Quantum Majority Vote

Publikation: Bidrag til bog/antologi/rapportKonferenceabstrakt i proceedingsForskningfagfællebedømt


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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.
Titel14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Antal sider1
ForlagSchloss Dagstuhl - Leibniz-Zentrum für Informatik
ISBN (Elektronisk)978-3-95977-263-1
StatusUdgivet - 2023
Begivenhed14th Innovations in Theoretical Computer Science Conference (ITCS 2023) - MIT, Cambridge, MASS, USA
Varighed: 10 jan. 202313 jan. 2023


Konference14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
ByCambridge, MASS
NavnLeibniz International Proceedings in Informatics, LIPIcs

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