Multiple Hadamard Gates in Parallel: Uniform Superposition in Quantum Computing

When N Hadamard Gates Act on N Qubits

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One of the most important and commonly occurring multiple qubit gates is Hadamard gate. Before we have seen matrix representation of Hadamard gate and on a separate post studied several simple quantum circuits involving Hadamard gate. In this post we will explore uniform superposition, which is the basis of Grover’s Algorithm. This post will be short and involve some mathematics but if you have gone through the previous posts and have a grasp on graduate level math, this won’t be difficult at all. Let’s get started!

2 Hadamard Gates in Parallel:

We have discussed this circuit before and here let’s review it once again. We get started by importing ‘qiskit’ and then adding 2 H gates respectively to 2 qubits in parallel. Below is the code for creating this simple circuit.

!pip3 install qiskit
import qiskit as q 
qr = q.QuantumRegister(2)
cr = q.ClassicalRegister(2)
circuit = q.QuantumCircuit(qr, cr)
circuit.h(qr[0]) # apply hadamard gate on first qubit.
circuit.h(qr[1]) # apply hadamard gate on second…