SWAP Test for an Arbitrary Number of Quantum States

Gitiaux, Xavier; Morris, Ian; Emelianenko, Maria; Tian, Mingzhen

doi:10.48550/arxiv.2110.13261

Cited by 2 publications

(2 citation statements)

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“…In order to obtain the overlap | φ i | φ j | 2 between arbitrary two states |φ i , |φ j (i, j = 1, 2, ..., m; i = j), there is a trivial solution which requires n(n−1) 2 Swap Tests and n(n−1) 2 ancillary qubits. In [21], X. Gitiaux In this paper, following the idea of [21], we design a new circuit U 4 with two ancillaries, two controlled-swap(CSWAP) gates , and two simple Swap Test.…”

Section: Introductionmentioning

confidence: 99%

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Multi-state Swap Test Algorithm

Li¹,

Yin²,

Wang³

et al. 2022

Preprint

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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 |φ 1 ...φ n 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 | φ i |φ j | 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.

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Section: Introductionmentioning

confidence: 99%

“…In [21], X. Gitiaux In this paper, following the idea of [21], we design a new circuit U 4 with two ancillaries, two controlled-swap(CSWAP) gates , and two simple Swap Test. We also present two rules to swap four groups of quantum states.…”

Section: Introductionmentioning

confidence: 99%