Low-depth quantum error correction via three-qubit gates in Rydberg atom arrays

Abstract: Quantum error correction (QEC) requires the execution of deep quantum circuits with large numbers of physical qubits to protect information against errors. Designing protocols that can reduce gate and space-time overheads of QEC is therefore crucial to enable more efficient QEC in near-term experiments. Multiqubit gates offer a natural path towards fast and low-depth stabilizer measurement circuits. However, they typically introduce high-weight correlated errors that can degrade the circuit-level distance, leading to slower scalings of the logical error probabilities. In this work, we show how to realize fast and efficient surface code stabilizer readout using only two $CZ_2$ gates -- instead of four $CZ$ -- while preserving fault tolerance, and provide a blueprint for implementation in Rydberg atom arrays. We derive the time-optimal pulses implementing the gates and perform extensive QEC numerical simulations with leakage errors. Compared to the standard protocol using four $CZ$ gates, our scheme is faster, uses fewer gates and crucially maintains fault tolerance with comparable logical error probabilities. Fault-tolerant generalizations of this scheme to other QEC codes, such as quantum Low-Density Parity-Check codes, are also discussed.