How to create a Quantum circuit to implement the generation of 3-qubit uniform superposition wavefunction

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I want to know experimentally or circuit wise diagram to know how to create a circuit that will produce 3-qubit uniform superposition wave function Can somebody help me in that Thank you in advance

Abhinil Agarwal

Posted 2020-05-31T01:06:23.907

Reputation: 19

Welcome. What have you done so far? Where are you needing the most help? – Mark S – 2020-05-31T02:33:50.427

Answers

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A uniformly distributed superposition can be prepared by Hadamard gate. If you apply a Hadamard on single qubit in state $|0\rangle$ you get state $\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$. Both states $|0\rangle$ and $|1\rangle$ are measured with same probability $50 \%$.

To prepare uniformly distributed state having $n$ qubits, simply apply Hadamard on each of them. This leads to a operator $H \otimes H \otimes \dots \otimes H = \otimes^nH$. A state produced by this operation after application on initial state $|00\cdots00\rangle$ is

$$\frac{1}{\sqrt{2^n}}\big(|00\dots00\rangle+|00\dots01\rangle + |00\dots10\rangle+\cdots+|11\dots10\rangle+|11\dots11\rangle\big),$$

i.e. all combinations of $0$ and $1$ on $n$ qubits are presented with equal probability.

Martin Vesely

Posted 2020-05-31T01:06:23.907

Reputation: 7 763