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arXiv · 2110.13261

SWAP Test for an Arbitrary Number of Quantum States

Xavier Gitiaux·Ian Morris·Maria Emelianenko·Mingzhen Tian
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Abstract

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 of $m$ arbitrary pure states. Our construction relies on a pairing unitary that generates a superposition state where every pair of input states is labelled by a basis state formed by the ancillaries.

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Xavier Gitiaux, Ian Morris, Maria Emelianenko, Mingzhen Tian. 2021-10-25. SWAP Test for an Arbitrary Number of Quantum States. https://arxiv.org/abs/2110.13261

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