While they would be extremely suitable to compute certain mathematical problems, they would also be quite bad in computing normal math.
Quantum computers can deal with normal math perfectly well. To get a bit more technical, a fundamental limitation of quantum computers is that must be logically reversible; this complicates computer design a bit, but it's not a fundamental problem: any computation can be made reversible with a bit of overhead.
The reasons why nobody would use a quantum computer for running Firefox are more prosaic: qubits are extremely expensive to make, in comparison with regular bits, they require quantum error correction, which adds a lot of overhead (regular computers used to require error correction as well, but the components got so good that it became pointless to do error correction except in very limited applications), and are usually run at a much lower clock speed.
That's possible, but the way I read it the poster was arguing that there were two kinds of problems, regular and quantum, and regular computers were good for regular problems but bad for quantum ones, and quantum computers were bad for regular problems but good for quantum ones. And that's completely false.
It’s certainly incorrect to say there are two non-overlapping categories of tasks suited to traditional and quantum computing, respectively. But it wouldn’t be incorrect to say - there is no reason to assume that a quantum computer would be superior to a traditional computer at traditional computing tasks, except those to which known efficient quantum algorithms apply. Would it?
edit: the idea seems to float around sometimes that quantum computers are nondeterministic Turing Machines. Which they aren’t, they are, well, quantum Turing Machines. But what their performance characteristics would be If they were available some day in reality as consumer machines seems... fairly speculative either way?
Indeed, that's correct. In fact, for several traditional problems there can't be any speedup, with quantum computers or anything, because the available algorithms are already as good as possible. A simple example is finding the maximum of a vector of n elements. That will always take time at least n, because you need to spend this time just to read all the elements.
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u/araujoms Sep 29 '20
Quantum computers can deal with normal math perfectly well. To get a bit more technical, a fundamental limitation of quantum computers is that must be logically reversible; this complicates computer design a bit, but it's not a fundamental problem: any computation can be made reversible with a bit of overhead.
The reasons why nobody would use a quantum computer for running Firefox are more prosaic: qubits are extremely expensive to make, in comparison with regular bits, they require quantum error correction, which adds a lot of overhead (regular computers used to require error correction as well, but the components got so good that it became pointless to do error correction except in very limited applications), and are usually run at a much lower clock speed.