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

Parshuram Budhathoki; Rainer Steinwandt

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arXiv · 1401.2437

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

Parshuram Budhathoki·Rainer Steinwandt

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Abstract

Implementing the group arithmetic is a cost-critical task when designing quantum circuits for Shor's algorithm to solve the discrete logarithm problem. We introduce a tool for the automatic generation of addition circuits for ordinary binary elliptic curves, a prominent platform group for digital signatures. Our Python software generates circuit descriptions that, without increasing the number of qubits or T-depth, involve less than 39% of the number of T-gates in the best previous construction. The software also optimizes the (CNOT) depth for GF(2)-linear operations by means of suitable graph colorings.

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BibTeX RIS

Parshuram Budhathoki, Rainer Steinwandt. 2014-01-10. Automatic synthesis of quantum circuits for point addition on ordinary binary elliptic curves. https://arxiv.org/abs/1401.2437

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