Python赋能量子计算：算法创新与应用拓展

 from qiskit import QuantumCircuit, Aer, execute

    
  
    
 # 创建量子电路
    
 qc = QuantumCircuit(2, 2)
    
 qc.h(0)  # 对第一个量子比特应用Hadamard门
    
 qc.cx(0, 1)  # 对两个量子比特应用CNOT门
    
 qc.measure([0, 1], [0, 1])  # 测量量子比特
    
  
    
 # 运行量子电路
    
 simulator = Aer.get_backend('qasm_simulator')
    
 job = execute(qc, simulator, shots=1000)
    
 result = job.result()
    
 counts = result.get_counts(qc)
    
 print(counts)
    
    
    
    

 import numpy as np

    
 from qiskit import QuantumCircuit, Aer, execute
    
  
    
 n = 3
    
 qc = QuantumCircuit(n, n)
    
  
    
 # 应用Hadamard门
    
 for qubit in range(n):
    
     qc.h(qubit)
    
  
    
 # 应用受控相位门
    
 for qubit in range(n):
    
     for k in range(qubit + 1, n):
    
     qc.cp(2 * np.pi / 2 ** (k - qubit), qubit, k)
    
  
    
 # 逆序量子比特
    
 for qubit in range(n // 2):
    
     qc.swap(qubit, n - qubit - 1)
    
  
    
 # 测量
    
 qc.measure(range(n), range(n))
    
  
    
 simulator = Aer.get_backend('qasm_simulator')
    
 job = execute(qc, simulator, shots=1000)
    
 result = job.result()
    
 counts = result.get_counts(qc)
    
 print(counts)
    
    
    
    

 import cirq

    
 import numpy as np
    
 from scipy.optimize import minimize
    
  
    
 # 定义量子比特和量子电路
    
 qubit1 = cirq.GridQubit(0, 0)
    
 qubit2 = cirq.GridQubit(0, 1)
    
 circuit = cirq.Circuit()
    
 circuit.append(cirq.H(qubit1))
    
 circuit.append(cirq.CNOT(qubit1, qubit2))
    
  
    
 # 定义目标函数
    
 def objective_function(params):
    
     updated_circuit = circuit.copy()
    
     # 更新电路参数
    
     updated_circuit.append(cirq.Rz(params[0])(qubit1))
    
     estimator = cirq.experiments.measurement_based_estimator(
    
     sampler=cirq.Simulator(), observables=[cirq.Z(qubit1)]
    
     )
    
     result = estimator.run(updated_circuit)
    
     return result.mean[0]
    
  
    
 # 优化
    
 initial_params = np.random.rand(1)
    
 result = minimize(objective_function, initial_params, method='Nelder-Mead')
    
 print(result)
    
    
    
    

 from qiskit import QuantumCircuit, Aer

    
 from sklearn.datasets import load_iris
    
 from sklearn.preprocessing import StandardScaler
    
 from sklearn.model_selection import train_test_split
    
  
    
 # 数据预处理
    
 iris = load_iris()
    
 X = iris.data
    
 y = iris.target
    
 scaler = StandardScaler()
    
 X_scaled = scaler.fit_transform(X)
    
 X_train, X_test, y_train, y_test = train_test_split(X_scaled, y, test_size=0.2, random_state=42)
    
  
    
 # 数据编码
    
 def encode_data(data):
    
     n_qubits = len(data)
    
     qc = QuantumCircuit(n_qubits)
    
     for i, value in enumerate(data):
    
     theta = 2 * np.arccos(np.sqrt(value))
    
     qc.ry(theta, i)
    
     return qc
    
  
    
 # 构建量子支持向量机电路
    
 def build_qsvm_circuit(X_train, y_train):
    
     n_samples = len(X_train)
    
     n_qubits = len(X_train[0])
    
     qc = QuantumCircuit(n_qubits * n_samples, n_samples)
    
     for i, data in enumerate(X_train):
    
     encoded_qc = encode_data(data)
    
     qc.compose(encoded_qc, inplace=True, qubits=range(i * n_qubits, (i + 1) * n_qubits))
    
     return qc
    
  
    
 qc = build_qsvm_circuit(X_train, y_train)
    
 simulator = Aer.get_backend('qasm_simulator')
    
 job = execute(qc, simulator, shots=1000)
    
 result = job.result()
    
 counts = result.get_counts(qc)
    
 print(counts)
    
    
    
    

 from qiskit import QuantumCircuit, Aer

    
 from sklearn.metrics import log_loss
    
 from scipy.optimize import minimize
    
  
    
 # 构建量子神经网络
    
 input_qubits = 2
    
 hidden_qubits = 3
    
 output_qubits = 1
    
  
    
 qc = QuantumCircuit(input_qubits + hidden_qubits + output_qubits, output_qubits)
    
 for qubit in range(input_qubits):
    
     qc.h(qubit)
    
 for i in range(hidden_qubits):
    
     qc.cx(input_qubits + i, input_qubits + hidden_qubits)
    
  
    
 # 定义损失函数
    
 def loss_function(params):
    
     updated_qc = qc.copy()
    
     # 更新量子门参数
    
     for i, param in enumerate(params):
    
     updated_qc.ry(param, i)
    
     simulator = Aer.get_backend('qasm_simulator')
    
     job = execute(updated_qc, simulator, shots=1000)
    
     result = job.result()
    
     counts = result.get_counts(updated_qc)
    
     # 计算损失
    
     loss = log_loss(y_true, counts)
    
     return loss
    
  
    
 # 优化
    
 initial_params = np.random.rand(5)
    
 result = minimize(loss_function, initial_params, method='Nelder-Mead')
    
 print(result)
    
    
    
    

 from dwave.system import DWaveSampler, EmbeddingComposite

    
 import numpy as np
    
  
    
 n = 5  # 城市数量
    
 distance_matrix = np.array([[0, 10, 15, 20, 25],
    
                         [10, 0, 35, 25, 30],
    
                         [15, 35, 0, 30, 15],
    
                         [20, 25, 30, 0, 20],
    
                         [25, 30, 15, 20, 0]])
    
  
    
 Q = np.zeros((n * n, n * n))
    
 for i in range(n):
    
     for j in range(n):
    
     for k in range(n):
    
         Q[i * n + j][k * n + (j + 1) % n] += distance_matrix[i][k]
    
  
    
 sampler = EmbeddingComposite(DWaveSampler())
    
 response = sampler.sample_qubo(Q, num_reads=1000, anneal_time=20)
    
  
    
 best_solution = min(response.record, key=lambda r: r.energy)
    
 solution = np.array(best_solution.sample).reshape(n, n)
    
 optimal_path = []
    
 for j in range(n):
    
     for i in range(n):
    
     if solution[i][j] == 1:
    
         optimal_path.append(i)
    
 print("最优路径:", optimal_path)
    
    
    
    

 from qiskit import QuantumCircuit, Aer

    
 from sklearn.preprocessing import StandardScaler
    
  
    
 # 数据预处理
    
 scaler = StandardScaler()
    
 X_scaled = scaler.fit_transform(X)
    
  
    
 # 构建量子电路
    
 n_qubits = len(X_scaled)
    
 qc = QuantumCircuit(n_qubits)
    
 qc.h(range(n_qubits))
    
 for i in range(n_qubits - 1):
    
     qc.cx(i, i + 1)
    
  
    
 simulator = Aer.get_backend('qasm_simulator')
    
 job = execute(qc, simulator, shots=1000)
    
 result = job.result()
    
 counts = result.get_counts(qc)
    
 print(counts)
    
    
    
    

 量子支持向量机模型准确率: 0.9667

    
 传统支持向量机准确率: 0.9667
    
    
    
    

 量子神经网络在MNIST数据集上的准确率: 0.967

    
 传统卷积神经网络准确率: 0.985