Transversal diagonal logical operators for stabiliser codes
Storing quantum information in a quantum error correction code can protect it from errors, but the ability to transform the stored quantum information in a fault tolerant way is equally important. Logical Pauli group operators can be implemented on Calderbank-Shor-Steane (CSS) codes, a commonly-stud...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/acfc5f |
| _version_ | 1797661265528619008 |
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| author | Mark A Webster Armanda O Quintavalle Stephen D Bartlett |
| author_facet | Mark A Webster Armanda O Quintavalle Stephen D Bartlett |
| author_sort | Mark A Webster |
| collection | DOAJ |
| description | Storing quantum information in a quantum error correction code can protect it from errors, but the ability to transform the stored quantum information in a fault tolerant way is equally important. Logical Pauli group operators can be implemented on Calderbank-Shor-Steane (CSS) codes, a commonly-studied category of codes, by applying a series of physical Pauli X and Z gates. Logical operators of this form are fault-tolerant because each qubit is acted upon by at most one gate, limiting the spread of errors, and are referred to as transversal logical operators. Identifying transversal logical operators outside the Pauli group is less well understood. Pauli operators are the first level of the Clifford hierarchy which is deeply connected to fault-tolerance and universality. In this work, we study transversal logical operators composed of single- and multi-qubit diagonal Clifford hierarchy gates. We demonstrate algorithms for identifying all transversal diagonal logical operators on a CSS code that are more general or have lower computational complexity than previous methods. We also show a method for constructing CSS codes that have a desired diagonal logical Clifford hierarchy operator implemented using single qubit phase gates. Our methods rely on representing operators composed of diagonal Clifford hierarchy gates as diagonal XP operators and this technique may have broader applications. |
| first_indexed | 2024-03-11T18:42:55Z |
| format | Article |
| id | doaj.art-91480f1faac54e88a370d4566b177985 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-11T18:42:55Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-91480f1faac54e88a370d4566b1779852023-10-12T09:31:27ZengIOP PublishingNew Journal of Physics1367-26302023-01-01251010301810.1088/1367-2630/acfc5fTransversal diagonal logical operators for stabiliser codesMark A Webster0https://orcid.org/0000-0002-5300-1643Armanda O Quintavalle1https://orcid.org/0000-0001-5101-5673Stephen D Bartlett2https://orcid.org/0000-0003-4387-670XCentre for Engineered Quantum Systems, School of Physics, University of Sydney , Sydney, NSW 2006, Australia; Sydney Quantum Academy , Sydney, NSW, AustraliaDepartment of Physics and Astronomy, University of Sheffield , Sheffield S3 7RH, United KingdomCentre for Engineered Quantum Systems, School of Physics, University of Sydney , Sydney, NSW 2006, AustraliaStoring quantum information in a quantum error correction code can protect it from errors, but the ability to transform the stored quantum information in a fault tolerant way is equally important. Logical Pauli group operators can be implemented on Calderbank-Shor-Steane (CSS) codes, a commonly-studied category of codes, by applying a series of physical Pauli X and Z gates. Logical operators of this form are fault-tolerant because each qubit is acted upon by at most one gate, limiting the spread of errors, and are referred to as transversal logical operators. Identifying transversal logical operators outside the Pauli group is less well understood. Pauli operators are the first level of the Clifford hierarchy which is deeply connected to fault-tolerance and universality. In this work, we study transversal logical operators composed of single- and multi-qubit diagonal Clifford hierarchy gates. We demonstrate algorithms for identifying all transversal diagonal logical operators on a CSS code that are more general or have lower computational complexity than previous methods. We also show a method for constructing CSS codes that have a desired diagonal logical Clifford hierarchy operator implemented using single qubit phase gates. Our methods rely on representing operators composed of diagonal Clifford hierarchy gates as diagonal XP operators and this technique may have broader applications.https://doi.org/10.1088/1367-2630/acfc5fquantum error correctionquantum computationquantum information |
| spellingShingle | Mark A Webster Armanda O Quintavalle Stephen D Bartlett Transversal diagonal logical operators for stabiliser codes New Journal of Physics quantum error correction quantum computation quantum information |
| title | Transversal diagonal logical operators for stabiliser codes |
| title_full | Transversal diagonal logical operators for stabiliser codes |
| title_fullStr | Transversal diagonal logical operators for stabiliser codes |
| title_full_unstemmed | Transversal diagonal logical operators for stabiliser codes |
| title_short | Transversal diagonal logical operators for stabiliser codes |
| title_sort | transversal diagonal logical operators for stabiliser codes |
| topic | quantum error correction quantum computation quantum information |
| url | https://doi.org/10.1088/1367-2630/acfc5f |
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