Low-distance Surface Codes under Realistic Quantum Noise

By Yu Tomita, Krysta Marie Svore. arXiv.org, 2014

327 citations recorded by the source corpus.

We study the performance of distance-three surface code layouts under realistic multi-parameter noise models. We first calculate their thresholds under depolarizing noise. We then compare a Pauli-twirl approximation of amplitude and phase damping to amplitude and phase damping. We find the approximate channel results in a pessimistic estimate of the logical error rate, indicating the realistic threshold may be higher than previously estimated. From Monte-Carlo simulations, we identify experimental parameters for which these layouts admit reliable computation. Due to its low resource cost and superior performance, we conclude that the 17-qubit layout should be targeted in early experimental implementations of the surface code. We find that architectures with gate times in the 5-40 ns range and T1 times of at least 1-2 us range will exhibit improved logical error rates with a 17-qubit surface code encoding.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/f6fc40a3ef1763a86b71a6b9c60e755c94314918

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Citations in the corpus

Fault-tolerant quantum error correction for Steane’s seven-qubit color code with few or no extra qubits (2018, background): “Since the complete graph K4 has a length-three cycle, joining the [[19, 1, 5]] color code blocks along it will give only a distance-three, [[28, 4, 3]], code.”
Realizing repeated quantum error correction in a distance-three surface code (2021, methodology): “To ensure that such correlated two-qubit Ẑ or X̂ errors do not result in logical errors in the decoding process, we choose the last two CZ gates of each of the Ŝ (Ŝ) measurements to involve data qubits which are not aligned parallel to the data-qubit strings forming the logical operators ẐL (X̂L) [2”
Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code (2019, methodology): “[39] Y.”
Suppressing quantum errors by scaling a surface code logical qubit (2022, unknown): “This is a quantum trajectories simulation [73, 74], meaning that each experimental sample corresponds to propagating the noisy evolution of the full quantum state vector.”
Quantum information processing with superconducting circuits: a review (2016, methodology): “TU Delft is pres ently developing and testing a scalable architecture [31] for executing the errorcorrection cycle of a monolithic surface code fabric (Surface17 [383]), composed of fastfluxtunable transmon qubits with nearestneighbor coupling.”