A FaultTolerant Honeycomb Memory
Abstract
Recently, Hastings & Haah introduced a quantum memory defined on the honeycomb lattice. Remarkably, this honeycomb code assembles weightsix parity checks using only twolocal measurements. The sparse connectivity and twolocal measurements are desirable features for certain hardware, while the weightsix parity checks enable robust performance in the circuit model. In this work, we quantify the robustness of logical qubits preserved by the honeycomb code using a correlated minimumweight perfectmatching decoder. Using Monte Carlo sampling, we estimate the honeycomb code's threshold in different error models, and project how efficiently it can reach the "teraquop regime" where trillions of quantum logical operations can be executed reliably. We perform the same estimates for the rotated surface code, and find a threshold of $0.2\%0.3\%$ for the honeycomb code compared to a threshold of $0.5\%0.7\%$ for the surface code in a controllednot circuit model. In a circuit model with native twobody measurements, the honeycomb code achieves a threshold of $1.5\% < p <2.0\%$, where $p$ is the collective error rate of the twobody measurement gate  including both measurement and correlated data depolarization error processes. With such gates at a physical error rate of $10^{3}$, we project that the honeycomb code can reach the teraquop regime with only $600$ physical qubits.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.10457
 Bibcode:
 2021arXiv210810457G
 Keywords:

 Quantum Physics
 EPrint:
 17 pages, 10 figures, 2 tables