Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Barak, Boaz; Chou, Chi-Ning; Gao, Xun https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-135699
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Spoofing Linear Cross-Entropy Benchmarking in Shallow Quantum Circuits

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Abstract

The linear cross-entropy benchmark (Linear XEB) has been used as a test for procedures simulating quantum circuits. Given a quantum circuit C with n inputs and outputs and purported simulator whose output is distributed according to a distribution p over {0,1}ⁿ, the linear XEB fidelity of the simulator is ℱ_C(p) = 2ⁿ 𝔼_{x ∼ p} q_C(x) -1, where q_C(x) is the probability that x is output from the distribution C |0ⁿ⟩. A trivial simulator (e.g., the uniform distribution) satisfies ℱ_C(p) = 0, while Google’s noisy quantum simulation of a 53-qubit circuit C achieved a fidelity value of (2.24 ±0.21)×10^{-3} (Arute et. al., Nature'19).
In this work we give a classical randomized algorithm that for a given circuit C of depth d with Haar random 2-qubit gates achieves in expectation a fidelity value of Ω(n/L⋅15^{-d}) in running time poly(n,2^L). Here L is the size of the light cone of C: the maximum number of input bits that each output bit depends on. In particular, we obtain a polynomial-time algorithm that achieves large fidelity of ω(1) for depth O(√{log n}) two-dimensional circuits. This is the first such result for two dimensional circuits of super-constant depth. Our results can be considered as an evidence that fooling the linear XEB test might be easier than achieving a full simulation of the quantum circuit.

BibTeX - Entry

@InProceedings{barak_et_al:LIPIcs.ITCS.2021.30,
  author =	{Boaz Barak and Chi-Ning Chou and Xun Gao},
  title =	{{Spoofing Linear Cross-Entropy Benchmarking in Shallow Quantum Circuits}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{30:1--30:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{James R. Lee},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13569},
  URN =		{urn:nbn:de:0030-drops-135699},
  doi =		{10.4230/LIPIcs.ITCS.2021.30},
  annote =	{Keywords: Quantum supremacy, Linear cross-entropy benchmark}
}

Keywords: Quantum supremacy, Linear cross-entropy benchmark
Seminar: 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)
Issue date: 2021
Date of publication: 04.02.2021


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