pyqpanda_alg.QLuoShu.q_elliptic_pdou

Module Contents

Functions

q_elliptic_pdou(p, a, b, P)

Quantum Circuit for Point Addition of Elliptic Curves over Prime Field (\(p>2\)).
pyqpanda_alg.QLuoShu.q_elliptic_pdou.q_elliptic_pdou(p, a, b, P)

Quantum Circuit for Point Addition of Elliptic Curves over Prime Field (\(p>2\)).

Parameters:

\(p\): int

represents the character of prime field \(\mathbb{F}_{p}\)

\(a,b\) : int

represent an elliptic curve \(E/\mathbb{F}_{p}: y^{2}=x^{3}+ax+b\)

\(P\): vector

represents a point on the elliptic curve \(E/\mathbb{F}_{p}\)

Return:

The quantum states of the \(x-\) coordinate and \(y-\) coordinate of \([2]P\).

The function is used to compute point addition \(P+Q\) with \(P \neq Q\) on elliptic curves \(y^{2}=x^{3}+ax+b\) over finite field \(\mathbb{F}_{p}\) (\(p>2\)). The circuit of point doubling is constructed by some variant modulo arithmetic and based on classical addition formulas.

Example:

If \(E/\mathbb{F}_{11}: y^{2}=x^{3}+7x+9\), \(P =(5,2)\), by the function, we can get the quantum state of \([2]P\), which is \(|0110 \rangle|0101 \rangle\). So, \([2]P=(6,5)\).

from pyqpanda import *
import math
from pyqpanda_alg.QLuoShu import q_elliptic_pdou

if __name__ == "__main__":
    p = 11
    a = 7
    b = 9
    P = [5, 2]
    q_elliptic_pdou.q_elliptic_pdou(p, a, b, P)

The function above would give results:

The elliptic curve：y^{2}=x^{3}+7x+9

P=(5,2)

0110 :1.0000000000000255

0101 :1.0000000000000255

2P=(6,5)