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Does anyone know how you can obtain a new state |z> from two pre-existing states |x> and |y> using the Tensor product in Q#? i.e. |z> = |x> ⊗|y> ?
Thanks in advance for the help!
Edit: for clarity, the states that I am working with are
$|x\rangle = \frac{1}{\sqrt{2}} \sum^{3}_{j=0} \sin \frac{\pi (j + 0.5)}{4} |j\rangle$
$|y\rangle = \sum^{1}_{i=0} b_i |i\rangle$
where the $b_i$'s are just real numbers.
If you have an array of Qubit objects, and you prepare the individual qubits into arbitrary states, then the array effectively contains the tensor product of all of the original qubits.
To quickly illustrate what I mean:
using (qubits = Qubit[2]) {
// do something to prepare qubits[0] individually
// do something to prepare qubits[1] individually
// now the state of "qubits" is the tensor product of the two
// individual qubit states that you prepared
}
This also generalizes if you're preparing groups of qubits within the array that you allocated.
Qubitobjects, not states. So if you have twoQubitobjects and they are not entangled, then essentially they are already in a tensor product state. $\endgroup$Qubitobjects :Qubit[2]andQubit[1]and used thePrepareArbitraryStateoperation in order to map those qubits to the states|x>and|y>(I edited the question so you can see how my states look like). Now I want to encode in a new variable of typeQubit[]the result of the tensor product between|x>and|y>. $\endgroup$Qubit[3]array and put all three qubits in there. Just putting them in an array is enough, you don't need to do anything special. $\endgroup$