Year: 2023
Type: conference-paper
Abstract: 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.
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: New insights in quantum algorithms and complexity, QuantAlgo: Quantum algorithms and applications, G2437637443, Quantum Software Consortium, G2926334671, G420050720, G5025975358, G565383568, EPSRC Hub in Quantum Computing and Simulation, Mathematics of Quantum Algorithms, G7352392636, Quantum Algorithms from Foundations to Applications, Prosperity Partnership in Quantum Software for Modeling and Simulation
OpenAlex ID: W4412254746