前幾天的實驗都是基於無噪音版本的BB84通訊協定，由於現實世界總是會有一些雜訊發生，這在通訊上會產生錯誤。
在無噪音版本的協定中，我們遇到一個錯誤，我們就會立即停止通訊，但這在現實世界是很浪費的事情。
因此我們會再BB84工作流程中加入資訊協調的步驟來實現

資訊協調是 Asja 和 Balvis 之間透過經典通道進行的一種糾錯形式。
目標是修正最終金鑰字串中的錯誤，以確保兩個金鑰相同。
同時，我們需要為 QBER 值設定一定的閾值，這樣即使金鑰字串的某些部分包含錯誤，我們也可以繼續。

下面的程式將加入NoisyChannel來模擬真實環境，NoisyChannel將引入12.5%的錯誤量子位進入通訊中

# import all necessary objects and methods for quantum circuits
from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, execute, Aer
from random import randrange

#Initial source: awards/teach_me_qiskit_2018/cryptography/Cryptography.ipynb

#Code modified to introduce noise in communication channel

def NoisyChannel(qc1, qc2, qc1_name):
    ''' This function takes the output of a circuit qc1 (made up only of x and 
        h gates, simulate noisy quantum channel, where Pauli errors (X - bit flip; Z - phase flip
        will occur in qc2 and then initializes another circuit qc2 with introduce noise.
    ''' 
    
    # Quantum state is retrieved from qasm code of qc1
    qs = qc1.qasm().split(sep=';')[4:-1]

    # Process the code to get the instructions
    for index, instruction in enumerate(qs):
        qs[index] = instruction.lstrip()

     # Parse the instructions and apply to new circuit
    for instruction in qs:
        if instruction[0] == 'x':
            if instruction[5] == '[':
                old_qr = int(instruction[6:-1])
            else:
                old_qr = int(instruction[5:-1])
            qc2.x(qreg[old_qr])
        elif instruction[0] == 'h':
            if instruction[5] == '[':
                old_qr = int(instruction[6:-1])
            else:
                old_qr = int(instruction[5:-1])
            qc2.h(qreg[old_qr])
        elif instruction[0] == 'm': # exclude measuring:
            pass
        else:
            raise Exception('Unable to parse instruction')
    
    ### Introducing noise
    for instruction in qs:
        if randrange(7)<1:
            if instruction[5] == '[':
                old_qr = int(instruction[6:-1])
            else:
                old_qr = int(instruction[5:-1])
            qc2.x(qreg[old_qr]) #apply bit-flip error
        if randrange(7)<1:
            if instruction[5] == '[':
                old_qr = int(instruction[6:-1])
            else:
                old_qr = int(instruction[5:-1])
            qc2.z(qreg[old_qr]) #apply phase-flip error

下面將NoisyChannel引入Sifting和QBER

def print_outcomes_in_reserve(counts): # takes a dictionary variable
    for outcome in counts: # for each key-value in dictionary
        reverse_outcome = ''
        for i in outcome: # each string can be considered as a list of characters
            reverse_outcome = i + reverse_outcome # each new symbol comes before the old symbol(s)
    return reverse_outcome    

qreg = QuantumRegister(16) # quantum register with 16 qubits
creg = ClassicalRegister(16) # classical register with 16 bits

send=[] #Initial bit string to send
asja_basis=[] #Register to save information about encoding basis
balvis_basis=[] #Register to save information about decoding basis

#Asja
asja = QuantumCircuit(qreg, creg, name='Asja')

for i in range(16):
    bit = randrange(2)
    send.append(bit)
    
for i, n in enumerate(send):
    if n==1: asja.x(qreg[i]) # apply x-gate
        
for i in range(16):
    r=randrange(2) #Asja randomly pick a basis
    if r==0: #if bit is 0, then she encodes in Z basis
        asja_basis.append('Z')
    else: #if bit is 1, then she encodes in X basis
        asja.h(qreg[i])
        asja_basis.append('X')

balvis = QuantumCircuit(qreg, creg, name='Balvis') #Defining Balvis circuit
NoisyChannel(asja, balvis, 'Asja') #Asja sends noisy states to Balvis

#Balvis 
for i in range(16):
    r=randrange(2) #Balvis randomly pick a basis
    if r==0: #if bit is 0, then measures in Z basis
        balvis.measure(qreg[i],creg[i])
        balvis_basis.append('Z')
    else: #if bit is 1, then measures in X basis
        balvis.h(qreg[i])
        balvis.measure(qreg[i],creg[i])
        balvis_basis.append('X')

job = execute(balvis,Aer.get_backend('qasm_simulator'),shots=1)
counts = job.result().get_counts(balvis)
counts = print_outcomes_in_reserve(counts)
received = list(map(int, counts))


#Sifting
asja_key=[] #Asjas register for matching rounds
balvis_key=[] #Balvis register for matching rounds
for j in range(0,len(asja_basis)): #Going through list of bases 
    if asja_basis[j] == balvis_basis[j]: #Comparing
        asja_key.append(send[j])
        balvis_key.append(received[j]) #Keeping key bit if bases matched
    else:
        pass #Discard round if bases mismatched


#QBER
rounds = len(asja_key)//3
errors=0
for i in range(rounds):
    bit_index = randrange(len(asja_key)) 
    tested_bit = asja_key[bit_index]
    if asja_key[bit_index]!=balvis_key[bit_index]: #comparing tested rounds
        errors=errors+1 #calculating errors
    #removing tested bits from key strings
    del asja_key[bit_index] #Use del to specify the index of the element you want to delete
    del balvis_key[bit_index]
QBER=errors/rounds #calculating QBER

print("QBER value =", QBER)
print("Asja's secret key =", asja_key)
print("Balvis' secret key =", balvis_key)

參考資料:womanium教材