Vectors are commonly written in column format. Sometimes, we also use shorthand format such as (3, 4).

In quantum computing, the state |0> corresponds to vector (1, 0), and |1> corresponds to vector (0, 1).

Commonly used quantum gates, quantum circuit symbols, and math representations:

The Bloch sphere representation of X (NOT), H (Hadamard), and Z, S, T (phase) gates.

We can see that

- X gate rotates along X axis 180 degree (or less depending on the initial angle to Z axis). (NOT)
- H gate rotates along Y axis 90 degree (or less).
- Z, S, T gates rotate along Z axis at certain degree. (phase)

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