: 99%

Adaptive Quantum State Tomography with Active Learning

Lange¹,

Kebrič²,

Buser³

et al. 2022

Preprint

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“…Despite the encouraging results obtained from our quantum-based models, we foresee a significant space for potential improvements regarding all the generative models used in this study and some not explored here. In particular, one can embed constraints into generative models such as in U (1)-symmetric tensor networks [39] and U (1)-symmetric RNNs [41,42]. Furthermore, including other state-of-theart generative models with different variations is vital for establishing a more comprehensive comparison.…”

Section: Conclusion and Outlooksmentioning

confidence: 99%

A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models

Hibat-Allah¹,

Mauri²,

Carrasquilla³

et al. 2023

Preprint

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Generative modeling has seen a rising interest in both classical and quantum machine learning, and it represents a promising candidate to obtain a practical quantum advantage in the near term. In this study, we build over the framework proposed in Gili et al. [1] for evaluating the generalization performance of generative models, and we establish the first quantitative comparative race towards practical quantum advantage (PQA) between classical and quantum generative models, namely Quantum Circuit Born Machines (QCBMs), Transformers (TFs), Recurrent Neural Networks (RNNs), Variational Autoencoders (VAEs), and Wasserstein Generative Adversarial Networks (WGANs). After defining four types of PQAs scenarios, we focus on what we refer to as potential PQA, aiming to compare quantum models with the best-known classical algorithms for the task at hand. We let the models race on a well-defined and application-relevant competition setting, where we illustrate and demonstrate our framework on 20 variables (qubits) generative modeling task. Our results suggest that QCBMs are more efficient in the data-limited regime than the other state-of-the-art classical generative models. Such a feature is highly desirable in a wide range of real-world applications where the available data is scarce.

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“…Recently, NNs have been used to perform QST [11,[80][81][82]. In particular, a wide class of states can be modeled by a so-called Restricted Boltzmann Machine (RBM) (Box B and Fig.…”

Section: [N]mentioning

confidence: 99%