International Association for Cryptologic Research (IACR)
Abstract
Quadratic form reduction enjoys broad uses both in classical and quantum algorithms
such as in the celebrated LLL algorithm for lattice reduction. In this paper, we propose the first quantum
circuit for definite binary quadratic form reduction that achieves O(n log n) depth, O(n^2)
width and O(n^2 log(n)) quantum gates. The proposed work is based on a
binary variant of the reduction algorithm of the definite quadratic form. As
side results, we show a quantum circuit performing bit rotation
with O(log n) depth, O(n) width, and O(n log n) gates, in addition to a circuit performing
integer logarithm computation with O(log n) depth, O(n) width, and O(n) gates
