The small stellated dodecahedron code and friends

Jonathan Conrad; C. Chamberland; N. P. Breuckmann; B. M. Terhal

doi:10.1098/rsta.2017.0323

The small stellated dodecahedron code and friends

Jonathan Conrad, C. Chamberland, N. P. Breuckmann, B. M. Terhal^*

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

17 Citations (Scopus)

Abstract

We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small stellated dodecahedron code can be located on the edges respectively vertices of a small stellated dodecahedron, making this code suitable for threedimensional connectivity. This code encodes eight logical qubits into 30 physical qubits (plus 22 ancilla qubits for parity checkmeasurements) in contrast with one logical qubit into nine physical qubits (plus eight ancilla qubits) for the surface code. We develop faulttolerant parity check circuits and a decoder for this code, allowing us to numerically assess the circuitbased pseudo-threshold. This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.

Original language	English
Article number	20170323
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	376
Issue number	2123
DOIs	https://doi.org/10.1098/rsta.2017.0323
Publication status	Published - 13 Jul 2018

Bibliographical note

Funding Information:
Data accessibility. This article has no additional data. Competing interests. We declare we have no competing interests. Funding. We acknowledge support through the EU via the ERC GRANT EQEC no. 682726. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. C.C. acknowledges the support of NSERC through the PGS D scholarship. Acknowledgements. We thank Kasper Duivenvoorden and Christophe Vuillot for useful discussions. We acknowledge the use of valuable computing time on the RWTH Aachen Compute Cluster. We thank Koen Bertels for quick access to the 4 machines at Computer Engineering TU Delft and Steve Weiss for the use of computing clusters at IQC Waterloo. C.C. acknowledges TU Delft for its hospitality where the work was completed.

Publisher Copyright:
© 2018 Royal Society Publishing. All rights reserved.

Keywords

Fault tolerance
Homological quantum codes
Quantum error correction

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abstract = "We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small stellated dodecahedron code can be located on the edges respectively vertices of a small stellated dodecahedron, making this code suitable for threedimensional connectivity. This code encodes eight logical qubits into 30 physical qubits (plus 22 ancilla qubits for parity checkmeasurements) in contrast with one logical qubit into nine physical qubits (plus eight ancilla qubits) for the surface code. We develop faulttolerant parity check circuits and a decoder for this code, allowing us to numerically assess the circuitbased pseudo-threshold. This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.",

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author = "Jonathan Conrad and C. Chamberland and Breuckmann, {N. P.} and Terhal, {B. M.}",

note = "Funding Information: Data accessibility. This article has no additional data. Competing interests. We declare we have no competing interests. Funding. We acknowledge support through the EU via the ERC GRANT EQEC no. 682726. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. C.C. acknowledges the support of NSERC through the PGS D scholarship. Acknowledgements. We thank Kasper Duivenvoorden and Christophe Vuillot for useful discussions. We acknowledge the use of valuable computing time on the RWTH Aachen Compute Cluster. We thank Koen Bertels for quick access to the 4 machines at Computer Engineering TU Delft and Steve Weiss for the use of computing clusters at IQC Waterloo. C.C. acknowledges TU Delft for its hospitality where the work was completed. Publisher Copyright: {\textcopyright} 2018 Royal Society Publishing. All rights reserved.",

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N2 - We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small stellated dodecahedron code can be located on the edges respectively vertices of a small stellated dodecahedron, making this code suitable for threedimensional connectivity. This code encodes eight logical qubits into 30 physical qubits (plus 22 ancilla qubits for parity checkmeasurements) in contrast with one logical qubit into nine physical qubits (plus eight ancilla qubits) for the surface code. We develop faulttolerant parity check circuits and a decoder for this code, allowing us to numerically assess the circuitbased pseudo-threshold. This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.

AB - We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small stellated dodecahedron code can be located on the edges respectively vertices of a small stellated dodecahedron, making this code suitable for threedimensional connectivity. This code encodes eight logical qubits into 30 physical qubits (plus 22 ancilla qubits for parity checkmeasurements) in contrast with one logical qubit into nine physical qubits (plus eight ancilla qubits) for the surface code. We develop faulttolerant parity check circuits and a decoder for this code, allowing us to numerically assess the circuitbased pseudo-threshold. This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.

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The small stellated dodecahedron code and friends

Abstract

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Keywords

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