Читать книгу Principles of Superconducting Quantum Computers - Daniel D. Stancil - Страница 15

A classical bit must either be a “0” or a “1.” In contrast, a qubit can also be in a superposition state that is part “0” and part “1.” If the qubit is in a “1” or “0” state, we say the qubit is in a basis state.¹ For basis states, the state of the qubit can be measured any number of times without changing the state, much like measuring the state of a classical gate. A superposition state will also yield either a “0” or a “1” when measured, with a probability determined by the mixture. In this case the action of making the measurement will “collapse” the superposition state onto one of the constituent basis states, and the information stored in the superposition state will be lost. For example, if |ψ⟩ happens to represent a superposition state, then measuring the qubit at any time will collapse the state to either |0⟩ or |1⟩, destroying the information in the superposition state. From this point on, repeated measurement of the qubit will always yield the same result as the first measurement, just like a classical bit.

Mathematically the superposition state can be written

, (1.1)

where α and β are complex constants.

As mentioned, if such a superposition state is measured, it will always give either |0⟩ or |1⟩ but with probabilities of each determined by α and β. Specifically, the probabilities of measuring the two possible outcomes are given by

(1.2)

If these are the only two possible outcomes of the measurement, then the probabilities must sum to 1, or

(1.3)

This ability to represent superposition states is one of the secrets to the power of quantum computing: there is a sense in which the qubits are able to explore multiple possibilities in parallel.