pyqpanda_alg.QLuoShu.VarModMul

Module Contents

Functions

VarModMul(qvec1, qvec2, qvec3, auxadd, aux, N)

Quantum Circuit of Variant Modular Multiplication for Odd Modulo.

pyqpanda_alg.QLuoShu.VarModMul.VarModMul(qvec1, qvec2, qvec3, auxadd, aux, N)

Quantum Circuit of Variant Modular Multiplication for Odd Modulo.

Parameters:

qvec1 & qvec2 : qlist

the qubits list, holds the integer \(x\) & \(y\)

qvec3 : qlist

store the result \(x*y \mod N\)

auxadd & aux : qubit

an auxiliary qubit for the operation of QAdder and control constant modulo addition

\(N\) : int

the constant modulo

Return:

circuit: pq.QCircuit

The circuit is used to compute modular multiplication that \(|x \rangle|y \rangle|0 \rangle \rightarrow |x \rangle|y \rangle|x*y \mod N \rangle\) and replaces the third input with the result. Modular multiplication can be computed by repeated modular doublings and conditional modular additions. The circuit computes the product \(z=x \cdot y \mod N\) for constant odd integer \(N\) by using a simple expansion of the product along a binary decomposition of the first multiplicand, i.e.,

\(x * y=\sum_{i=0}^{n-1} x_{i} 2^i * y=x_0 y+2(x_1 y+2(x_2 y+...+2(x_{n-2} y+2(x_{n-1} y)) ...))\).

It uses \(3n + 2\) qubits with \(n=\lceil \log_{2}N \rceil\).

Example:

If \(x =7,y=5, N=11\), putting \(x\) held in \(|qvec1\rangle\) and putting \(y\) held in \(|qvec2 \rangle\). By the circuit, the result \(|0010 \rangle\) will be held in the \(|qvec3 \rangle\), i.e., \(7*5 \mod 11=2\).

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

if __name__ == "__main__":
    N = 11
    x = 7
    y = 5
    n = math.ceil(math.log(N, 2))
    qvm = init_quantum_machine(QMachineType.CPU)
    prog = QProg()

    qvec1 = qvm.qAlloc_many(n)
    qvec2 = qvm.qAlloc_many(n)
    qvec3 = qvm.qAlloc_many(n)
    auxadd = qvm.qAlloc()
    aux = qvm.qAlloc_many(1)

    prog << bind_nonnegative_data(x, qvec1) \
         << bind_nonnegative_data(y, qvec2) \
         << VarModMul.VarModMul(qvec1, qvec2, qvec3, auxadd, aux, N)
    result = prob_run_dict(prog, qvec3, 1)

    for key in result:
        print(key + ":" + str(result[key]))
        c = int(key, 2)
    print("%d*%d mod %d=%d" % (x, y, N, c))

0010:1.0000000000000047
7*5 mod 11=2

Note that: N is an odd integer.