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Is there any systematic way to decompose a two-level unitary matrix into single-qubit and CNOT operations?

By : Thyagu raja
Date : September 30 2020, 11:00 PM
this one helps. A universal method to decompose 2-qubit unitaries into primitive gates is sometimes referred to as "Krauss-Cirac decomposition". Here are several sources:
Optimal Quantum Circuits for General Two-Qubit Gates by Vatan and Williams, Optimal Creation of Entanglement Using a Two–Qubit Gate by Kraus and Cirac. “Explorations in Quantum Computing” by Williams, chapter 2.
code :

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Is there a way in numpy to test whether a matrix is Unitary

By : Ming Zhao
Date : March 29 2020, 07:55 AM
fixed the issue. Will look into that further I was wondering if there is any function in numpy to determine whether a matrix is Unitary? , Let's take an obviously unitary array:
code :
>>> a = 0.7
>>> b = (1-a**2)**0.5
>>> m = np.array([[a,b],[-b,a]])
>>> m.dot(m.conj().T)
array([[ 1.,  0.],
       [ 0.,  1.]])
>>> is_unitary(m)
Traceback (most recent call last):
  File "<ipython-input-28-8dc9ddb462bc>", line 1, in <module>
  File "<ipython-input-20-3758c2016b67>", line 5, in is_unitary
    error = np.linalg.norm(np.eye(n) - matrix.dot( matrix.transpose().conjugate()))
ValueError: operands could not be broadcast together with shapes (4,4) (2,2) 
>>> m.size
>>> np.eye(m.size)
array([[ 1.,  0.,  0.,  0.],
       [ 0.,  1.,  0.,  0.],
       [ 0.,  0.,  1.,  0.],
       [ 0.,  0.,  0.,  1.]])
>>> is_unitary(m)
>>> np.allclose(np.eye(len(m)), m.dot(m.T.conj()))

Convert from qubit density matrix to Bloch vector

By : Dimitris Nikolaou
Date : March 29 2020, 07:55 AM
I wish this help you The conversion depends on a couple arbitrary choices:
Do you want |0⟩ at the top or the bottom? Do you want the coordinate system to be right-handed or left-handed?
code :
def toBloch(matrix):
    [[a, b], [c, d]] = matrix
    x = complex(c + b).real
    y = complex(c - b).imag
    z = complex(d - a).real
    return x, y, z
print(toBloch([[1, 0],
               [0, 0]])) #Off, Z=-1
# (0.0, 0.0, -1.0)

print(toBloch([[0, 0],
               [0, 1]])) #On, Z=+1
# (0.0, 0.0, 1.0)

print(toBloch([[0.5, 0.5],
               [0.5, 0.5]])) #On+Off, X=-1
# (-1.0, 0.0, 0.0)

print(toBloch([[0.5, 0.5j],
               [-0.5j, 0.5]])) #On+iOff, Y=-1
# (0.0, -1.0, 0.0)

print(toBloch([[0.5, 0.0],
               [0.0, 0.5]])) #maximally mixed state, X=Y=Z=0
# (0.0, 0.0, 0.0)

How to print out whole matrix from unitary simulator

By : user3588310
Date : March 29 2020, 07:55 AM
Hope this helps On Jupyter Notebook, I had simulated eight qubits quantum's circuit with Unitary_simulator. And then, I would like to print out the whole matrix, but what I get is matrix from unitary simulator. The code that I used is: , The output is a 2D array, so you could print it as
code :
for row in unitary:

How to make a parity check matrix from non-systematic to systematic in Matlab? thanks

By : vinu
Date : March 29 2020, 07:55 AM
wish helps you I am trying to make a parity check matrix from non-systematic to systematic. Hence, I am attaching my code below. Somewhat it is correct, but there are some problems. It would be really great if someone could help me in this. Subject: Information theory and coding. I am working on LDPC coding and decoding. Please check the code below , Here is how I'd do it (using Gauss-Jordan elimination):

Diagonalizing sparse unitary matrix

By : Rayhan
Date : March 29 2020, 07:55 AM
I wish did fix the issue. The following code eventually defines pdeig which returns the eigenvalues of a matrix which is a pdmatrix i.e. a product of a permutation and diagonal matrix, or in other words a matrix like the question describes. Calculating the eigenvectors quickly is also possible (they have an explicit formula):
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