License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2021.5
URN: urn:nbn:de:0030-drops-140001
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14000/
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Prabhu, Prithviraj ; Reichardt, Ben W.

Fault-Tolerant Syndrome Extraction and Cat State Preparation with Fewer Qubits

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LIPIcs-TQC-2021-5.pdf (9 MB)


Abstract

We reduce the extra qubits needed for two fault-tolerant quantum computing protocols: error correction, specifically syndrome bit measurement, and cat state preparation. For fault-tolerant syndrome extraction, we show an exponential reduction in qubit overhead over the previous best protocol. For a weight-w stabilizer, we demonstrate that stabilizer measurement tolerating one fault (distance-three) needs at most ⌈ log₂ w ⌉ + 1 ancillas. If qubits reset quickly, four ancillas suffice. We also study the preparation of cat states, simple yet versatile entangled states. We prove that the overhead needed for distance-three fault tolerance is only logarithmic in the cat state size. These results could be useful both for near-term experiments with a few qubits, and for the general study of the asymptotic resource requirements of syndrome measurement and state preparation.
For 'a' measured flag bits, there are 2^a possible flag patterns that can identify faults. Hence our results come from solving a combinatorial problem: the construction of maximal-length paths in the a-dimensional hypercube, corresponding to maximal-weight stabilizers or maximal-weight cat states.

BibTeX - Entry

@InProceedings{prabhu_et_al:LIPIcs.TQC.2021.5,
  author =	{Prabhu, Prithviraj and Reichardt, Ben W.},
  title =	{{Fault-Tolerant Syndrome Extraction and Cat State Preparation with Fewer Qubits}},
  booktitle =	{16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)},
  pages =	{5:1--5:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-198-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{197},
  editor =	{Hsieh, Min-Hsiu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14000},
  URN =		{urn:nbn:de:0030-drops-140001},
  doi =		{10.4230/LIPIcs.TQC.2021.5},
  annote =	{Keywords: Quantum error correction, fault tolerance, quantum state preparation, combinatorics}
}

Keywords: Quantum error correction, fault tolerance, quantum state preparation, combinatorics
Collection: 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)
Issue Date: 2021
Date of publication: 22.06.2021


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