2026-07-22T01:29:22Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:9255 2024-03-06T10:43:48Z ddc:004 open_access

Two-qubit Stabilizer Circuits with Recovery II: Analysis van Dam, Wim Wong, Raymond stabilizer circuit recovery circuit magic state We study stabilizer circuits that use non-stabilizer qubits and Z-measurements to produce other non-stabilizer qubits. These productions are successful when the correct measurement outcome occurs, but when the opposite outcome is observed, the non-stabilizer input qubit is potentially destroyed. In preceding work [arXiv:1803.06081 (2018)] we introduced protocols able to recreate the expensive non-stabilizer input qubit when the two-qubit stabilizer circuit has an unsuccessful measurement outcome. Such protocols potentially allow a deep computation to recover from such failed measurements without the need to repeat the whole prior computation. Possible complications arise when the recovery protocol itself suffers from a failed measurement. To deal with this, we need to use nested recovery protocols. Here we give a precise analysis of the potential advantage of such recovery protocols as we examine its optimal nesting depth. We show that if the expensive input qubit has cost d, then typically a depth O(log d) recovery protocol is optimal, while a certain special case has optimal depth O(sqrt{d}). We also show that the recovery protocol can achieve a cost reduction by a factor of at most two over circuits that do not use recovery. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Wim van Dam and Raymond Wong 2018 Is Part Of LIPIcs, Volume 111, 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TQC.2018.8 urn:nbn:de:0030-drops-92551 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2018.8 eng https://creativecommons.org/licenses/by/3.0/legalcode