Create code.py

Author: mhjensen

doc/Programs/Sensing/code.py

@@ -0,0 +1,61 @@
+import numpy as np
+from scipy.linalg import expm
+import matplotlib.pyplot as plt
+
+# Define single-qubit operations, Identity, Pauli, Hadamard and S matrices
+Id = np.array([[1, 0], [0, 1]], dtype=complex)
+X = np.array([[0, 1], [1, 0]], dtype=complex)
+Y = np.array([[0, -1j], [1j, 0]], dtype=complex)
+Z = np.array([[1, 0], [0, -1]], dtype=complex)
+Had = np.array([[1, 1],[1, -1]], dtype=complex) / np.sqrt(2)
+S = np.array([[1, 0],[0, 1j]], dtype=complex)
+# Define two-qubit gates
+CNOT01 = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]], dtype=complex)
+CNOT10 = np.array([[1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]], dtype=complex)
+SWAP = np.array([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]], dtype=complex)
+
+times = np.linspace(0, 1, 100)  # Time range from 0 to 1 seconds
+
+# Initial state for each qubit
+psi_1 =  np.array([1, 0], dtype=complex) # start with |0> for qubits 1 and 2
+psi_2 =  np.array([1, 0], dtype=complex) # start with |0> for qubits 1 and 2
+# possible basis states for measurements
+basis_00 = np.array([1, 0, 0, 0], dtype=complex)
+basis_01 = np.array([0, 1, 0, 0], dtype=complex)
+basis_10 = np.array([0, 0, 1, 0], dtype=complex)
+basis_11 = np.array([0, 0, 0, 1], dtype=complex)
+# then act with Hadamard on first qubit only
+psi_1 = Had @ psi_1
+# Initial two-qubit state
+Psi_0 = np.kron(psi_1,psi_2)
+# Define parameters
+# Then we act on this state in order to get a Bell state 1/sqrt(2)(|00>+|11)
+Psi_0 = CNOT01 @ Psi_0
+B = 1.0  # Strength of the magnetic field (in arbitrary units)
+omega = B  # Frequency associated with the magnetic field
+# Constructing the Hamiltonian H = -omega/2 * (Z * I + I * Z)
+H_z_I = -omega / 2 * np.kron(Z, Id)  # Z * I
+I_H_z = -omega / 2 * np.kron(Id, Z)    # I * Z
+# Total Hamiltonian, try a more complicated one
+H = H_z_I + I_H_z   
+# Lists to store expectation values
+expect_00, expect_11 = [], []
+for t in times:
+   # Calculate time evolution operator
+   U = expm(-1j * H * t)
+   # Evolve the initial state
+   Psi_t = U @ Psi_0
+   # Calculate probabilities of measuring specific states: P(|00>) and P(|11>)
+   # Calculate expectation values
+   expect_00.append(abs(np.dot(basis_00.conj(), Psi_t))**2)
+   expect_11.append(abs(np.dot(basis_11.conj(), Psi_t))**2)
+
+# Plotting results using matplotlib
+plt.figure(figsize=(10, 6))
+plt.plot(times, expect_00, label='Probability |00>')
+plt.plot(times, expect_11, label='Probability |11>')
+plt.xlabel('Time')
+plt.ylabel('Probability')
+plt.title('Quantum Sensing Simulation')
+plt.legend()
+plt.show()