Quantum Computing and the Four Images (Part One)

An ordinary bit has only two states, 0 and 1, whereas a qubit can have more states — but it also has the two cases of 0 and 1, usually recorded as the two states |1⟩ or |0⟩. If expressed with matrices, they are respectively:

[latex]
|0\rangle =
\begin{bmatrix}
1 \\
0 \\
\end{bmatrix}
[/latex]
[latex]
|1\rangle =
\begin{bmatrix}
0 \\
1 \\
\end{bmatrix}
[/latex]

1|0⟩+0|1⟩ expresses the superposition state of 0 — that is, the superposition of yin — corresponding to a yin state of probability 1 superimposed with a yang state of probability 0, forming the 10 state, which is the young yin (shaoyin) state.
0|0⟩+1|1⟩ expresses the superposition state of 1 — that is, the superposition of yang — corresponding to a yin state of probability 0 superimposed with a yang state of probability 1, forming the 01 state, which is the young yang (shaoyang) state.

If it is a mixed superposition state of 0 and 1, it is expressed as:

[latex]\frac{\sqrt{2} }{2}|0\rangle+ \frac{\sqrt{2} }{2}|1\rangle[/latex]

Whether the final result is 0 or 1 is the outcome of quantum measurement. Before the qubit is measured, it is in a mixed state, and the square of the coefficient [latex]\frac{\sqrt{2} }{2}[/latex], namely [latex]\frac{1}{2}[/latex], is the respective probability of the yin state and the yang state — expressing a 50% chance of yin and a 50% chance of yang.

In theory, as long as the sum of the two squared probabilities equals 1, the formula holds. So [latex]\frac{\sqrt{2} }{2}[/latex] need not necessarily be the precise probability of yin and yang. In other words, as long as the coefficients, when squared individually, sum to 1, that is sufficient.

In practice, adopting values such as [latex]\frac{\sqrt{2} }{2}[/latex] gives special positions when expressed on a circle — they fall exactly on the eight directions, corresponding to the Eight Trigrams.