I read the article and it seems too rudimentary to provide a manual how to build a quantum computer home. It also contain some "half-truth" about quantum computers, e.g.:
Quantum computers take advantage of strange properties from quantum mechanics to filter through possible solutions much more quickly than conventional computers. When someone asks about the many ways a drug can impact a cancer cell...
and
A quantum computer, on the other hand, has a unique way of sorting through possible solutions and can have an answer in a matter of minutes!
This is true for some tasks but not for all. There are some problems that quantum computer cannot solve faster than classical computer.
Regarding the noise:
One way to reduce noise is to make the quantum system cold. Very cold. As close as possible to the coldest temperature that can be physically reached
and
Next, you will have to limit other types of energy that create noise, such as external magnetic or electric fields ... (Finding clever ways of reducing noise is an ongoing problem and is a big barrier for scientists developing these computers.)
From these quotes, it is obvious that to build quantum computer at home is impossible. Firstly, how to reach temperature close to absolute zero? Reducing vibration is also very difficult and expensive. So, there is no easy way how to do so at your own.
Quotes from the second article:
While the MIT experiment to validate the protocol won't immediately make large-scale quantum computers practically viable, it is a major step toward making them more precise.
According to the research team, there are still years of additional work required in order to perfect the detection and cancellation of noise in quantum systems. In particular, future research will move from a single-sensor system to a two-sensor system, enabling the characterization of noise correlations across different qubits.
You can see that even for scientists with the state-of-art equipment, it is difficult to apply the knowledge about the noise to reduce it and to build a big quantum computer which can be widely used.
Please consider the first articles as and introduction (with some inaccuracies) for laymen how a quatum computers work. Overall, it seems impossible to build a quantum computer in easy and cheap way at home. But please do not feel discouradged and continue to study quantum computing.