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Multiple Hadamard gates Transformation on N qbits

There is a formula for the Hadamard transform on $N$ qubits. $$ H^{\otimes N}=\frac{1}{\sqrt{2^N}}\sum_{x,y\in\{0,1\}^N}(-1)^{x\cdot y}|y\rangle\langle x| $$ In this case, $$ x\cdot y=\sum_{i=1}^...
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