A Caltech Library Service

Performance and structure of single-mode bosonic codes

Albert, Victor V. and Noh, Kyungjoo and Duivenvoorden, Kasper and Young, Dylan J. and Brierley, R. T. and Reinhold, Philip and Vuillot, Christophe and Li, Linshu and Shen, Chao and Girvin, S. M. and Terhal, Barbara M. and Jiang, Liang (2018) Performance and structure of single-mode bosonic codes. Physical Review A, 97 (3). Art. No. 032346. ISSN 2469-9926. doi:10.1103/PhysRevA.97.032346.

[img] PDF - Published Version
See Usage Policy.

[img] PDF - Submitted Version
See Usage Policy.

[img] Mathematica Notebook (NB) (Mathematica notebook with numerical code states) - Supplemental Material
See Usage Policy.


Use this Persistent URL to link to this item:


The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat-binomial-GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one- and two-mode binomial as well as multiqubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a multiqudit code.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Albert, Victor V.0000-0002-0335-9508
Noh, Kyungjoo0000-0002-6318-8472
Jiang, Liang0000-0002-0000-9342
Additional Information:© 2018 American Physical Society. Received 16 September 2017; published 30 March 2018. The authors acknowledge Steven T. Flammia, David Poulin, Saikat Guha, Richard Kueng, Mazyar Mirrahimi, John Preskill, R. J. Schoelkopf, Matti Silveri, Murphy Yuezhen Niu, and Bei Zeng for enlightening discussions. V.V.A. thanks Misha Guy and the Yale Center for Research Computing for resources and support and acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech. V.V.A., K.N., C.S., L.L., and L.J. acknowledge support through the ARL-CDQI, ARO (Grants No. W911NF-14-1-0011 and No. W911NF-14-1-0563), ARO MURI (W911NF-16-1-0349), NSF (EFMA-1640959), AFOSR MURI (FA9550-14-1-0052 and FA9550-15-1-0015), the Alfred P. Sloan Foundation (BR2013-049), and the Packard Foundation (2013-39273). K.D., C.V., and B.M.T. acknowledge support through ERC Consolidator Grant No. 682726. S.M.G. acknowledges support through the NSF (DMR-1609326) and ARO (W911NF1410011).
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Army Research LaboratoryUNSPECIFIED
Army Research Office (ARO)W911NF-14-1-0011
Army Research Office (ARO)W911NF-14-1-0563
Army Research Office (ARO)W911NF-16-1-0349
Air Force Office of Scientific Research (AFOSR)FA9550-14-1-0052
Air Force Office of Scientific Research (AFOSR)FA9550-15-1-0015
Alfred P. Sloan FoundationBR2013-049
David and Lucile Packard Foundation2013-39273
European Research Council (ERC)682726
Issue or Number:3
Record Number:CaltechAUTHORS:20180330-091105009
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85523
Deposited By: Tony Diaz
Deposited On:30 Mar 2018 19:30
Last Modified:15 Nov 2021 20:29

Repository Staff Only: item control page