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 singly-controlled $Z$ gates acting simultaneously on two target qubits, i.e. two $CZ_2$ gates -- instead of four $CZ$. We show that this scheme is fault-tolerant, 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 Rydberg decay 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 biased and erasure-dominant noise models, as well as to other QEC codes, such as quantum Low-Density Parity-Check codes, are also discussed.