What are Probability Amplitudes

Introduction to Quantum Computing

When a qubit that is in a superposition state is measured, quantum mechanics tells us that the qubit state will be projected onto our measurement basis.

If measuring along the z-axis, that is, the axis which represents states |0> and |1>, measurements must give a classical result, and so any given measurement will result in one of the classical states: either state |0> or state |1>. A superposition state is never measured directly.

If this is identically prepared and then the state |ψ> is measured multiple times, then state |0> will be obtained with probability |α| squared  and the state |1> with probability |β| squared .

The coefficients α and β are the probability amplitudes, since their magnitude squared will yield the probability that their respective states are measured.

These probability amplitudes can be found by projecting the vector representing state |ψ> onto the vectors representing the states |0> and |1>.

Thus and