Low-distance Surface Codes under Realistic Quantum Noise

Abstract

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.

15 pages, 15 figures, 4 tables, comments welcome

References in corpus (10)

• Surface codes: Towards practical large-scale quantum computation
• Quantum computing with trapped ions
• Fault-tolerant quantum computation with high threshold in two dimensions
• High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
• Local Fault-tolerant Quantum Computation
• Surface code with decoherence: An analysis of three superconducting architectures
• Two-dimensional cavity grid for scalable quantum computation with superconducting circuits
• Approximation of real error channels by Clifford channels and Pauli measurements

Cited by in corpus (8)

• Detecting bit-flip errors in a logical qubit using stabilizer measurements
• Robust two-qubit gates in a linear ion crystal using a frequency-modulated driving force
• Comparison of a quantum error correction threshold for exact and approximate errors
• Fault-tolerance thresholds for the surface code with fabrication errors
• QVECTOR: an algorithm for device-tailored quantum error correction
• Measurement-free implementations of small-scale surface codes for quantum dot qubits
• Generalized surface codes and packing of logical qubits
• Error correcting power of small topological codes