SWAP Test for an Arbitrary Number of Quantum States

• URL: http://arxiv.org/abs/2110.13261v1
• Date: Mon, 25 Oct 2021 20:53:44 GMT
• Title: SWAP Test for an Arbitrary Number of Quantum States
• Authors: Xavier Gitiaux, Ian Morris, Maria Emelianenko, Mingzhen Tian
• Abstract summary: We develop an algorithm to generalize the quantum SWAP test for an arbitrary number $m$ of quantum states. We construct a quantum circuit able to simultaneously measure overlaps of $m$ arbitrary pure states.
• Score: 4.989480853499916
• License: http://creativecommons.org/licenses/by/4.0/
• 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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