# How do I embed classical data into qubits?

How do I embed classical data into qubits? I have a classical data [0 1] and I want to encode it as quantum amplitude to a superposition? What are the gates used to achieve that? I am a beginner to quantum programming?

Depending on your data there are multiple ways of doing so.

Consider the case of normalized and standardized data (i.e. data on the unit circle). A data point can be given by $$(a, b)$$ with $$|a|^2+|b|^2=1$$.

Now we can choose an angle $$\theta$$ such that $$R_Y(\theta)\lvert 0\rangle = a\lvert 0\rangle + b\lvert 1\rangle.$$ In a similar fashion this can be done for data on the unit sphere.

If your data is more than two-dimensional, you have a similar trick. Suppose you have data given by $$(a_1, a_2,\dots,a_{2^n})$$, with $$\sum_i |a_i|^2 = 1$$.

Now choose angles $$\vec{\theta}$$ such that $$U(\vec{\theta})\lvert 0\rangle = \sum_i a_i \lvert i\rangle,$$ for a suitable $$U$$. The difficulty with this is that you have to decompose $$U$$ in a sequence of one- and two-qubit gates.

• Hello @nipponn I did as you said but when I set $\theta$ to greater than 180 or less than 0, in order to create a normalized vector that contain a negative element within it, it seems it doesn't work
– Aman
Nov 7 '19 at 14:04
• Some quantum languages work with double angles for $\theta$ in $R_Y$. I'm not sure that's it, but it is worth checking. Nov 13 '19 at 6:53

To embed classical data, you don't need superpositions. Bit values 0 and 1 correspond directly to the quantum states of a qubit written as $$|0\rangle$$ and $$|1\rangle$$. From a theorist's perspective, we don't worry about making these; it's a fundamental assertion that you can prepare, say, the $$|0\rangle$$ state. Then one just has to apply the bit-flip gate (also known as Pauli-X) to convert the 0 into a 1.

It's also worth noting that if you only want to perform a classical computation on these bit values (OK, why would you go to the effort of using qubits? but for the sake of argument...), you just rewrite your classical circuit as a classical reversible circuit. This can be implemented directly on the qubits. Each step will work exactly the same as it did on bits, it's just that instead of a register of $$n$$ bit values $$x\in\{0,1\}^n$$, you have a state vector $$|x\rangle$$ of $$n$$ qubits.