Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction

Abstract

We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation and decoding schemes that effectively convert every circuit-level error into an erasure error, leveraging the cluster state's high threshold against such errors. We find a set of codes for which such a conversion is possible, and study their performance against the standard circuit-level depolarizing model. Our best performing scheme, which is based on a concatenation with a classical code, improves the threshold by $16.5\%$ and decreases the spacetime overhead by $32\%$ compared to the scheme without concatenation, with each scheme subject to a physical error rate of $10^{-3}$ and achieving a logical error rate of $10^{-6}$.

11+3 pages, 9+12 figures

References in corpus (14)

• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological fault-tolerance in cluster state quantum computation
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Topological quantum computing with a very noisy network and local error rates approaching one percent
• Foliated Quantum Codes
• Optimal and Efficient Decoding of Concatenated Quantum Block Codes
• Fault-Tolerant Postselected Quantum Computation: Schemes
• Fault-Tolerant Postselected Quantum Computation: Threshold Analysis
• Implementing Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code
• A local pre-decoder to reduce the bandwidth and latency of quantum error correction
• Techniques for combining fast local decoders with global decoders under circuit-level noise
• Hierarchical decoding to reduce hardware requirements for quantum computing
• Polylog-overhead highly fault-tolerant measurement-based quantum computation: all-Gaussian implementation with Gottesman-Kitaev-Preskill code
• Optimal Bacon-Shor codes

Cited by in corpus (4)

• Mitigating errors in logical qubits
• Classical product code constructions for quantum Calderbank-Shor-Steane codes
• Minimizing readout-induced noise for early fault-tolerant quantum computers
• Fault-tolerant Quantum Error Correction Using a Linear Array of Emitters