How close are we in achieving computation over reals using quantum qubits? [duplicate]

I recently attended a seminar where a professor of quantum cryptography told the audience that one quantum qubit can theoretically store "infinite information". I was very intrigued by this statement, and me being an absolute novice in this domain, do not have the means of verifying the validity of his statement. My questions are as follows:

1. Can we really compute the distance $$|x - y| < \epsilon$$ using a quantum qubit? If so, can anyone throw light on how this is done?
2. Also, if not, how far along are we in actually computing this quantity?
3. Can we measure if quantum computers approximate this quantity better (or worse?) than classical computers?

• 1. What are $x$ and $y$? 2. You should probably ask the 4th question in a new thread. – Sanchayan Dutta Nov 20 '19 at 15:49
• Hi @evil_potato! I agree with @Sanchayan - questions 1-3 look very similar to the linked question. However, the linked question might not address your fourth question - which I assume is in relation to Blum-Shub-Smale machines. I recommend reviewing the linked question along with the answers therein, and reposting another question with focus on quantum computing and BSS machines... – Mark S Nov 20 '19 at 16:41
• Sorry for the late reply: The question linked by @SanchayanDutta got me pointed in the right direction. I have edited out the 4th question and will be posting a separate question related to BSS models in the quantum domain. Thank you guys for the speedy response and I apologize for the inconvenience. This question can now be marked closed by mods :) – evil_potato Nov 21 '19 at 4:05