2020
DOI: 10.1109/tit.2019.2956142
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Permutation-Invariant Constant-Excitation Quantum Codes for Amplitude Damping

Abstract: The increasing interest in using quantum error correcting codes in practical devices has heightened the need for designing quantum error correcting codes that can correct against specialized errors, such as that of amplitude damping errors which model photon loss. Although considerable research has been devoted to quantum error correcting codes for amplitude damping, not so much attention has been paid to having these codes simultaneously lie within the decoherence free subspace of their underlying physical sy… Show more

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Cited by 34 publications
(27 citation statements)
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“…It is easy to see that the eigenspaces of H are spanned by states |x 1 ⊗· · ·⊗|x N with a constant total excitation number. Schemes based on such constant-excitation subspaces have also recently been studied [6,7].…”
Section: Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…It is easy to see that the eigenspaces of H are spanned by states |x 1 ⊗· · ·⊗|x N with a constant total excitation number. Schemes based on such constant-excitation subspaces have also recently been studied [6,7].…”
Section: Resultsmentioning
confidence: 99%
“…Spurious phase errors that would have resulted from the natural dynamics of the system's evolution can thereby be intrinsically avoided. Such encodings into DFSs have been explored both in the context of quantum computation [1][2][3] and quantum error correction [4][5][6][7]. Combined with carefully tailored active control on the underlying physical system [8,9], decoherence can be substantially mitigated.…”
Section: Introductionmentioning
confidence: 99%
“…Together constructions on permutation-invariant quantum codes [14,15], this implies the existence of quantum codes that correct separable insertions. Broad range of permutation-invariant quantum codes [14,18,19] could be advantageous to use both in quantum storage [17] and quantum metrology [20] when both insertions and deletions occur. is supported in part by NUS startup grants (R-263-000-E32-133 and R-263-000-E32-731), and the National Research Foundation, Prime Minister's Office, Singapore and the Ministry of Education, Singapore under the Research Centres of Excellence programme.…”
Section: Discussionmentioning
confidence: 99%
“…Permutation-invariant quantum codes are quantum codes that are invariant under any permutation of their underlying particles. Such codes have been studied in the qubit [22], [23], [20], [24], the qudit [25], and the bosonic [26] settings. These quantum codes are interesting because of not only their capability to correct non-trivial errors such as quantum deletions [27], [28] and insertions [29], but also their potential applications as quantum memories [30] and for robust quantum metrology [31].…”
Section: B Linear Programming Bounds For Permutation-invariant Quantu...mentioning
confidence: 99%