Quantum Gates

Hadamard Superposition

Hadamard spreads one basis state across two exact amplitudes. This is a toy exact table; real quantum algorithms also use complex amplitudes and interference.

Example

Hadamard spreads one basis state across two exact amplitudes. 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.

H on |0>[1/sqrt(2),1/sqrt(2)]\begin{array}{c|c}\text{H on |0>}&\hlmath{\text{[1/sqrt(2),1/sqrt(2)]}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

H on |0>[1/sqrt(2),1/sqrt(2)]H on |1>[1/sqrt(2),-1/sqrt(2)]\begin{array}{c|c}\text{H on |0>}&\text{[1/sqrt(2),1/sqrt(2)]}\\\text{H on |1>}&\hlmath{\text{[1/sqrt(2),-1/sqrt(2)]}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

H on |0>[1/sqrt(2),1/sqrt(2)]H on |1>[1/sqrt(2),-1/sqrt(2)]measure H|0>P(0)=1/2 P(1)=1/2\begin{array}{c|c}\text{H on |0>}&\text{[1/sqrt(2),1/sqrt(2)]}\\\text{H on |1>}&\text{[1/sqrt(2),-1/sqrt(2)]}\\\text{measure H|0>}&\hlmath{\text{P(0)=1/2 P(1)=1/2}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

H on |0>[1/sqrt(2),1/sqrt(2)]H on |1>[1/sqrt(2),-1/sqrt(2)]measure H|0>P(0)=1/2 P(1)=1/2measure H|1>P(0)=1/2 P(1)=1/2\begin{array}{c|c}\text{H on |0>}&\text{[1/sqrt(2),1/sqrt(2)]}\\\text{H on |1>}&\text{[1/sqrt(2),-1/sqrt(2)]}\\\text{measure H|0>}&\text{P(0)=1/2 P(1)=1/2}\\\text{measure H|1>}&\hlmath{\text{P(0)=1/2 P(1)=1/2}}\end{array}
logic-computation Every row is intentionally ordered and pinned to the lesson specification.