I've just started to learn Quantum annealing and I have found that I have to convert my problem into its quadratic form. I have to use something named QUBO.
To start with, I have tried to find a solution for a lineal regression problem (from machine learning).
This is the cost function for this algorithm:
$$J(\theta_0,\theta_1)=\frac{1}{2m}\sum_{i=0}^m(h_\theta(x_i)-y_i)^2$$
where
$$h_\theta(x_i)=\theta_0+\theta_1x_i$$
In a linear regression problem you have a set of input values, $x_i$, and their corresponding outputs, $y_i$. For example, you have a set of houses' size, $x_i$, and their prices, $y_i$.
To goal of a linear regression problem is to find a formula, $h_\theta(x_i)$, that a produces the value of $y_i$ when you input it the value of $x_i$.
In the cost function, I square the difference between the guessed value, $h_\theta(x_i)$, minus the real value $y_i$.
Do you know if I can convert the cost function into a quadratic formula?
By the way, I'm not asking about how to minimize $J(\theta_0,\theta_1)$, I'm asking about how to convert into its quadratic form.