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arXiv:2008.06378 · IEEE Transactions on Neural Networks and Learning Systems

Reconstructing Quantum States With Quantum Reservoir Networks

Sanjib Ghosh, Andrzej Opala, Michał Matuszewski, Tomasz Paterek, T. C. H. Liew

Published Jul 31, 2020• 63 citations
arXivHTMLPDF

Abstract

Reconstructing quantum states is an important task for various emerging quantum technologies. The process of reconstructing the density matrix of a quantum state is known as quantum state tomography. Conventionally, tomography of arbitrary quantum states is challenging as the paradigm of efficient protocols has remained in applying specific techniques for different types of quantum states. Here, we introduce a quantum state tomography platform based on the framework of reservoir computing. It forms a quantum neural network and operates as a comprehensive device for reconstructing an arbitrary quantum state (finite-dimensional or continuous variable). This is achieved with only measuring the average occupation numbers in a single physical setup, without the need of any knowledge of optimum measurement basis or correlation measurements.

DOI
10.1109/tnnls.2020.3009716

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Reconstructing quantum states is an important task for various emerging quantum technologies. The process of reconstructing the density matrix of a quantum state is known as quantum state tomography. Conventionally, tomography of arbitrary quantum states is challenging as the paradigm of efficient protocols has remained in applying specific techniques for different types of quantum states. Here, we introduce a quantum state tomography platform based on the framework of reservoir computing. It forms a quantum neural network and operates as a comprehensive device for reconstructing an arbitrary quantum state (finite-dimensional or continuous variable). This is achieved with only measuring the average occupation numbers in a single physical setup, without the need of any knowledge of optimum measurement basis or correlation measurements.
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.
Quantum state tomography is an essential component of modern quantum technology. In application to continuous-variable harmonic-oscillator systems, such as the electromagnetic field, existing tomography methods typically reconstruct the state in discrete bases, and are hence limited to states with relatively low amplitudes and energies. Here, we overcome this limitation by utilizing a feed-forward neural network to obtain the density matrix directly in the continuous position basis. An important benefit of our approach is the ability to choose specific regions in the phase space for detailed reconstruction. This results in a relatively slow scaling of the amount of resources required for the reconstruction with the state amplitude, and hence allows us to dramatically increase the range of amplitudes accessible with our method.
Abstract Quantum state tomography (QST) aiming at reconstructing the density matrix of a quantum state plays an important role in various emerging quantum technologies. Recognizing the challenges posed by imperfect measurement data, we develop a unified neural network (NN)-based approach for QST under constrained measurement scenarios, including limited measurement copies, incomplete measurements, and noisy measurements. Through comprehensive comparison with other estimation methods, we demonstrate that our method improves the estimation accuracy in scenarios with limited measurement resources, showcasing notable robustness in noisy measurement settings. These findings highlight the capability of NNs to enhance QST with constrained measurements.
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.
The evaluation of unknown states for a given quantum system is one of the key problems in quantum information processing. The most efficient method of state characterization is quantum state tomography (QST), where the full-density matrices are reconstructed from the experimental measurements or numerical simulations performed on quantum states. The improvement of the computational performance in quantum state tomography and its related problems is a challenging task for modern theoretical physics. The general scheme of computing deals with the input information that goes into a quantum reservoir through a recurrent evolution. After the evolution, the final output is obtained as the linear combination of the readout elements. In our approach, the quantum reservoir is modeled with the Lindbladian equation. The control over performance is made by the coherent coupling parameter between the input quantum state and the reservoir. The control feedback algorithm is represented with the set of Kolesnikov’s target attractor algorithm to drive certain parameters of quantum state tomography, particularly, the outputs for the density matrix. Here we formulate the target attractor feedback in a discrete form to improve the training performance of QST and then develop a basic example of the state tomography for the quantum system of spin 1/2. We conclude by mentioning the basic features of our algorithm and its possible development.
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. 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 the XXZ model in 1D and 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 and measurement configurations, but with randomly chosen basis configurations. Our scheme is highly relevant to gain physical insights in quantum many-body systems as well as for benchmarking and characterizing quantum devices, e.g. for quantum simulation, and paves the way for scalable adaptive protocols to probe, prepare, and manipulate quantum systems.