Fault-tolerant quantum error correction provides a strategy to protect information processed by aquantum computer against noise which would otherwise corrupt the data. A fault-tolerant universalquantum computer must implement a universal gate set on the logical level in order to perform arbi-trary calculations to in principle unlimited precision. In this manuscript, we characterize the recentdemonstration of a fault-tolerant universal gate set in a trapped-ion quantum computer [Postler etal. Nature 605.7911 (2022)] and identify aspects to improve the design of experimental setups toreach an advantage of logical over physical qubit operation. We show that various criteria to assessthe break-even point for fault-tolerant quantum operations are within reach for the ion trap quan-tum computing architecture under consideration. Furthermore, we analyze the influence of crosstalkin entangling gates for logical state preparation circuits. These circuits can be designed to respectfault tolerance for specific microscopic noise models. We find that an experimentally-informed de-polarizing noise model captures the essential noise dynamics of the fault-tolerant experiment thatwe consider, and crosstalk is negligible in the currently accessible regime of physical error rates. Fordeterministic Pauli state preparation, we provide a fault-tolerant unitary logical qubit initializationcircuit, which can be realized without in-sequence measurement and feed-forward of classical infor-mation. Additionally, we show that non-deterministic state preparation schemes, i.e. repeat untilsuccess, for logical Pauli and magic states perform with higher logical fidelity over their deterministiccounterparts for the current and anticipated future regime of physical error rates. Our results offerguidance on improvements of physical qubit operations and validate the experimentally-informednoise model as a tool to predict logical failure rates in quantum computing architectures based ontrapped ions.

Physical review / A 107(4), 042422 (2023). doi:10.1103/PhysRevA.107.042422

Published by Inst., Woodbury, NY