Low-Depth Flag-Style Syndrome Extraction for Small Quantum Error-Correction Codes

Flag-style fault-tolerance has become a linchpin in the realization of small fault-tolerant quantum-error correction experiments. The flag protocol's utility hinges on low qubit over-head, which is typically much smaller than in other approaches. However, as in most fault-tolerance protocols, t...

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Bibliographic Details
Published in2023 IEEE International Conference on Quantum Computing and Engineering (QCE) Vol. 1; pp. 63 - 69
Main Authors Bhatnagar, Dhruv, Steinberg, Matthew, Elkouss, David, Almudever, Carmen G., Feld, Sebastian
Format Conference Proceeding
LanguageEnglish
Published IEEE 17.09.2023
Subjects
Fault tolerance
Fault tolerant systems
flag fault tolerance
Logic gates
Measurement uncertainty
Protocols
quantum computing
quantum-error correction
Qubit
stabilizer codes
syndrome extraction
Systematics
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DOI10.1109/QCE57702.2023.00016

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Summary:Flag-style fault-tolerance has become a linchpin in the realization of small fault-tolerant quantum-error correction experiments. The flag protocol's utility hinges on low qubit over-head, which is typically much smaller than in other approaches. However, as in most fault-tolerance protocols, the advantages of flag-style error correction come with a tradeoff: fault tolerance can be guaranteed, but such protocols involve high-depth circuits, due to the need for repeated stabilizer measurements. Here, we demonstrate that a dynamic choice of stabilizer measurements, based on past syndromes, and the utilization of elements from the full stabilizer group, leads to flag protocols with lower-depth syndrome-extraction circuits for the [[5], [1], [3]] code, as well as for the Steane code when compared to the standard methods in flag fault tolerance. We methodically prove that our new protocols yield fault-tolerant lookup tables, and demonstrate them with a pseudothreshold simulation, showcasing large improvements for all protocols when compared to previously-established methods. This work opens the dialogue on exploiting the properties of the full stabilizer group for reducing circuit overhead in fault-tolerant quantum-error correction.
DOI:10.1109/QCE57702.2023.00016