Python（Qiskit）について（１６）

概要

Qiskit について, 学習サイトのサンプルプログラムを動かしてみた.
動作環境は, Google Colaboratory で行った
実行プログラム, 解説は, 下記の参照サイトをご覧ください

感想

本家のサイトの学習教材が非常に詳しいので, 今後も, 時間を見つけて, 確認していこうと思う.

ドイチ-ジョサ(Deutsch-Jozsa)のアルゴリズム(演習問題)

本家のサイトにある, dj_oracle関数をベースに, 演習問題用のオラクルを実装してみた.
具体的には, n が, 1 ～ 4 で分布型, 5 で定値型となるようにしている.
出力結果(量子回路)については, n = 1 ～ 5 で同じ内容が出力されたと理解する.
グラフ(添付画像)については, n = 1 ～ 4 で ‘1111’ が, 100%, n = 5 で ‘0000’ が 100% だった.

# initialization
import numpy as np

# importing Qiskit
from qiskit import IBMQ, Aer
from qiskit.providers.ibmq import least_busy
from qiskit import QuantumCircuit, assemble, transpile

# import basic plot tools
from qiskit.visualization import plot_histogram

# n is between 1 and 5.
def dj_problem_oracle(n):
    # We need to make a QuantumCircuit object to return
    # This circuit has 5 qubits: the input size is 5, plus one output qubit.
    oracle_qc = QuantumCircuit(5)
    
    # Try changing the location of the X gate depending on the value of n.
    # If n is 4 or less, make the X gate act on the bit at the corresponding location.
    if n in [(i + 1) for i in range(4)]:
        oracle_qc.x(n - 1)
        
        # Controlled-NOT gates
        for qubit in range(4):
            oracle_qc.cx(qubit, 4)
    
    # If n is 5, do nothing
    if n == 5:
        pass
    
    # Convert to quantum gate.
    oracle_gate = oracle_qc.to_gate()
    
    # To show when we display the circuit.
    oracle_gate.name = "Deutsch-Jozsa Problem Oracle"
    
    # Return a quantum gate.
    return oracle_gate

# This function (dj_algorithm) quotes the contents of the following site.
# https://qiskit.org/textbook/ja/ch-algorithms/deutsch-jozsa.html
def dj_algorithm(oracle):
    dj_circuit = QuantumCircuit(5, 4)
    
    # Set up the output qubit:
    dj_circuit.x(4)
    dj_circuit.h(4)
    
    # And set up the input register:
    for qubit in range(4):
        dj_circuit.h(qubit)
    
    # Let's append the oracle gate to our circuit:
    dj_circuit.append(oracle, range(5))
    
    # Finally, perform the H-gates again and measure:
    for qubit in range(4):
        dj_circuit.h(qubit)
    
    for i in range(4):
        dj_circuit.measure(i, i)
    
    return dj_circuit

# oracle_gate = dj_problem_oracle(1)
# oracle_gate = dj_problem_oracle(2)
# oracle_gate = dj_problem_oracle(3)
# oracle_gate = dj_problem_oracle(4)
oracle_gate = dj_problem_oracle(5)
dj_circuit = dj_algorithm(oracle_gate)
dj_circuit.draw()

# initialization

import numpy as np

# importing Qiskit

from qiskit import IBMQ, Aer

from qiskit.providers.ibmq import least_busy

from qiskit import QuantumCircuit, assemble, transpile

# import basic plot tools

from qiskit.visualization import plot_histogram

# n is between 1 and 5.

def dj_problem_oracle(n):

# We need to make a QuantumCircuit object to return

# This circuit has 5 qubits: the input size is 5, plus one output qubit.

oracle_qc = QuantumCircuit(5)

# Try changing the location of the X gate depending on the value of n.

# If n is 4 or less, make the X gate act on the bit at the corresponding location.

if n in [(i + 1) for i in range(4)]:

oracle_qc.x(n - 1)

# Controlled-NOT gates

for qubit in range(4):

oracle_qc.cx(qubit, 4)

# If n is 5, do nothing

if n == 5:

pass

# Convert to quantum gate.

oracle_gate = oracle_qc.to_gate()

# To show when we display the circuit.

oracle_gate.name = "Deutsch-Jozsa Problem Oracle"

# Return a quantum gate.

return oracle_gate

# This function (dj_algorithm) quotes the contents of the following site.

# https://qiskit.org/textbook/ja/ch-algorithms/deutsch-jozsa.html

def dj_algorithm(oracle):

dj_circuit = QuantumCircuit(5, 4)

# Set up the output qubit:

dj_circuit.x(4)

dj_circuit.h(4)

# And set up the input register:

for qubit in range(4):

dj_circuit.h(qubit)

# Let's append the oracle gate to our circuit:

dj_circuit.append(oracle, range(5))

# Finally, perform the H-gates again and measure:

for qubit in range(4):

dj_circuit.h(qubit)

for i in range(4):

dj_circuit.measure(i, i)

return dj_circuit

# oracle_gate = dj_problem_oracle(1)

# oracle_gate = dj_problem_oracle(2)

# oracle_gate = dj_problem_oracle(3)

# oracle_gate = dj_problem_oracle(4)

oracle_gate = dj_problem_oracle(5)

dj_circuit = dj_algorithm(oracle_gate)

dj_circuit.draw()

出力結果(量子回路, n = 1)

     ┌───┐     ┌───────────────────────────────┐┌───┐┌─┐         
q_0: ┤ H ├─────┤0                              ├┤ H ├┤M├─────────
     ├───┤     │                               │├───┤└╥┘┌─┐      
q_1: ┤ H ├─────┤1                              ├┤ H ├─╫─┤M├──────
     ├───┤     │                               │├───┤ ║ └╥┘┌─┐   
q_2: ┤ H ├─────┤2 Deutsch-Jozsa Problem Oracle ├┤ H ├─╫──╫─┤M├───
     ├───┤     │                               │├───┤ ║  ║ └╥┘┌─┐
q_3: ┤ H ├─────┤3                              ├┤ H ├─╫──╫──╫─┤M├
     ├───┤┌───┐│                               │└───┘ ║  ║  ║ └╥┘
q_4: ┤ X ├┤ H ├┤4                              ├──────╫──╫──╫──╫─
     └───┘└───┘└───────────────────────────────┘      ║  ║  ║  ║ 
c: 4/═════════════════════════════════════════════════╩══╩══╩══╩═
                                                      0  1  2  3

┌───┐ ┌───────────────────────────────┐┌───┐┌─┐

q_0: ┤ H ├─────┤0 ├┤ H ├┤M├─────────

├───┤ │ │├───┤└╥┘┌─┐

q_1: ┤ H ├─────┤1 ├┤ H ├─╫─┤M├──────

├───┤ │ │├───┤ ║ └╥┘┌─┐

q_2: ┤ H ├─────┤2 Deutsch-Jozsa Problem Oracle ├┤ H ├─╫──╫─┤M├───

├───┤ │ │├───┤ ║ ║ └╥┘┌─┐

q_3: ┤ H ├─────┤3 ├┤ H ├─╫──╫──╫─┤M├

├───┤┌───┐│ │└───┘ ║ ║ ║ └╥┘

q_4: ┤ X ├┤ H ├┤4 ├──────╫──╫──╫──╫─

└───┘└───┘└───────────────────────────────┘ ║ ║ ║ ║

c: 4/═════════════════════════════════════════════════╩══╩══╩══╩═

0 1 2 3

出力結果(量子回路, n = 2)

     ┌───┐     ┌───────────────────────────────┐┌───┐┌─┐         
q_0: ┤ H ├─────┤0                              ├┤ H ├┤M├─────────
     ├───┤     │                               │├───┤└╥┘┌─┐      
q_1: ┤ H ├─────┤1                              ├┤ H ├─╫─┤M├──────
     ├───┤     │                               │├───┤ ║ └╥┘┌─┐   
q_2: ┤ H ├─────┤2 Deutsch-Jozsa Problem Oracle ├┤ H ├─╫──╫─┤M├───
     ├───┤     │                               │├───┤ ║  ║ └╥┘┌─┐
q_3: ┤ H ├─────┤3                              ├┤ H ├─╫──╫──╫─┤M├
     ├───┤┌───┐│                               │└───┘ ║  ║  ║ └╥┘
q_4: ┤ X ├┤ H ├┤4                              ├──────╫──╫──╫──╫─
     └───┘└───┘└───────────────────────────────┘      ║  ║  ║  ║ 
c: 4/═════════════════════════════════════════════════╩══╩══╩══╩═
                                                      0  1  2  3

┌───┐ ┌───────────────────────────────┐┌───┐┌─┐

q_0: ┤ H ├─────┤0 ├┤ H ├┤M├─────────

├───┤ │ │├───┤└╥┘┌─┐

q_1: ┤ H ├─────┤1 ├┤ H ├─╫─┤M├──────

├───┤ │ │├───┤ ║ └╥┘┌─┐

q_2: ┤ H ├─────┤2 Deutsch-Jozsa Problem Oracle ├┤ H ├─╫──╫─┤M├───

├───┤ │ │├───┤ ║ ║ └╥┘┌─┐

q_3: ┤ H ├─────┤3 ├┤ H ├─╫──╫──╫─┤M├

├───┤┌───┐│ │└───┘ ║ ║ ║ └╥┘

q_4: ┤ X ├┤ H ├┤4 ├──────╫──╫──╫──╫─

└───┘└───┘└───────────────────────────────┘ ║ ║ ║ ║

c: 4/═════════════════════════════════════════════════╩══╩══╩══╩═

0 1 2 3

出力結果(量子回路, n = 3)

     ┌───┐     ┌───────────────────────────────┐┌───┐┌─┐         
q_0: ┤ H ├─────┤0                              ├┤ H ├┤M├─────────
     ├───┤     │                               │├───┤└╥┘┌─┐      
q_1: ┤ H ├─────┤1                              ├┤ H ├─╫─┤M├──────
     ├───┤     │                               │├───┤ ║ └╥┘┌─┐   
q_2: ┤ H ├─────┤2 Deutsch-Jozsa Problem Oracle ├┤ H ├─╫──╫─┤M├───
     ├───┤     │                               │├───┤ ║  ║ └╥┘┌─┐
q_3: ┤ H ├─────┤3                              ├┤ H ├─╫──╫──╫─┤M├
     ├───┤┌───┐│                               │└───┘ ║  ║  ║ └╥┘
q_4: ┤ X ├┤ H ├┤4                              ├──────╫──╫──╫──╫─
     └───┘└───┘└───────────────────────────────┘      ║  ║  ║  ║ 
c: 4/═════════════════════════════════════════════════╩══╩══╩══╩═
                                                      0  1  2  3

┌───┐ ┌───────────────────────────────┐┌───┐┌─┐

q_0: ┤ H ├─────┤0 ├┤ H ├┤M├─────────

├───┤ │ │├───┤└╥┘┌─┐

q_1: ┤ H ├─────┤1 ├┤ H ├─╫─┤M├──────

├───┤ │ │├───┤ ║ └╥┘┌─┐

q_2: ┤ H ├─────┤2 Deutsch-Jozsa Problem Oracle ├┤ H ├─╫──╫─┤M├───

├───┤ │ │├───┤ ║ ║ └╥┘┌─┐

q_3: ┤ H ├─────┤3 ├┤ H ├─╫──╫──╫─┤M├

├───┤┌───┐│ │└───┘ ║ ║ ║ └╥┘

q_4: ┤ X ├┤ H ├┤4 ├──────╫──╫──╫──╫─

└───┘└───┘└───────────────────────────────┘ ║ ║ ║ ║

c: 4/═════════════════════════════════════════════════╩══╩══╩══╩═

0 1 2 3

出力結果(量子回路, n = 4)

     ┌───┐     ┌───────────────────────────────┐┌───┐┌─┐         
q_0: ┤ H ├─────┤0                              ├┤ H ├┤M├─────────
     ├───┤     │                               │├───┤└╥┘┌─┐      
q_1: ┤ H ├─────┤1                              ├┤ H ├─╫─┤M├──────
     ├───┤     │                               │├───┤ ║ └╥┘┌─┐   
q_2: ┤ H ├─────┤2 Deutsch-Jozsa Problem Oracle ├┤ H ├─╫──╫─┤M├───
     ├───┤     │                               │├───┤ ║  ║ └╥┘┌─┐
q_3: ┤ H ├─────┤3                              ├┤ H ├─╫──╫──╫─┤M├
     ├───┤┌───┐│                               │└───┘ ║  ║  ║ └╥┘
q_4: ┤ X ├┤ H ├┤4                              ├──────╫──╫──╫──╫─
     └───┘└───┘└───────────────────────────────┘      ║  ║  ║  ║ 
c: 4/═════════════════════════════════════════════════╩══╩══╩══╩═
                                                      0  1  2  3

┌───┐ ┌───────────────────────────────┐┌───┐┌─┐

q_0: ┤ H ├─────┤0 ├┤ H ├┤M├─────────

├───┤ │ │├───┤└╥┘┌─┐

q_1: ┤ H ├─────┤1 ├┤ H ├─╫─┤M├──────

├───┤ │ │├───┤ ║ └╥┘┌─┐

q_2: ┤ H ├─────┤2 Deutsch-Jozsa Problem Oracle ├┤ H ├─╫──╫─┤M├───

├───┤ │ │├───┤ ║ ║ └╥┘┌─┐

q_3: ┤ H ├─────┤3 ├┤ H ├─╫──╫──╫─┤M├

├───┤┌───┐│ │└───┘ ║ ║ ║ └╥┘

q_4: ┤ X ├┤ H ├┤4 ├──────╫──╫──╫──╫─

└───┘└───┘└───────────────────────────────┘ ║ ║ ║ ║

c: 4/═════════════════════════════════════════════════╩══╩══╩══╩═

0 1 2 3

出力結果(量子回路, n = 5)

     ┌───┐     ┌───────────────────────────────┐┌───┐┌─┐         
q_0: ┤ H ├─────┤0                              ├┤ H ├┤M├─────────
     ├───┤     │                               │├───┤└╥┘┌─┐      
q_1: ┤ H ├─────┤1                              ├┤ H ├─╫─┤M├──────
     ├───┤     │                               │├───┤ ║ └╥┘┌─┐   
q_2: ┤ H ├─────┤2 Deutsch-Jozsa Problem Oracle ├┤ H ├─╫──╫─┤M├───
     ├───┤     │                               │├───┤ ║  ║ └╥┘┌─┐
q_3: ┤ H ├─────┤3                              ├┤ H ├─╫──╫──╫─┤M├
     ├───┤┌───┐│                               │└───┘ ║  ║  ║ └╥┘
q_4: ┤ X ├┤ H ├┤4                              ├──────╫──╫──╫──╫─
     └───┘└───┘└───────────────────────────────┘      ║  ║  ║  ║ 
c: 4/═════════════════════════════════════════════════╩══╩══╩══╩═
                                                      0  1  2  3

┌───┐ ┌───────────────────────────────┐┌───┐┌─┐

q_0: ┤ H ├─────┤0 ├┤ H ├┤M├─────────

├───┤ │ │├───┤└╥┘┌─┐

q_1: ┤ H ├─────┤1 ├┤ H ├─╫─┤M├──────

├───┤ │ │├───┤ ║ └╥┘┌─┐

q_2: ┤ H ├─────┤2 Deutsch-Jozsa Problem Oracle ├┤ H ├─╫──╫─┤M├───

├───┤ │ │├───┤ ║ ║ └╥┘┌─┐

q_3: ┤ H ├─────┤3 ├┤ H ├─╫──╫──╫─┤M├

├───┤┌───┐│ │└───┘ ║ ║ ║ └╥┘

q_4: ┤ X ├┤ H ├┤4 ├──────╫──╫──╫──╫─

└───┘└───┘└───────────────────────────────┘ ║ ║ ║ ║

c: 4/═════════════════════════════════════════════════╩══╩══╩══╩═

0 1 2 3

補足

上記だけだと分かりづらい印象があったため, dj_problem_oracle関数内の量子回路(オラクル)も確認した.

# initialization
import numpy as np

# importing Qiskit
from qiskit import IBMQ, Aer
from qiskit.providers.ibmq import least_busy
from qiskit import QuantumCircuit, assemble, transpile

# import basic plot tools
from qiskit.visualization import plot_histogram

# n is between 1 and 5.
def dj_problem_oracle(n):
    # We need to make a QuantumCircuit object to return
    # This circuit has 5 qubits: the input size is 5, plus one output qubit.
    oracle_qc = QuantumCircuit(5)
    
    # Try changing the location of the X gate depending on the value of n.
    # If n is 4 or less, make the X gate act on the bit at the corresponding location.
    if n in [(i + 1) for i in range(4)]:
        oracle_qc.x(n - 1)
        
        # Controlled-NOT gates
        for qubit in range(4):
            oracle_qc.cx(qubit, 4)
    
    # If n is 5, do nothing
    if n == 5:
        pass
    
    # Return a QuantumCircuit.
    return oracle_qc

# oracle_qc = dj_problem_oracle(1)
# oracle_qc = dj_problem_oracle(2)
# oracle_qc = dj_problem_oracle(3)
# oracle_qc = dj_problem_oracle(4)
oracle_qc = dj_problem_oracle(5)
oracle_qc.draw()

# initialization

import numpy as np

# importing Qiskit

from qiskit import IBMQ, Aer

from qiskit.providers.ibmq import least_busy

from qiskit import QuantumCircuit, assemble, transpile

# import basic plot tools

from qiskit.visualization import plot_histogram

# n is between 1 and 5.

def dj_problem_oracle(n):

# We need to make a QuantumCircuit object to return

# This circuit has 5 qubits: the input size is 5, plus one output qubit.

oracle_qc = QuantumCircuit(5)

# Try changing the location of the X gate depending on the value of n.

# If n is 4 or less, make the X gate act on the bit at the corresponding location.

if n in [(i + 1) for i in range(4)]:

oracle_qc.x(n - 1)

# Controlled-NOT gates

for qubit in range(4):

oracle_qc.cx(qubit, 4)

# If n is 5, do nothing

if n == 5:

pass

# Return a QuantumCircuit.

return oracle_qc

# oracle_qc = dj_problem_oracle(1)

# oracle_qc = dj_problem_oracle(2)

# oracle_qc = dj_problem_oracle(3)

# oracle_qc = dj_problem_oracle(4)

oracle_qc = dj_problem_oracle(5)

oracle_qc.draw()

出力結果(オラクル／量子回路, n = 1)

     ┌───┐                    
q_0: ┤ X ├──■─────────────────
     └───┘  │                 
q_1: ───────┼────■────────────
            │    │            
q_2: ───────┼────┼────■───────
            │    │    │       
q_3: ───────┼────┼────┼────■──
          ┌─┴─┐┌─┴─┐┌─┴─┐┌─┴─┐
q_4: ─────┤ X ├┤ X ├┤ X ├┤ X ├
          └───┘└───┘└───┘└───┘

┌───┐

q_0: ┤ X ├──■─────────────────

└───┘ │

q_1: ───────┼────■────────────

│ │

q_2: ───────┼────┼────■───────

│ │ │

q_3: ───────┼────┼────┼────■──

┌─┴─┐┌─┴─┐┌─┴─┐┌─┴─┐

q_4: ─────┤ X ├┤ X ├┤ X ├┤ X ├

└───┘└───┘└───┘└───┘

出力結果(オラクル／量子回路, n = 2)

q_0: ───────■─────────────────
     ┌───┐  │                 
q_1: ┤ X ├──┼────■────────────
     └───┘  │    │            
q_2: ───────┼────┼────■───────
            │    │    │       
q_3: ───────┼────┼────┼────■──
          ┌─┴─┐┌─┴─┐┌─┴─┐┌─┴─┐
q_4: ─────┤ X ├┤ X ├┤ X ├┤ X ├
          └───┘└───┘└───┘└───┘

q_0: ───────■─────────────────

┌───┐ │

q_1: ┤ X ├──┼────■────────────

└───┘ │ │

q_2: ───────┼────┼────■───────

│ │ │

q_3: ───────┼────┼────┼────■──

┌─┴─┐┌─┴─┐┌─┴─┐┌─┴─┐

q_4: ─────┤ X ├┤ X ├┤ X ├┤ X ├

└───┘└───┘└───┘└───┘

出力結果(オラクル／量子回路, n = 3)

q_0: ───────■─────────────────
            │                 
q_1: ───────┼────■────────────
     ┌───┐  │    │            
q_2: ┤ X ├──┼────┼────■───────
     └───┘  │    │    │       
q_3: ───────┼────┼────┼────■──
          ┌─┴─┐┌─┴─┐┌─┴─┐┌─┴─┐
q_4: ─────┤ X ├┤ X ├┤ X ├┤ X ├
          └───┘└───┘└───┘└───┘

q_0: ───────■─────────────────

│

q_1: ───────┼────■────────────

┌───┐ │ │

q_2: ┤ X ├──┼────┼────■───────

└───┘ │ │ │

q_3: ───────┼────┼────┼────■──

┌─┴─┐┌─┴─┐┌─┴─┐┌─┴─┐

q_4: ─────┤ X ├┤ X ├┤ X ├┤ X ├

└───┘└───┘└───┘└───┘

出力結果(オラクル／量子回路, n = 4)

q_0: ───────■─────────────────
            │                 
q_1: ───────┼────■────────────
            │    │            
q_2: ───────┼────┼────■───────
     ┌───┐  │    │    │       
q_3: ┤ X ├──┼────┼────┼────■──
     └───┘┌─┴─┐┌─┴─┐┌─┴─┐┌─┴─┐
q_4: ─────┤ X ├┤ X ├┤ X ├┤ X ├
          └───┘└───┘└───┘└───┘

q_0: ───────■─────────────────

│

q_1: ───────┼────■────────────

│ │

q_2: ───────┼────┼────■───────

┌───┐ │ │ │

q_3: ┤ X ├──┼────┼────┼────■──

└───┘┌─┴─┐┌─┴─┐┌─┴─┐┌─┴─┐

q_4: ─────┤ X ├┤ X ├┤ X ├┤ X ├

└───┘└───┘└───┘└───┘

出力結果(オラクル／量子回路, n = 5)

q_0: 
     
q_1: 
     
q_2: 
     
q_3: 
     
q_4:

q_0:

q_1:

q_2:

q_3:

q_4:

参照サイト

ドイチ-ジョサのアルゴリズム

概要

感想

ドイチ-ジョサ(Deutsch-Jozsa)のアルゴリズム(演習問題)

補足

参照サイト

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