update

Author: mhjensen

doc/pub/week9/ipynb/ipynb-week9-src.tar.gz

@@ -0,0 +1,36 @@
+import numpy as np
+def qft(n):
+
+   # Inputs n qubits and returns QFT matrix of size (2^n, 2^n)
+   dim = 2 ** n  # Dimension of the Hilbert space
+   omega = np.exp(2j * np.pi / dim)  # Primitive root of unity
+   # Initialize QFT matrix
+   QFT = np.zeros((dim, dim), dtype=complex)
+   # Construct the QFT matrix
+   for i in range(dim):
+       for j in range(dim):
+           QFT[i, j] = omega ** (i * j) / np.sqrt(dim)
+   return QFT
+
+def apply_qft(state):
+   n = int(np.log2(len(state)))  # Number of qubits
+   qft_matrix = qft(n)
+   return qft_matrix @ state
+# Example: 3-qubit system
+n_qubits = 4  # QFT on 3 qubits (8 dimensions)
+dim = 2 ** n_qubits
+
+# Define an example quantum state (|5⟩ in computational basis)
+state = np.zeros(dim, dtype=complex)
+state[0] = 1  # |5⟩ = [0,0,0,0,0,1,0,0]
+
+print("Initial State |5⟩:", state)
+# Apply QFT
+qft_state = apply_qft(state)
+print("\nState after QFT:")
+print(np.round(qft_state, 4))  # Rounded for better readability
+# Verify QFT is unitary (QFT * QFT† = I)
+qft_matrix = qft(n_qubits)
+identity = np.dot(qft_matrix, qft_matrix.conj().T)
+print("\nQFT * QFT† = Identity Matrix (Rounded):")
+print(np.round(identity, 4))