DQCode: Fault-Tolerant Zero State Preparation for Small qLDPC Codes on Near-Term Distributed Quantum Architectures
T.J. Neumann (TU Delft - Applied Sciences)
S. Feld – Mentor (TU Delft - QCD/Feld Group)
L.P. Prielinger – Mentor (TU Delft - QID/Vardoyan Group)
T.J. Coopmans – Graduation committee member (TU Delft - QCD/Coopmans Group)
M.F. Russ – Graduation committee member (TU Delft - QCD/Rimbach-Russ)
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Abstract
The intersection of Quantum Error Correction (QEC) and Distributed Quantum Computing (DQC) promises a pathway to scalable fault-tolerant quantum computing; in particular, qLDPC codes and Type-II architectures both constitute candidates for near-term implementations. In this work, we introduce DQCode for optimised fault-tolerant logical zero state preparation of the Trivariate Bicycle-[[12, 2, 3]] and Bivariate Bicycle-[[18, 4, 4]] qLDPC codes on distributed Type-II quantum systems.
Based on a QEC cycle-aware qubit mapping, we use a Genetic Algorithm to discover state preparation circuits with optimised telegate counts. Combined with verification circuits for post-selection of runs, this enables efficient fault-tolerant state encoding, which we simulate with open-source Julia software in a realistic DQC setting under circuit-level and Bell pair initialisation noise. Across codes and distributed architectures, we obtain approximately quadratic scaling of the logical initialisation error rate (LIER) with respect to the physical error rate p under suitable conditions, matching theoretical expectation. Furthermore, we find pseudothresholds of approximately 10-4 and 10-5 for the Trivariate and Bivariate Bicycle codes, respectively, below which the LIER outperforms p for sufficiently high remote-entanglement fidelities. Despite noise floors for very small p, all systems tolerate remote entanglement being noisier than local operations at the identified thresholds, while maintaining high post-selection acceptance rates.
Assuming improvements of DQC candidate platforms, our results indicate the near-term viability of encoding small qLDPC codes on Type-II architectures. By providing circuits for proof-of-principle experiments of small-scale instances, we expect our work to benefit the benchmarking of early near-term distributed systems.
Related dataset 4TU.ResearchData:
https://doi.org/10.4121/8543d5ea-2ae8-4af2-84dd-4364799e9b7a
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