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For my undergraduate final project I am working on a Quantum Inspired Genetic Algorithm.

For this I am using IBM Q real devices and I need to set a custom initial state on qubits. Using the statevector simulator this was possible, however I am not sure how to do so on real quantum hardware. For example I want to put qubit into state $|\psi\rangle = \sqrt{0.3}|0\rangle + \sqrt{0.7}|1\rangle$.

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    $\begingroup$ Hi! Were you using qc.initialize() before? This can still be run on the real devices $\endgroup$ – met927 Feb 6 at 18:06
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    $\begingroup$ Did you have an issue with running it? I just tested and was able to $\endgroup$ – met927 Feb 6 at 18:12
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    $\begingroup$ Just note that quantum tomography is used for a quantum state measurement, not for qubits initialization. $\endgroup$ – Martin Vesely Feb 6 at 18:16
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    $\begingroup$ You can run qc.initialize([1,0], 0) to initialize it into the |0> state, where the 1st param is the vector to use and the 2nd is the qubits to apply it to. The state you are describing isn't a valid quantum state, as a^2 + b^2 = 1 $\endgroup$ – met927 Feb 6 at 18:17
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    $\begingroup$ I understand that Adhisha is looking for method how to initialize state of qubit and I edited the question accordingly. $\endgroup$ – Martin Vesely Feb 6 at 22:12
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To prepare an arbitrary single qubit state it is possible to use $\mathrm{U3}$ gate. The gate is defined by a matrix

$$ \mathrm{U3}(\theta, \phi, \lambda)= \begin{pmatrix} \cos(\theta/2) & -\mathrm{e}^{i\lambda}\sin(\theta/2) \\ \mathrm{e}^{i\phi}\sin(\theta/2) & \mathrm{e}^{i(\phi+\lambda)}\cos(\theta/2) \end{pmatrix}. $$

When then gate is applied on a qubit in state $|0\rangle$ (i.e. initial state of all qubits on IBM Q), it is transformed to state

$$ |\varphi_0\rangle = \cos(\theta/2)|0\rangle + \mathrm{e}^{i\phi}\sin(\theta/2)|1\rangle. $$

Setting parameters $\theta$ and $\phi$ allows you to get any single qubit state you need.

In your case $|\psi\rangle = \sqrt{0.3}|0\rangle + \sqrt{0.7}|1\rangle$, so obviously $\phi = 0$.

Since $\cos(\theta/2) = \sqrt{0.3}$ parameter $\theta$ is given as

$$ \theta = 2 \arccos(\sqrt{0.3}) = 1.9823. $$

Note 1: In case $\alpha$ and $\beta$ are real numbers, $\phi = 0$ always and you can apply $\mathrm{Ry}(\theta)$ gate (i.e. y-rotation) with same parameter $\theta$ instead because $\mathrm{Ry}(\theta) = \mathrm{U3}(\theta,0,0)$.

Note 2: To preare any multiqubit quantum state, a method introduced in Transformation of quantum states using uniformly controlled rotations can be employed.

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