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Comment by derekp7 | Hacker News Reader

I like to draw an analogy to slide rules. A typical slide rule has a precision of about 3 - 4 significant digits (it gets worse at the higher end of the scale, better at the lower end). To get another digit out of it, you need one 10 times long, or a way to make the markings 10 times more accurate. So effectively you have an intractable problem trying to build a slide rule that is precise to a large number of significant digits.

Is the issue with quantum computers somewhat similar? I know next to nothing about the mechanical aspects of them, but based on the what I've read it is considered a breakthrough whenever another qubit is added.

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As a historical note, this is a primary reason why digital computers replaced analog computers. If you want another digit of accuracy out of an analog computer, you need components that are 10 times as accurate, requiring expensive precision resistors and capacitors. But if you want another digit of accuracy out of a digital computer, you just process four more bits and you can still use cheap, inaccurate components.

While analog computers are almost entirely forgotten now, they were widely used even into the 1970s. They could solve differential equations almost instantaneously, while digital computers needed to chug through calculations before producing the answer. But digital computers steadily became faster until they could generate answers in real-time, but more accurate and easier to program.

This is a pretty good analogy for the state of quantum computers right now!

One difference is that (in principle) it is possible to do quantum error correction. Essentially this turns a number of imperfect "physical" qubits into a perfect "logical" qubit. However, this requires extremely low error rates of the physical qubits to begin with and creates a lot of overhead. All existing quantum computers are much too small and noisy to implement quantum error correction except for some proof-of-principle experiments. I am somewhat pessimistic that any of the current technologies can be improved enough to make it possible in practice.

It’s certainly not a breakthrough when another qubit is added. It’s currently typically a breakthrough when another 9 to the fidelity is added, or a 0 to the qubit lifetime is added.

Quantum computers are like that until you get to 1%-0.1% error rates, at which point error correction becomes possible [1].

1: https://en.wikipedia.org/wiki/Quantum_threshold_theorem

I think its much too early to tell. We know really well about slide rules. We are still learning what the best way to build quantum computers are, and how different methods scale.

So far the empirical evidence is pretty unanimous: None of the methods scale.

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