Stabilizer Formalism for Operator Algebra Quantum Error Correction
We introduce a stabilizer formalism for the general quantum error correction framework called operator algebra quantum error correction (OAQEC), which generalizes Gottesman's formulation for traditional quantum error correcting codes (QEC) and Poulin's for operator quantum error correction...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2024-02-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2024-02-21-1261/pdf/ |
| _version_ | 1797300991067947008 |
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| author | Guillaume Dauphinais David W. Kribs Michael Vasmer |
| author_facet | Guillaume Dauphinais David W. Kribs Michael Vasmer |
| author_sort | Guillaume Dauphinais |
| collection | DOAJ |
| description | We introduce a stabilizer formalism for the general quantum error correction framework called operator algebra quantum error correction (OAQEC), which generalizes Gottesman's formulation for traditional quantum error correcting codes (QEC) and Poulin's for operator quantum error correction and subsystem codes (OQEC). The construction generates hybrid classical-quantum stabilizer codes and we formulate a theorem that fully characterizes the Pauli errors that are correctable for a given code, generalizing the fundamental theorems for the QEC and OQEC stabilizer formalisms. We discover hybrid versions of the Bacon-Shor subsystem codes motivated by the formalism, and we apply the theorem to derive a result that gives the distance of such codes. We show how some recent hybrid subspace code constructions are captured by the formalism, and we also indicate how it extends to qudits. |
| first_indexed | 2024-03-07T23:14:58Z |
| format | Article |
| id | doaj.art-53dcb5210c9c42238e1eea03e32d8ad8 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-07T23:14:58Z |
| publishDate | 2024-02-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-53dcb5210c9c42238e1eea03e32d8ad82024-02-21T13:07:22ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2024-02-018126110.22331/q-2024-02-21-126110.22331/q-2024-02-21-1261Stabilizer Formalism for Operator Algebra Quantum Error CorrectionGuillaume DauphinaisDavid W. KribsMichael VasmerWe introduce a stabilizer formalism for the general quantum error correction framework called operator algebra quantum error correction (OAQEC), which generalizes Gottesman's formulation for traditional quantum error correcting codes (QEC) and Poulin's for operator quantum error correction and subsystem codes (OQEC). The construction generates hybrid classical-quantum stabilizer codes and we formulate a theorem that fully characterizes the Pauli errors that are correctable for a given code, generalizing the fundamental theorems for the QEC and OQEC stabilizer formalisms. We discover hybrid versions of the Bacon-Shor subsystem codes motivated by the formalism, and we apply the theorem to derive a result that gives the distance of such codes. We show how some recent hybrid subspace code constructions are captured by the formalism, and we also indicate how it extends to qudits.https://quantum-journal.org/papers/q-2024-02-21-1261/pdf/ |
| spellingShingle | Guillaume Dauphinais David W. Kribs Michael Vasmer Stabilizer Formalism for Operator Algebra Quantum Error Correction Quantum |
| title | Stabilizer Formalism for Operator Algebra Quantum Error Correction |
| title_full | Stabilizer Formalism for Operator Algebra Quantum Error Correction |
| title_fullStr | Stabilizer Formalism for Operator Algebra Quantum Error Correction |
| title_full_unstemmed | Stabilizer Formalism for Operator Algebra Quantum Error Correction |
| title_short | Stabilizer Formalism for Operator Algebra Quantum Error Correction |
| title_sort | stabilizer formalism for operator algebra quantum error correction |
| url | https://quantum-journal.org/papers/q-2024-02-21-1261/pdf/ |
| work_keys_str_mv | AT guillaumedauphinais stabilizerformalismforoperatoralgebraquantumerrorcorrection AT davidwkribs stabilizerformalismforoperatoralgebraquantumerrorcorrection AT michaelvasmer stabilizerformalismforoperatoralgebraquantumerrorcorrection |