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Pair-cat codes: autonomous error-correction with low-order nonlinearity

Albert, Victor V. and Mundhada, Shantanu O. and Grimm, Alexander and Touzard, Steven and Devoret, Michel H. and Jiang, Liang (2019) Pair-cat codes: autonomous error-correction with low-order nonlinearity. Quantum Science and Technology, 4 (3). Art. No. 035007. ISSN 2058-9565. doi:10.1088/2058-9565/ab1e69.

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We introduce a driven-dissipative two-mode bosonic system whose reservoir causes simultaneous loss of two photons in each mode and whose steady states are superpositions of pair-coherent/Barut-Girardello coherent states. We show how quantum information encoded in a steady-state subspace of this system is exponentially immune to phase drifts (cavity dephasing) in both modes. Additionally, it is possible to protect information from arbitrary photon loss in either (but not simultaneously both) of the modes by continuously monitoring the difference between the expected photon numbers of the logical states. Despite employing more resources, the two-mode scheme enjoys two advantages over its one-mode cat-qubit counterpart with regards to implementation using current circuit QED technology. First, monitoring the photon number difference can be done without turning off the currently implementable dissipative stabilizing process. Second, a lower average photon number per mode is required to enjoy a level of protection at least as good as that of the cat-codes. We discuss circuit QED proposals to stabilize the code states, perform gates, and protect against photon loss via either active syndrome measurement or an autonomous procedure. We introduce quasiprobability distributions allowing us to represent two-mode states of fixed photon number difference in a two-dimensional complex plane, instead of the full four-dimensional two-mode phase space. The two-mode codes are generalized to multiple modes in an extension of the stabilizer formalism to non-diagonalizable stabilizers. The M-mode codes can protect against either arbitrary photon losses in up to M − 1 modes or arbitrary losses and gains in any one mode.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Albert, Victor V.0000-0002-0335-9508
Mundhada, Shantanu O.0000-0002-5952-0743
Grimm, Alexander0000-0002-6247-1145
Jiang, Liang0000-0002-0000-9342
Alternate Title:Multimode cat codes
Additional Information:© 2019 IOP Publishing Ltd. Received 12 December 2018; Accepted 1 May 2019; Published 11 June 2019. The authors thank Mazyar Mirrahimi and Kyungjoo Noh for fruitful discussions. We acknowledge support from 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 No. FA9550-15-1-0015), the Alfred P. Sloan Foundation (BR2013-049), the Packard Foundation (2013-39273), and the Walter Burke Institute for Theoretical Physics at Caltech.
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 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
Air Force Office of Scientific Research (AFOSR)BR2013-049
David and Lucile Packard Foundation2013-39273
Army Research LaboratoryUNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20190207-153140844
Persistent URL:
Official Citation:Victor V Albert et al 2019 Quantum Sci. Technol. 4 035007
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92772
Deposited By: Bonnie Leung
Deposited On:15 Feb 2019 21:06
Last Modified:16 Nov 2021 03:53

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