Two-qubit silicon quantum processor with operation fidelity exceeding 99%
science.org
science.org
https://en.wikipedia.org/wiki/Quantum_threshold_theorem
Basically, if the error rate on an individual gate is low enough, you can use the gate to construct larger (less efficient) gates with arbitrarily low amounts of error. 99%, as you say, is a bit low and you'd need impractically large circuits to use these gates.
You want error correction with classical computers too, it just works differently.
On the other hand, current quantum computers are analog. Each quantum gate will get the coefficients of its output states a little bit wrong, and after a few tens of operations only noise is left in the qubits. In principle, quantum error correction could be used to measure and compensate for these errors. But none of the technologies demonstrated so far are anywhere near good enough for this.
The error rates are not zero. Low, but not zero. Trillions of operations is what, a split-second of runtime on a five-year-old GPU?
"High-reliability" systems invariably use some form of error correction or error detection. You can do this at different levels of abstraction. At a low level, you can build redundant gates. At a company I used to work for, this was a product we sold--it would synthesize ICs from an HDL and incorporate error correction. (This particular feature forced the company to get ITAR export licenses.) At a different company I worked for, we did our error correction at a high level using software. We encountered hardware errors on a regular basis. I'm not even talking about ECC--I'm talking about CPU errors.
The only reason why you can think that imperfections and noise don't matter is because there isn't much noise in your environment and you aren't dealing with enough data that you'll notice any errors.
Deal with a large enough amount of data, enough CPUs, enough RAM, and error becomes a certainty.
The "quantum computers are analog" line is at best profoundly misleading. If your definition of "analog" extends to quantum computers, then I'd say that digital computers are also analog. Which is not an incorrect thing to say.
The transistors inside a digital CPU are of course analog devices. However, the digital interpretation of the logic levels means that analog errors do not propagate between gates. If the voltage fluctuations are small enough, the probability of triggering a logic gate incorrectly becomes astronomically small. Analog computers (such as all current quantum computers) do not have this feature. Each operation adds a little bit of error to the quantity that is being processed. This could be the voltage in an electronic analog computer, or the state coefficients in a quantum computer.
This brings us back to the Quantum threshold theorem, which says that it's possible to design a quantum computer so that you can perform as many operations as you like without accumulating additional error, as long as individual gates in the quantum computer have a bounded amount of error.
This is one of the reasons why thinking of a quantum computer as "analog" will lead you astray. Quantum computers are more like classical digital computers than like analog computers.
I'm not a quantum computing expert, but I wonder if a SEU would even matter in some parts of a quantum system. The bits are in an undefined state during operation anyway.
11 = 21
10 = 7
01 = 3
00 = FileNotFound
(Edit: I have a mathematical physics degree; everything I’ve said here is sarcastic/jokingly. The person I’m replying to is right, this is not how Shor’s algorithm works although I’d hope that was obvious from my original tongue in cheek comment)
I think the current goal is the factorization of 15. There is no reason to suggest insane levels of challenge like 21.
Thing is that, as you add more qubits, "operation fidelity" (as they call it) goes down exponentially, maybe even superexponentially (?), so it's very hard to keep it within an acceptable range on larger systems.
If you look at the theorem, it is definitely sub-exponential in the number of qubits needed to correct for error.
"Quantum mechanical states are extremely fragile and require near absolute isolation from the environment. Such conditions are hard to create and typically require temperatures near absolute zero and shielding from radiation. Thus, building quantum computers is expensive and difficult. The challenge increases dramatically with increasing size (number of qubits and the length of time they must be coherent) and thus only small to medium scale computers have been built so far.", from [1]. Also, I recommend reading out the whole article as it gives a nice, broad, overview of the challenges in place, it's not as easy as putting 1 qubit + 1 qubit together.
1: Quantum Computing: An Overview Across the System Stack, https://arxiv.org/pdf/1905.07240.pdf
Even in architectures with nearest neighbor gates, the (multiplicative) overhead stemming from error correction will only need to be logarithmic in the size of the computation. The constants may be unfavorable, but a log is still a log. See for example https://arxiv.org/abs/1208.0928 and https://arxiv.org/abs/1310.2984
The paper you linked to names challenges, but it only states those in respect to reaching practical scaling, which is a result of the constant that is associated with the growth rate, but not the growth rate itself.