# If measurement collapses the information and we lose information, what's the point of using a qubit?

It's a basic question, I'm new to the domain and still studying qubit. To my knowledge, One of the most important advantages of a qubit over a classical bit is that it can store more information than just a 1 or 0 but as we measure a 2-state quantum system (qubit) it instantly collapses to one of the states which is why we call measuring a "destructive action", so what is the use of storing more information when we can practically not retrieve or read it?

• Analogy: why would you use a boat if your destination is on land? Commented Oct 6, 2022 at 16:22
• But, If it's a cargo boat, I would expect it to unload the stuff I loaded on it, right? If I have to throw away stuff before I dock, what's the use? Commented Oct 6, 2022 at 16:34
• @BeetranDahiya in this analogy, the sea is the full set of possible quantum states, while the land are the classical states you might prepare as input, and be interested in processing via measurements of the output. Even though what you're interested in is getting from land to land, ie process purely classical information, you might do so more efficiently by "passing through the sea", ie exploring the richer dynamics offered by QM. You might not be able to access all the information in a qubit during the evolution, but that still affects what you will measure at the hand (also, great analogy!)
– glS
Commented Oct 6, 2022 at 21:28

Your question gets to the heart of why developing good quantum computing algorithms is tricky.

If we have a set of qubits and naively encode every possible input, evaluate some function, and then measure the output with them, our final state is going to collapse to the value of that function on one of those inputs. So now we only have a single evaluation of that function and worse, we don't even know which input gave of us that answer.

To make a useful QC algorithm, you have to be able to make the most of out of that single measurement. This is usually done by some sort of operation (like the Quantum Fourier Transform) after the function evaluation that uses the superposition of "wrong" inputs to cancel each other out while amplifying the "correct" input such that the single measurement at the end is very likely to give the desired result in just a few attempts.

Broadly speaking, we can set up our computation so that the measurement outcome tells us something meaningful about the problem we are trying to solve. A nice example of this is the Deutsch–Jozsa algorithm. While we can prepare the state $$|\psi\rangle=\frac{1}{\sqrt{2^n}}\sum_{\mathbf{x}\in\{0,1\}^n}|\mathbf{x}\rangle$$ and feed it to $$f$$ to calculate all possible values of $$f(x)$$ in parallel, when we do a measurement we will get only one outcome (i.e $$f$$ evaluated at one specific input). But if we act smarter, we can still solve the problem using only one evaluation of $$f$$ (as you can see on the Wikipedia page).

As Chris E. said in his answer, this is exactly what makes designing quantum algorithms a hard task. Though, that doesn't render quantum computers useless.