2026-07-23T20:32:25Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17532 2024-03-06T10:59:50Z ddc:004 open_access

Quantum Majority Vote Buhrman, Harry Linden, Noah Mančinska, Laura Montanaro, Ashley Ozols, Maris quantum algorithms quantum majority vote Schur-Weyl duality Majority vote is a basic method for amplifying correct outcomes that is widely used in computer science and beyond. While it can amplify the correctness of a quantum device with classical output, the analogous procedure for quantum output is not known. We introduce quantum majority vote as the following task: given a product state |ψ_1⟩ ⊗ … ⊗ |ψ_n⟩ where each qubit is in one of two orthogonal states |ψ⟩ or |ψ^⟂⟩, output the majority state. We show that an optimal algorithm for this problem achieves worst-case fidelity of 1/2 + Θ(1/√n). Under the promise that at least 2/3 of the input qubits are in the majority state, the fidelity increases to 1 - Θ(1/n) and approaches 1 as n increases. We also consider the more general problem of computing any symmetric and equivariant Boolean function f: {0,1}ⁿ → {0,1} in an unknown quantum basis, and show that a generalization of our quantum majority vote algorithm is optimal for this task. The optimal parameters for the generalized algorithm and its worst-case fidelity can be determined by a simple linear program of size O(n). The time complexity of the algorithm is O(n⁴ log n) where n is the number of input qubits. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Harry Buhrman and Noah Linden and Laura Mančinska and Ashley Montanaro and Maris Ozols 2023 Is Part Of LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2023.29 urn:nbn:de:0030-drops-175321 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.29 eng https://creativecommons.org/licenses/by/4.0/legalcode