Low-Depth Flag-Style Syndrome Extraction for Small Quantum Error-Correction Codes
Dhruv Bhatnagar (Student TU Delft)
Matthew Steinberg (TU Delft - QCD/Feld Group)
David Elkouss (OIST Graduate University)
Carmen Almudever (Technical University of Valencia)
Sebastian Feld (TU Delft - Quantum Circuit Architectures and Technology)
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Abstract
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.
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