SWAP test for an arbitrary number of quantum states

We develop a recursive algorithm to generalize the quantum SWAP test for an arbitrary number m of quantum states requiring O ( m ) controlled-swap (CSWAP) gates and O ( log m ) ancillary qubits. We construct a quantum circuit able to simultaneously measure overlaps | ⟨ ϕ i , ϕ j ⟩ | 2 of m arbitrary...

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Bibliographic Details
Published in:Quantum information processing 2022-10, Vol.21 (10), Article 344
Main Authors: Gitiaux, Xavier, Morris, Ian, Emelianenko, Maria, Tian, Mingzhen
Format: Article
Language:English
Subjects:
Data Structures and Information Theory
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
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Summary:We develop a recursive algorithm to generalize the quantum SWAP test for an arbitrary number m of quantum states requiring O ( m ) controlled-swap (CSWAP) gates and O ( log m ) ancillary qubits. We construct a quantum circuit able to simultaneously measure overlaps | ⟨ ϕ i , ϕ j ⟩ | 2 of m arbitrary pure states | ϕ 1 … ϕ m ⟩ . Our construction relies on a pairing unitary that generates a superposition state where every pair of input states is labeled by a basis state formed by the ancillaries. By implementing a simple genetic algorithm, we give numerical evidence indicating that our method of labeling each pair of inputs using CSWAP gates is optimal up to m = 8 . Potential applications of the new circuits in the context of quantum machine learning are discussed.
ISSN:1573-1332
1573-1332
DOI:10.1007/s11128-022-03643-1