TY - GEN
T1 - Low-Depth Flag-Style Syndrome Extraction for Small Quantum Error-Correction Codes
AU - Bhatnagar, Dhruv
AU - Steinberg, Matthew
AU - Elkouss, David
AU - Almudever, Carmen
AU - Feld, Sebastian
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - quantum-error correction
KW - stabilizer codes
KW - flag fault tolerance
KW - syndrome extraction
KW - quantum computing
UR - http://www.scopus.com/inward/record.url?scp=85180010826&partnerID=8YFLogxK
U2 - 10.1109/QCE57702.2023.00016
DO - 10.1109/QCE57702.2023.00016
M3 - Conference contribution
SN - 979-8-3503-4324-3
T3 - Proceedings - 2023 IEEE International Conference on Quantum Computing and Engineering, QCE 2023
SP - 63
EP - 69
BT - Proceedings - 2023 IEEE International Conference on Quantum Computing and Engineering, QCE 2023
A2 - Muller, Hausi
A2 - Alexev, Yuri
A2 - Delgado, Andrea
A2 - Byrd, Greg
PB - IEEE
T2 - 2023 IEEE International Conference on Quantum Computing and Engineering (QCE)
Y2 - 17 September 2023 through 22 September 2023
ER -