Empirical Sample Complexity Of Neural Network Mixed State Reconstruction

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Haimeng Zhao^1,2,3, Giuseppe Carleo^1,2, and Filippo Vicentini^1,2,4,5

¹Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
²Center for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
³Zhili College, Tsinghua University, Beijing 100084, China
⁴CPHT, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
⁵Collège de France, Université PSL, 11 place Marcelin Berthelot, 75005 Paris, France

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Abstract

Quantum state reconstruction using Neural Quantum States has been proposed as a viable tool to reduce quantum shot complexity in practical applications, and its advantage over competing techniques has been shown in numerical experiments focusing mainly on the noiseless case. In this work, we numerically investigate the performance of different quantum state reconstruction techniques for mixed states: the finite-temperature Ising model. We show how to systematically reduce the quantum resource requirement of the algorithms by applying variance reduction techniques. Then, we compare the two leading neural quantum state encodings of the state, namely, the Neural Density Operator and the positive operator-valued measurement representation, and illustrate their different performance as the mixedness of the target state varies. We find that certain encodings are more efficient in different regimes of mixedness and point out the need for designing more efficient encodings in terms of both classical and quantum resources.

Featured image: Sample complexity dependence on the reconstruction error with different temperature and NQS ansatze.

Popular summary

Quantum state reconstruction using Neural Quantum States (NQS) is an efficient way to characterize quantum systems based on measurement data collected from experiments. It has found wide applications in quantum metrology, bechmarking, verification, and error mitigation. In this work, we numerically investigate how its performance depends on the mixedness of the target states. We propose a variance reduction technique that can reduce the quantum resource requirement of these algorithms. Through this investigation, we shed some light on how different classes of mixed NQS ansatze perform, which is of interest not only for state reconstruction but also for finite-temperature and non-equilibrium simulations. Our work paves the way towards the design of more efficient encodings in terms of both classical and quantum resources.

► BibTeX data

@article{Zhao2024empiricalsample, doi = {10.22331/q-2024-05-23-1358}, url = {https://doi.org/10.22331/q-2024-05-23-1358}, title = {Empirical {S}ample {C}omplexity of {N}eural {N}etwork {M}ixed {S}tate {R}econstruction}, author = {Zhao, Haimeng and Carleo, Giuseppe and Vicentini, Filippo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {8}, pages = {1358}, month = may, year = {2024} }

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Cited by

[1] Hannah Lange, Anka Van de Walle, Atiye Abedinnia, and Annabelle Bohrdt, “From Architectures to Applications: A Review of Neural Quantum States”, arXiv:2402.09402, (2024).

[2] Hsin-Yuan Huang, John Preskill, and Mehdi Soleimanifar, “Certifying almost all quantum states with few single-qubit measurements”, arXiv:2404.07281, (2024).

[3] Adriano Macarone Palmieri, Guillem Müller-Rigat, Anubhav Kumar Srivastava, Maciej Lewenstein, Grzegorz Rajchel-Mieldzioć, and Marcin Płodzień, “Enhancing quantum state tomography via resource-efficient attention-based neural networks”, arXiv:2309.10616, (2023).

[4] Johannes Mellak, Enrico Arrigoni, and Wolfgang von der Linden, “Deep Neural Networks as Variational Solutions for Correlated Open Quantum Systems”, arXiv:2401.14179, (2024).

[5] Adriano Macarone-Palmieri, Leonardo Zambrano, Maciej Lewenstein, Antonio Acin, and Donato Farina, “Deep Neural Network-assisted improvement of quantum compressed sensing tomography”, arXiv:2405.10052, (2024).

The above citations are from SAO/NASA ADS (last updated successfully 2024-05-23 14:41:51). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2024-05-23 14:41:50: Could not fetch cited-by data for 10.22331/q-2024-05-23-1358 from Crossref. This is normal if the DOI was registered recently.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2024-05-23-1358/

Time Stamp: May 23, 2024

Time Stamp: Jun 27, 2022

Empirical Sample Complexity of Neural Network Mixed State Reconstruction

Republished By Plato

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