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arXiv:2308.10327 · Quantum Machine Intelligence

Quantum state tomography using quantum machine learning

Nouhaila Innan, Owais Ishtiaq Siddiqui, Shivang Arora, Tamojit Ghosh, Yasemin Poyraz Koçak, Dominic Paragas, Abdullah Al Omar Galib, Muhammad Al-Zafar Khan, Mohamed Bennai

Published May 7, 2024• 32 citations
arXivHTMLPDF
DOI
10.1007/s42484-024-00162-3

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Adaptive Quantum State Tomography

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This paper proposed a quantum state tomography approach based on the extreme learning machine (ELM), which is available in the reconstruction of quantum states via a lightweight neural network. The key step of the proposed tomography approach is to employ the ELM to approximate the complex mapping between the measurement values sequence and the real density matrix. After obtaining the output of the ELM-based estimator, a matrix transformation technique is used to make the network outputs satisfy quantum state constraints. Compared with deep learning-based tomography approaches, our proposed ELM-based approach enables both high-fidelity and high-efficiency quantum state tomography with only one training process under the condition of very few numbers of training samples, network layers and hidden layer nodes. In addition, the proposed tomography approach is robust to noisy measurement values, since the ELM-based estimator is quite lightweight. Simulations on the tomography of eigenstates, superposition states and mixed states are presented to verify our theoretical findings. Also, the superiority of the ELM-based tomography approach is demonstrated in comparison with that based on the radial basis function network, convolutional neural network and maximum likelihood estimation approach.
Reconstructing quantum states from measurement data represents a formidable challenge in quantum information science, especially as system sizes grow beyond the reach of traditional tomography methods. While recent studies have explored quantum machine learning (QML) for quantum state tomography (QST), nearly all rely on idealized assumptions, such as direct access to the unknown quantum state as quantum data input, which are incompatible with current hardware constraints. In this work, we present a QML-based tomography protocol that operates entirely on classical measurement data and is fully executable on noisy intermediate-scale quantum (NISQ) devices. Our approach employs a variational quantum circuit trained to reconstruct quantum states based solely on measurement outcomes. We test the method in simulation, achieving high-fidelity reconstructions of diverse quantum states, including GHZ states, spin chain ground states, and states generated by random circuits. The protocol is then validated on quantum hardware from IBM and IonQ. Additionally, we demonstrate accurate tomography is possible using incomplete measurement bases, a crucial step towards scaling up our protocol. Our results in various scenarios illustrate successful state reconstruction with fidelity reaching 90% or higher. To our knowledge, this is the first QML-based tomography scheme that has been implemented on real quantum processors using exclusively classical measurements. This work establishes the feasibility of QML-based tomography on current quantum platforms and offers a scalable pathway for practical quantum state reconstruction.