Automatic synthesis of quantum circuits for point addition on ordinary binary elliptic curves

Automatic synthesis of quantum circuits for point addition on ordinary binary elliptic curves When designing quantum circuits for Shor’s algorithm to solve the discrete logarithm problem, implementing the group arithmetic is a cost-critical task. We introduce a software tool for the automatic generation of addition circuits for ordinary binary elliptic curves, a prominent platform group for digital signatures. The resulting circuits reduce the number of $$T$$ T -gates by a factor $$13/5$$ 13 / 5 compared to the best previous construction, without increasing the number of qubits or $$T$$ T -depth. The software also optimizes the (CNOT) depth for $${\mathbb F}_2$$ F 2 -linear operations by means of suitable graph colorings. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Automatic synthesis of quantum circuits for point addition on ordinary binary elliptic curves

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Publisher
Springer US
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-014-0851-6
Publisher site
See Article on Publisher Site

Abstract

When designing quantum circuits for Shor’s algorithm to solve the discrete logarithm problem, implementing the group arithmetic is a cost-critical task. We introduce a software tool for the automatic generation of addition circuits for ordinary binary elliptic curves, a prominent platform group for digital signatures. The resulting circuits reduce the number of $$T$$ T -gates by a factor $$13/5$$ 13 / 5 compared to the best previous construction, without increasing the number of qubits or $$T$$ T -depth. The software also optimizes the (CNOT) depth for $${\mathbb F}_2$$ F 2 -linear operations by means of suitable graph colorings.

Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 18, 2014

References

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