For many applications in quantum computing, it is useful to express a quantum state in another basis. For example, you might have already learned that we can express the |+> state in the Z-basis as an equal superposition:
But how does this generally work? Postdoctoral researcher Ben Criger (QuTech) explains how you can do this decomposition for any (arbitrary) basis!
- Bra-ket notation
- X, Y and Z basis of a qubit
- Basic linear algebra
How would you decompose the |0> state in the Y-basis? Note: the basis states of the Y-basis are:
Take a look at some more examples of state decomposition. For example: