Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 67, Issue 10, Pages 6644-6652Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2021.3102873
Keywords
Error correction codes; channel models; quantum mechanics
Funding
- QuantERA ERANET Cofund in Quantum Technologies through the European Union's Horizon 2020 Programme by the project Engineering and Physical Sciences Research Council (EPSRC)
- QuantERA ERANET Cofund in Quantum Technologies through the European Union's Horizon 2020 Programme by the project Quantum Code Design and Architectures (QCDA) [EP/M024261/1, EP/R043825/1]
- National University of Singapore (NUS) [R-263-000-E32-133, R-263-000-E32-731]
- National Research Foundation, Prime Minister's Office, Singapore
- Ministry of Education, Singapore
- EPSRC [EP/M024261/1, EP/R043825/1] Funding Source: UKRI
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Quantum codes typically rely on large numbers of degrees of freedom for low error rates, but each additional degree introduces new error mechanisms. Utilizing fewer degrees of freedom can be helpful, one solution is encoding quantum information into bosonic modes. By using multiple modes, good approximate quantum error correction codes can be achieved for Gaussian dephasing and amplitude damping errors of any finite magnitude.
Quantum codes typically rely on large numbers of degrees of freedom to achieve low error rates. However each additional degree of freedom introduces a new set of error mechanisms. Hence minimizing the degrees of freedom that a quantum code utilizes is helpful. One quantum error correction solution is to encode quantum information into one or more bosonic modes. We revisit rotation-invariant bosonic codes, which are supported on Fock states that are gapped by an integer g apart, and the gap g imparts number shift resilience to these codes. Intuitively, since phase operators and number shift operators do not commute, one expects a trade-off between resilience to number-shift and rotation errors. Here, we obtain results pertaining to the non-existence of approximate quantum error correcting g-gapped single-mode bosonic codes with respect to Gaussian dephasing errors. We show that by using arbitrarily many modes, g-gapped multi-mode codes can yield good approximate quantum error correction codes for any finite magnitude of Gaussian dephasing and amplitude damping errors.
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