Hyperbolic and semi-hyperbolic surface codes for quantum storage

Nikolas P. Breuckmann*, Christophe Vuillot, Earl Campbell, Anirudh Krishna, Barbara M. Terhal

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

43 Citations (Scopus)


We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3%for the {4, 5}-hyperbolic surface code in a phenomenological noise model (as compared with 2.9% for the toric code). In this code family, parity checks are of weight 4 and 5, while each qubit participates in four different parity checks. We introduce a family of semi-hyperbolic codes that interpolate between the toric code and the {4, 5}-hyperbolic surface code in terms of encoding rate and threshold. We show how these hyperbolic codes outperform the toric code in terms of qubit overhead for a target logical error probability. We show how Dehn twists and lattice code surgery can be used to read and write individual qubits to this quantum storage medium.

Original languageEnglish
Article number035007
JournalQuantum Science and Technology
Issue number3
Publication statusPublished - Sept 2017

Bibliographical note

Funding Information:
We thank Kasper Duivenvoorden and Michael Kastoryano for fruitful discussions. BMT, NB and CV acknowledge support through the EU via the ERC GRANT EQEC (No. 682726), CV also acknowledges support by the Excellence Initiative of DFG and ETC is supported by the EPSRC (EP/M024261/1). AK would like to thank the IQI and RWTH Aachen University for their hospitality during his stay.

Publisher Copyright:
© 2017 IOP Publishing Ltd.


  • quantum codes
  • quantum error correction
  • quantum fault-tolerance


Dive into the research topics of 'Hyperbolic and semi-hyperbolic surface codes for quantum storage'. Together they form a unique fingerprint.

Cite this