Outcome determinism in measurement-based quantum computation with qudits
In measurement-based quantum computing (MBQC), computation is carried out by a sequence of measurements and corrections on an entangled state. Flow, and related concepts, are powerful techniques for characterising the dependence of the corrections on previous measurement outcomes. We introduce flow-...
| Prif Awduron: | , , , , |
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| Fformat: | Journal article |
| Iaith: | English |
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IOP Publishing
2023
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| _version_ | 1826312936442822656 |
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| author | Booth, RI Kissinger, A Markham, D Meignant, C Perdrix, S |
| author_facet | Booth, RI Kissinger, A Markham, D Meignant, C Perdrix, S |
| author_sort | Booth, RI |
| collection | OXFORD |
| description | In measurement-based quantum computing (MBQC), computation is carried out by a sequence of measurements and corrections on an entangled state. Flow, and related concepts, are powerful techniques for characterising the dependence of the corrections on previous measurement outcomes. We introduce flow-based methods for MBQC with qudit graph states, which we call Z d -flow, when the local dimension is an odd prime. Our main results are a proof that Z d -flow is a necessary and sufficient condition for a strong form of outcome determinism. Along the way, we find a suitable generalisation of the concept of measurement planes to this setting and characterise the allowed measurements in a qudit MBQC. We also provide a polynomial-time algorithm for finding an optimal Z d -flow whenever one exists. |
| first_indexed | 2024-09-25T04:03:07Z |
| format | Journal article |
| id | oxford-uuid:216a67bb-587c-4f21-9e72-06cf16e1783f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:03:07Z |
| publishDate | 2023 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | oxford-uuid:216a67bb-587c-4f21-9e72-06cf16e1783f2024-05-09T13:58:01ZOutcome determinism in measurement-based quantum computation with quditsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:216a67bb-587c-4f21-9e72-06cf16e1783fEnglishSymplectic ElementsIOP Publishing2023Booth, RIKissinger, AMarkham, DMeignant, CPerdrix, SIn measurement-based quantum computing (MBQC), computation is carried out by a sequence of measurements and corrections on an entangled state. Flow, and related concepts, are powerful techniques for characterising the dependence of the corrections on previous measurement outcomes. We introduce flow-based methods for MBQC with qudit graph states, which we call Z d -flow, when the local dimension is an odd prime. Our main results are a proof that Z d -flow is a necessary and sufficient condition for a strong form of outcome determinism. Along the way, we find a suitable generalisation of the concept of measurement planes to this setting and characterise the allowed measurements in a qudit MBQC. We also provide a polynomial-time algorithm for finding an optimal Z d -flow whenever one exists. |
| spellingShingle | Booth, RI Kissinger, A Markham, D Meignant, C Perdrix, S Outcome determinism in measurement-based quantum computation with qudits |
| title | Outcome determinism in measurement-based quantum computation with qudits |
| title_full | Outcome determinism in measurement-based quantum computation with qudits |
| title_fullStr | Outcome determinism in measurement-based quantum computation with qudits |
| title_full_unstemmed | Outcome determinism in measurement-based quantum computation with qudits |
| title_short | Outcome determinism in measurement-based quantum computation with qudits |
| title_sort | outcome determinism in measurement based quantum computation with qudits |
| work_keys_str_mv | AT boothri outcomedeterminisminmeasurementbasedquantumcomputationwithqudits AT kissingera outcomedeterminisminmeasurementbasedquantumcomputationwithqudits AT markhamd outcomedeterminisminmeasurementbasedquantumcomputationwithqudits AT meignantc outcomedeterminisminmeasurementbasedquantumcomputationwithqudits AT perdrixs outcomedeterminisminmeasurementbasedquantumcomputationwithqudits |