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In quantum algorithms we need to initialize the qubits at the start of our algorithm in some quantum register. Suppose that if we are working with a four qubit quantum register we can initialize the register into values such as $|0000\rangle$ or another value such as $|0101\rangle$, which means that the first and third qubits are in basis $|0\rangle$ state and the second and fourth qubits are in basis $|1\rangle$ state. Once we have initialized these qubits as such we can then proceed to apply various quantum gates on them.

My question is that in a physical quantum computer (not a simulator) where say we represent qubits with electron spin, how do we manupulate such electrons so that we can initialize a Quantum register, say with the value $|0101\rangle$?

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It very much depends on your physical realisation. In some realisations, such as when using photons, the process of producing the photon typically produces it in a fixed polarisation (which is probably what you’re using to encode a qubit). Alternatively, you pass the photon through a polarisation filter. This is equivalent to the most typical strategy - measure the qubit in some basis. That way, you know the definite state that the qubit is in, and you can convert it into the right state. As a final option, many systems have a natural Hamiltonian that is applied to them, and the system is cooled in order to produce the ground state of that Hamiltonian. Again, you’ve got a fixed state (typically the all zero state) and you can convert that into whatever initial state you want.

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Well the procedure depends on the physical system that you are using to realize the quantum register. An example I can give is of Diamond NV-Center. In simplest case, the vacancy electron is modelled as spin-1 particle here(there are reasons to model it like this) and nitrogen-14 nuclei has spin 1. So total system lies in a Hilbert space of 9-Dimensions or you can say there are 9 energy levels. Lets say you want to realise a 2-qubit register, then you would need 4-energy levels. Define the levels as $|00\rangle$, $|01\rangle$, $|10\rangle$ and $|11\rangle$. Lets say in equilibrium system is in $|00\rangle$ state, if you want to initialize the system in $|01\rangle$ state then all you would need is an electromagnetic pulse of energy being equal to the energy difference of $|01\rangle$ and $|00\rangle$ levels. In NV-Center, normally microwave and radio-frequency pulses are used.

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One of the simplest way to think about physical realization of qubits is using Photons.

Let's say you have a photon that is vertically or horizontally polarized. There are physical devices to create and measure polarizations of these photons. So, you can mark the horizontally polarized photons as the state $\lvert 0 \rangle$ and the vertically polarized one as the $\lvert 1 \rangle$ state.

Additionally, you could use photon polarizer to change a particular photons polarization to turn a $\lvert 0 \rangle$ to a $\lvert 1 \rangle$ or vice versa. This wiki article would help you a bit. Moreover, you could check out this cool video from professor Allan Adams where real life photon polarization is demonstrated. (link)

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