Qubit and Basis States - Logic, Gates, and Computation Step by Step

A qubit table stores amplitudes; measurement uses squared magnitudes. This is a toy exact table; real quantum algorithms also use complex amplitudes and interference.

logic-computation Every row is intentionally ordered and pinned to the lesson specification.

Example

A qubit table stores amplitudes; measurement uses squared magnitudes. This is a toy exact table; real quantum algorithms also use complex amplitudes and interference.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{classical 0}&\hlmath{\text{state=[1,0] probs=(1,0)}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{classical 0}&\text{state=[1,0] probs=(1,0)}\\\text{classical 1}&\hlmath{\text{state=[0,1] probs=(0,1)}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{classical 0}&\text{state=[1,0] probs=(1,0)}\\\text{classical 1}&\text{state=[0,1] probs=(0,1)}\\\text{balanced qubit}&\hlmath{\text{state=[1/sqrt(2),1/sqrt(2)]}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{classical 0}&\text{state=[1,0] probs=(1,0)}\\\text{classical 1}&\text{state=[0,1] probs=(0,1)}\\\text{balanced qubit}&\text{state=[1/sqrt(2),1/sqrt(2)]}\\\text{measure balanced qubit}&\hlmath{\text{probs=(1/2,1/2)}}\end{array}

Read the table verdict

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{classical 0}&\text{state=[1,0] probs=(1,0)}\\\text{classical 1}&\text{state=[0,1] probs=(0,1)}\\\text{balanced qubit}&\text{state=[1/sqrt(2),1/sqrt(2)]}\\\text{measure balanced qubit}&\text{probs=(1/2,1/2)}\\\text{verdict}&\hlmath{\text{probabilities sum to 1}}\end{array}