Quantum Gates — Matrix memorization cheat sheet
It was indeed very challenging for me as a beginner to remember the matrix representation of the single-qubit and multi-qubit reversible,unitary operators viz. 𝑯, 𝝈𝒙, 𝝈𝒚, 𝝈𝒛, 𝑪𝑵𝑶𝑻, 𝝅/𝟖, Toffoli, Fredkin etc. Every now and then, I would forget them.
Any quantum enthusiast would agree, that these frequently used, yet fundamental operators in their arsenal are an absolute necessity to realize any quantum circuit.
As the problem turned out to be recurring, I decided to spend today’s afternoon devising an easy way to conquer these so-called “quantum devils”.
The result of the exercise is the cheat-sheet below.
I am happy that this help me remember the matrix notations easily going forward. As you can see, it is very intuitive and quite easy to follow.
Single Qubit Gates
These are namely Hadamard, Pauli-X, Pauli-Y, Pauli-Z, S (Phase gate), π/8.
If you look at the matrix and the image mnemonic to remember the matrix, you will see that it is very intuitive.
Example 1:
Solid blue lines indicate non-zero values (row and column)
Example 2:
Dotted lines denote 0 along the diagonal
Multi-Qubit Gates
These are namely CNOT, Tofolli, Controlled-Z, Controlled-Phase, Fredkin
Example 1:
I would also like to dedicate this as my first original contribution to the quantum community.
