Fault-tolerant quantum error correction for Steane’s seven-qubit color code with few or no extra qubits

By Ben W. Reichardt. Quantum Science and Technology, 2018

400 citations recorded by the source corpus.

Steane’s seven-qubit quantum code is a natural choice for fault-tolerance experiments because it is small and just two extra qubits are enough to correct errors. However, the two-qubit error-correction technique, known as ‘flagged’ syndrome extraction, works slowly, measuring only one syndrome at a time. This is a disadvantage in experiments with high qubit rest error rates. We extend the technique to extract multiple syndromes at once, without needing more qubits. Qubits for different syndromes can flag errors in each other. This gives equally fast and more qubit-efficient alternatives to Steane’s error-correction method, and also conforms to planar geometry constraints. We further show that Steane’s code and some others can be error-corrected with no extra qubits, provided there are at least two code blocks. The rough idea is that two seven-qubit codewords can be temporarily joined into a twelve-qubit code, freeing two qubits for flagged syndrome measurement.

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

View Paper: https://www.semanticscholar.org/paper/a76d7dbe1043c08cde3b33b9ef24f1251d40997b

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Citations in the corpus

Demonstration of fault-tolerant universal quantum gate operations (2021, neutral): “α β α β → cos(π/8)|0⟩( |0⟩ + |1⟩) + i sin(π/8)|1⟩( |1⟩ − |0⟩) (10) CY”
Realizing repeated quantum error correction in a distance-three surface code (2021, background): “6(2)%; see Methods and Supplementary Information (section IX).”
A Survey on Quantum Channel Capacities (2018, methodology): “The first,—but yet not complete—definitions of the quantum capacity of the quantum channel can be found in Shor’s work from 1995 [491], in which Shor has introduced a scheme for reducing decoherence in quantum computer memory, and in Schumacher’s articles from one year later [467, 468].”
Logical quantum processor based on reconfigurable atom arrays (2023, methodology): “Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.”
Quantum machine learning: a classical perspective (2017, methodology): “The theory of error correction is reviewed by Preskill [17].”