Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, Garching, Germany
Munich Center for Quantum Science and Technology, Munich, Germany
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Abstract
We propose efficient algorithms for classically simulating fermionic linear optics operations applied to non-Gaussian initial states. By gadget constructions, this provides algorithms for fermionic linear optics with non-Gaussian operations. We argue that this problem is analogous to that of simulating Clifford circuits with non-stabilizer initial states: Algorithms for the latter problem immediately translate to the fermionic setting. Our construction is based on an extension of the covariance matrix formalism which permits to efficiently track relative phases in superpositions of Gaussian states. It yields simulation algorithms with polynomial complexity in the number of fermions, the desired accuracy, and certain quantities capturing the degree of non-Gaussianity of the initial state. We study one such quantity, the fermionic Gaussian extent, and show that it is multiplicative on tensor products when the so-called fermionic Gaussian fidelity is. We establish this property for the tensor product of two arbitrary pure states of four fermions with positive parity.
Multimedia:
QIP24 talk: Classical simulation of non Gaussian fermionic circuits by Beatriz Cardoso Dias
and Quanta magazine feature.
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► References
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Cited by
[1] M. Cerezo, Martin Larocca, Diego García-Martín, N. L. Diaz, Paolo Braccia, Enrico Fontana, Manuel S. Rudolph, Pablo Bermejo, Aroosa Ijaz, Supanut Thanasilp, Eric R. Anschuetz, and Zoë Holmes, “Does provable absence of barren plateaus imply classical simulability? Or, why we need to rethink variational quantum computing”, arXiv:2312.09121, (2023).
[2] Oliver Hahn, Ryuji Takagi, Giulia Ferrini, and Hayata Yamasaki, “Classical simulation and quantum resource theory of non-Gaussian optics”, arXiv:2404.07115, (2024).
[3] Hiroki Hamaguchi, Kou Hamada, and Nobuyuki Yoshioka, “Handbook for Efficiently Quantifying Robustness of Magic”, arXiv:2311.01362, (2023).
[4] Joshua Cudby and Sergii Strelchuk, “Gaussian decomposition of magic states for matchgate computations”, arXiv:2307.12654, (2023).
[5] Michael Zurel, Lawrence Z. Cohen, and Robert Raussendorf, “Simulation of quantum computation with magic states via Jordan-Wigner transformations”, arXiv:2307.16034, (2023).
[6] Beatriz Dias and Robert Koenig, “Classical simulation of non-Gaussian bosonic circuits”, arXiv:2403.19059, (2024).
[7] Mykola Semenyakin, Yevheniia Cheipesh, and Yaroslav Herasymenko, “Classifying fermionic states via many-body correlation measures”, arXiv:2309.07956, (2023).
[8] Vsevolod I. Yashin and Maria A. Elovenkova, “Characterization of non-adaptive Clifford channels”, arXiv:2311.06133, (2023).
The above citations are from SAO/NASA ADS (last updated successfully 2024-05-21 15:47:39). 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 2024-05-21 15:47:37: Could not fetch cited-by data for 10.22331/q-2024-05-21-1350 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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