Intuitively Analyzing the Quantum Gate Matrix
By this point, you’ve topped up your toolkit with the equation for the quantum state, the Bloch sphere, Universal gates, and quantum gate matrices. Given any quantum gate, you can work out how it’ll modify any arbitrary quantum state. But before reaching into your arsenal, it is always worth trying to see if you can intuitively reason out how the gate acts on the qubit. This will come in handy when you’re designing your own quantum algorithms and want to quickly determine if the gate modifies the qubelets as you want, without getting distracted by the mathematics.
To demonstrate this way of thinking, we’ll work with the S gate defined by the following matrix:
We want to see how this gate affects ...
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