State decomposition

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!

Prerequisite knowledge

• Bra-ket notation
• X, Y and Z basis of a qubit
• Basic linear algebra

Further thinking

How would you decompose the |0> state in the Y-basis? Note: the basis states of the Y-basis are:   

Further reading

Take a look at some more examples of state decomposition. For example:

• http://people.uncw.edu/hermanr/qm/braket.pdf