Quantum Fourier addition simplified to Toffoli addition

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Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2022-10-27
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Language
en
Pages
6
1-6
Series
Physical Review A, Volume 106, issue 4
Abstract
Quantum addition circuits are considered being of two types: (1) Toffoli-adder circuits which use only classical reversible gates (controlled-not and Toffoli), and (2) QFT-adder circuits based on the quantum Fourier transformation. We present a systematic translation of the QFT addition circuit into a Toffoli-based adder. This result shows that QFT addition has fundamentally the same fault-tolerance cost (e.g., T count) as the most cost-efficient Toffoli adder: instead of using approximate decompositions of the gates from the QFT circuit, it is more efficient to merge gates. In order to achieve this, we formulated circuit identities for multicontrolled gates and apply the identities algorithmically. The employed techniques can be used to automate quantum circuit optimization heuristics.
Description
Funding Information: We thank Daniel Herr for correcting a first version of the circuit transformations. A.P. was supported by a Google Faculty Research Award and a Fulbright Senior Researcher Fellowship. Publisher Copyright: © 2022 American Physical Society.
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Citation
Paler , A 2022 , ' Quantum Fourier addition simplified to Toffoli addition ' , Physical Review A , vol. 106 , no. 4 , 042444 , pp. 1-6 . https://doi.org/10.1103/PhysRevA.106.042444