X and CNOT Gates - Logic, Gates, and Computation Step by Step

Some quantum gates permute basis rows exactly like reversible logic. This is a toy exact table; real quantum algorithms also use complex amplitudes and interference.

Example

Some quantum gates permute basis rows exactly like reversible logic. 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{X on |0>}&\hlmath{\text{|1>}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{X on |0>}&\text{|1>}\\\text{X on |1>}&\hlmath{\text{|0>}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{X on |0>}&\text{|1>}\\\text{X on |1>}&\text{|0>}\\\text{CNOT |00>}&\hlmath{\text{|00>}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{X on |0>}&\text{|1>}\\\text{X on |1>}&\text{|0>}\\\text{CNOT |00>}&\text{|00>}\\\text{CNOT |01>}&\hlmath{\text{|01>}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{X on |0>}&\text{|1>}\\\text{X on |1>}&\text{|0>}\\\text{CNOT |00>}&\text{|00>}\\\text{CNOT |01>}&\text{|01>}\\\text{CNOT |10>}&\hlmath{\text{|11>}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

\begin{array}{c|c}\text{X on |0>}&\text{|1>}\\\text{X on |1>}&\text{|0>}\\\text{CNOT |00>}&\text{|00>}\\\text{CNOT |01>}&\text{|01>}\\\text{CNOT |10>}&\text{|11>}\\\text{CNOT |11>}&\hlmath{\text{|10>}}\end{array}

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