Suppose I have 100 qubits that I want to entangle and put into superposition. To do so I construct a Hadamard gate to do this. By definition, the Hadamard is going to be a 2^100 X 2^100 matrix - which is huge.
How does one go about actually performing this operation? The size of the Hadamard matrix is exponential relative to the number of qubits (ie 2^100 X 2^100). Is there a way to perform this operation without actually making this huge matrix? Or can we only work with a 'small' number of qubits at once?
Follow up question: does using 100 4x4 Hadamard gates (one for each qubit) do the same thing as using a single 2^100 x 2^100 Hadamard gate? If so, how do these qubits become entangled?