Adding random matrix generators in math

Author: hJaffaliColibritd

mpqp/tools/maths.py

@@ -2,7 +2,10 @@
 
 from numbers import Complex, Real
 from typing import TYPE_CHECKING
+from qiskit import quantum_info
 
+from scipy.linalg import sqrtm, inv
+import math
 import numpy as np
 import numpy.typing as npt
 import sympy as sp
@@ -182,3 +185,63 @@ def exp(angle: Expr | Complex) -> sp.Expr | complex:
         res = sp.exp(angle)
         assert isinstance(res, Expr)
         return res
+
+
+def rand_orthogonal_matrix_seed(size: int, seed: int) -> Matrix:
+    """Generate a random orthogonal matrix with a given seed.
+
+    Args:
+        size: Size (number of columns, or rows) of the squared matrix to generate.
+        seed: Seed used to control the random generation of the matrix.
+
+    Returns:
+        A random orthogonal Matrix.
+    """
+    # TODO: to example
+    np.random.seed(seed)
+    m = np.random.rand(size, size)
+    return m.dot(inv(sqrtm(m.T.dot(m))))
+
+
+def rand_orthogonal_matrix(size) -> Matrix:
+    """Generate a random orthogonal matrix without a given seed"""
+    # TODO: to comment + examples
+    m = np.random.rand(size, size)
+    return m.dot(inv(sqrtm(m.T.dot(m))))
+
+
+def rand_clifford_matrix(nb_qubits) -> Matrix:
+    """Generate a random Clifford matrix"""
+    # TODO: to comment + examples
+    return quantum_info.random_clifford(nb_qubits).to_matrix()
+
+
+def rand_unitary_2x2_matrix() -> Matrix:
+    """Generate a random one-qubit unitary matrix"""
+    # TODO: to comment + examples
+    angles = np.random.rand(3)*2*math.pi
+    m = np.array([[np.cos(angles[0]/2), -np.exp(angles[2]*1j)*np.sin(angles[0]/2)],
+                           [np.exp(angles[1]*1j)*np.sin(angles[0]/2), np.exp((angles[1]+angles[2])*1j)*math.cos(angles[0]/2)]])
+    return m
+
+
+def rand_product_local_unitaries(nb_qubits) -> Matrix:
+    """Generate a random tensor product of unitary matrices"""
+    # TODO: to comment + examples
+    matrix = rand_unitary_2x2_matrix()
+    for _ in range(nb_qubits-1):
+        matrix = np.kron(matrix, rand_unitary_2x2_matrix())
+    return matrix
+
+
+def rand_hermitian_matrix(size) -> Matrix:
+    """Generate a random Hermitian matrix.
+
+    Args:
+        size: Size (number of columns, or rows) of the squared matrix to generate.
+
+    Returns:
+        A random orthogonal Matrix."""
+    # TODO: to comment + examples
+    m = np.random.rand(size, size)
+    return m + m.conjugate().transpose()