Читать книгу Principles of Superconducting Quantum Computers - Daniel D. Stancil - Страница 20

We have previously stated that the probability of measuring a given component of a superposition state is given by the magnitude squared of its coefficient. The act of measuring requires an apparatus that interacts with the qubit in order to extract information. The rules of quantum mechanics tell us that the apparatus can only give partial information, related to a set of basis states. For now, we will assume that measurement is always with respect to the standard basis states, |0⟩ and |1⟩, which is the case for most quantum computing systems. However, it is possible for a measurement apparatus to be associated with a different set of basis states. (We will discuss measurement in more detail in later chapters.)

When a qubit is measured: (a) the state is changed to one of the basis states associated with the measurement, and (b) the measurement apparatus tells us the resulting state. In general, the probability that a state |ψ⟩ will be found in the basis state |a⟩ when measured is given by

(1.9)

This is called the Born Rule. For example, the probability that the outcome of measuring the state |ψ⟩ above is |0⟩,|1⟩ is given by

(1.10)

(1.11)

as we found before.