pyqpanda_alg.QLuoShu.q_elliptic_padd

Module Contents

Functions

q_elliptic_padd(p, a, b, P, Q)

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

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

Parameters:

\(p\): int

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

\(a,b\) : int

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

\(P,Q\): vector

represent different points on the elliptic curve \(E/\mathbb{F}_{p}\)

Return:

The quantum states of the \(x-\) coordinate and \(y-\) coordinate of \(P+Q\).

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 \(\mathbb{F}_{p}\) with \(p>3\). The circuit of point addition is constructed by some variant modulo arithmetic and based on classical addition formulas. The circuit is inverse and can be used to compute \(P-Q\).

Example:

If \(E/\mathbb{F}_{11}: y^{2}=x^{3}+7x+9\), \(P =(0,3), Q=(6，5)\), by the function, we can get the quantum state of \(P + Q\), which is \(|1010 \rangle|0001 \rangle\). So, \(P+Q=(10,1)\).

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

if __name__ == "__main__":
    p = 11
    a = 7
    b = 9
    P = [0, 3]
    Q = [6, 5]
    q_elliptic_padd.q_elliptic_padd(p, a, b, P, Q)

The function above would give results:

The elliptic curve：y^{2}=x^{3}+7x+9

P=(0,3)

Q=(6,5)

1010 :1.0000000000000895

0001 :1.0000000000000895

P+Q=(10,1)