Читать книгу Principles of Superconducting Quantum Computers - Daniel D. Stancil - Страница 19

Since there are two components in a qubit’s state, we can represent the state as a two-dimensional vector, referred to as a state vector. The basis states can be written

(1.4)

It follows that we can express a general superposition state as a weighted sum of the basis states:

(1.5)

The notation |ψ⟩ is called a “ket.” The transpose complex conjugate⁴ of a ket is denoted ⟨ψ| and is called a “bra”:

(1.6)

where the † superscript indicates the transpose complex conjugate, also referred to as the Hermitian conjugate, or adjoint. The “bra” and “ket” terminology may seem strange until you multiply them together to form a “bra-ket.” For example,

(1.7)

(1.8)

(Note that when written as a bra-ket, only a single vertical bar is used in the center.) The bra-ket operation (i.e., multiplying a bra and ket) is also referred to as an “inner product.” Referring to (1.8), we see that the inner product of a state vector with itself gives the sum of the probabilities that each of the basis states will be obtained in a measurement. Since the sum of the probabilities of all possible outcomes must equal 1, we see that the state vectors must be properly normalized to a length of unity.