pyqpanda_alg.QLuoShu.QFTConAdd

Module Contents

Functions

egcd(a, b)	Extended Euclid's Algorithm.
modinv(a, N)	Modulo Inversr Algorithm.
getAngles(a, n)	Get the Array of Phases.
QFTConAdd(a, qvec)	Quantum Circuit of Constant Addition using QFT.

pyqpanda_alg.QLuoShu.QFTConAdd.egcd(a, b)

Extended Euclid’s Algorithm.

Parameters:

\(a\): int

an integer

\(b\): int

an integer

Return:

triples : \((g,x,y)\) satisfying: \(ax+by=g\)

Compute the g.c.d. of the integers \(a\) and \(b\). The returning result is (g, u,v) satisfying \(u*a+v*b=g\).

Example:

from pyqpanda import *
import numpy as np
import math

def egcd(a, b):
    if a == 0:
        return b, 0, 1
    else:
        g, y, x = egcd(b % a, a)
        return g, x - (b // a) * y, y
print(egcd(12,3))

(3, 0, 1)

pyqpanda_alg.QLuoShu.QFTConAdd.modinv(a, N)

Modulo Inversr Algorithm.

Parameters:

\(a\): int

an integer

\(N\): int

an integer

Return:

value: \(a^{-1} \mod N\)

Compute the inverse \(a^{-1} \mod N\).

Example:

def modinv(a, N):
    g, x, y = egcd(a, N)
    if g != 1:
        raise Exception('Waring: Modulo inverse is not exist.')
    else:
        return x % N

print(modinv(3,11))

4

pyqpanda_alg.QLuoShu.QFTConAdd.getAngles(a, n)

Get the Array of Phases.

Parameters:

\(a\): int

an integer expanded in QFT

\(n\): int

represent \(n\) arry with angles of \(a\) expended in QFT

Return:

array

Calculate the array of phases used in the Quantum Fourier transform.

Example:

def getAngles(a, n):
    s = bin(int(a))[2:].zfill(n)
    angles = np.zeros([n])
    for i in range(0, n):
        for j in range(i, n):
            if s[j] == '1':
                angles[n - i - 1] += math.pow(2, -(j - i))
        angles[n - i - 1] *= np.pi
    return angles
print(getAngles(3,5))

[3.14159265 4.71238898 2.35619449 1.17809725 0.58904862]

pyqpanda_alg.QLuoShu.QFTConAdd.QFTConAdd(a, qvec)

Quantum Circuit of Constant Addition using QFT.

Parameters:

\(a\): int

the integer to be added

qvec : qlist

the qubits list

Return:

circuit: pq.QCircuit

The circuit works on one quantum register \(|qvec \rangle\) holding the input integer \(x\) and one phase array from classical computation on a constant integer \(a\) to compute addition using QFT. The circuit is an in-place circuit, where the result of addition is deposited in the register \(|qvec \rangle\). The circuit needs \(n+1\) qubits with \(n=\max\{\lceil \log_{2}a \rceil, \lceil \log_{2}x \rceil\}\). The circuit is invertible, which can compute the subtraction of two integers.

Example:

If \(a =7, x=9\), putting x held in \(|qvec \rangle\). By the circuit, the result \(|10000 \rangle\) will be held in the \(|qvec \rangle\), i.e, \(7+9=16\).

from pyqpanda import *
import numpy as np
import math
from pyqpanda_alg.QLuoShu import QFTConAdd

if __name__ == "__main__":
    qvm = init_quantum_machine(QMachineType.CPU)
    prog = QProg()

    a = 7
    x = 9
    n = max(math.ceil(math.log(x, 2)), math.ceil(math.log(a, 2)))+1
    qvec = qvm.qAlloc_many(n)

    prog << bind_nonnegative_data(x, qvec)\
         << QFTConAdd.QFTConAdd(a, qvec)
    result = prob_run_dict(prog, qvec, 1)

    for key in result:
        print(key + ":" + str(result[key]))
        d = int(key, 2)
    print("%d+%d=%d" % (x,a,d))

10000:1.0000000000000018
9+7=16

Note that: if \(a=x\) and they are a power of 2, we need to make \(n=\lceil \log_{2}a \rceil+2\) in the Example.

Here, we give the circuit graph of the example in the above for the constant addition with 5 qubits:

                                       ┌─┐                 ┌────────────┐   ┌─┐
q_0:  |0>───────■────── ───────■────── ┤H├ X────────────── ┤RZ(1.374447)├ X ┤H├ ─────────■──────── ─────────■──────── >
                │┌─┐    ┌──────┴─────┐ └─┘ │┌────────────┐ └────────────┘ │ └─┘ ┌────────┴───────┐          │┌─┐      >
q_1:  |0>───────┼┤H├─── ┤CR(1.570796)├ X── ┼┤RZ(2.748894)├ X───────────── ┼ ─── ┤CR(1.570796).dag├ ─────────┼┤H├───── >
         ┌──────┴┴─┴──┐ ├────────────┤ │   │└────────────┘ │              │     └────────────────┘ ┌────────┴┴─┴────┐ >
q_2:  |0>┤CR(0.785398)├ ┤RZ(5.497787)├ ┼── ┼────────────── ┼───────────── ┼ ─── ────────────────── ┤CR(0.785398).dag├ >
         └────────────┘ └────────────┘ │   │┌────────────┐ │              │                        └────────────────┘ >
q_3:  |0>────────────── ────────────── X── ┼┤RZ(4.712389)├ X───────────── ┼ ─── ────────────────── ────────────────── >
                                           │└────────────┘ ┌────────────┐ │                                           >
q_4:  |0>────────────── ────────────── ─── X────────────── ┤RZ(3.141593)├ X ─── ────────────────── ────────────────── >
                                                           └────────────┘