https://doi.org/10.1140/epjqt/s40507-024-00259-5
Research
Quantum multi-state Swap Test: an algorithm for estimating overlaps of arbitrary number quantum states
1
State Key Laboratory of Media Convergence and Communication, Communication University of China, Beijing, China
2
School of Computer Science and Cybersecurity, Communication University of China, Beijing, China
3
Key Laboratory of Convergent Media and Intelligent Technology (Communication University of China), Communication University of China, Beijing, China
4
Aero-Engine Research Institute, Beihang University, Beijing, China
Received:
27
December
2022
Accepted:
15
July
2024
Published online:
25
July
2024
Estimating the overlap between two states is an important task with several applications in quantum information. However, the typical swap test circuit can only measure a sole pair of quantum states at a time. In this study, a recursive quantum circuit is designed to measure overlaps of n quantum states 
concurrently with 
controlled-swap(CSWAP) gates and 
ancillary qubits, where 
. All pairwise overlaps among input quantum states 
can be obtained in this circuit. Compared with existing scheme for measuring the overlap of multiple quantum states, the circuit provides higher precision and less consumption of ancillary qubits. In addition, some simulation experiments are performed on IBM quantum cloud platform to verify the superiority of this algorithm.
Key words: Quantum information / Swap Test / Multiple quantum states / Overlap
© The Author(s) 2024
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