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What are quantum computers good for?

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It’s more complex than that, surely?

Of course – but this is, at least, an accurate enough framework to act as a starting point. For instance, more complex quantum algorithms are robust to noise. In the case of the Deutsch-Jozsa algorithm, if a small chance of failure exists then there is a classical algorithm that performs just as well as Deutsch-Jozsa.

Quantum circuits create finely tuned probability distributions. Any noise makes our measurement that little bit uncertain: did we measure qubits superposed with the desired state, or did we merely observe noise? The solution to this in more sophisticated algorithms, like Shor’s famous factoring algorithm, is to repeat the process, and build up a distribution of the results, increasing the probability that we are observing an answer that is correct.

In other words, the output register (where we read the qubits) becomes a probabilistic summary of all the possible output states permitted by the algorithm you’re using.

Of course, it’s quite possible to generate probability distributions with a classical computer – but as your number of possible outcomes increases, so does the length of time needed to generate the distributions. But at some point, as it seems for many problems in the famous complexity class NP and for many of the problems that quantum computers are good for, a classical Turing machine can’t get there in polynomial time.

One of the reasons so much research is directed to how we handle and measure qubits is to give us more confidence in fewer measurements – without destroying the quantum states that we need for the quantum computer to work.

That is, of course, if we’re positive that quantum mechanics is indeed complete. That’s the deepest theoretical question of quantum mechanics, a question that’s almost metaphysical.

Rather than seeking an ultimate, final, indisputable proof that quantum mechanics is right, it’s probably easier to do what we’re doing: continue the research to reach a point at which we can test a quantum computer of reasonable scale, and let the proof come along later. After all, we happily use quantum mechanics to build lasers!

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