Multi-state Swap Test Algorithm
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 we designed
a recursive quantum circuit to measure overlaps of multiple quantum states
$|\phi_1...\phi_n\rangle$ concurrently with $O(n\log n)$ controlled-swap
(CSWAP) gates and $O(\log n)$ ancillary qubits. This circuit enables us to get
all pairwise overlaps among input quantum states
$|\langle\phi_i|\phi_j\rangle|^2$. Compared with existing schemes for measuring
the overlap of multiple quantum states, our scheme provides higher precision
and less consumption of ancillary qubits. In addition, we performed simulation
experiments on IBM quantum cloud platform to verify the superiority of the
scheme.
Wen Liu Han-Wen Yin Zhi-Rao Wang Wen-Qin Fan