In order to overcome the decay, we need gates with fidelity so close to one that the decay is negligible over the course of quantum algorithms we intend to run. This is indeed a major limitation of NISQ computers that imposes a stringent "depth budget". It is true that fidelity decays exponentially in the course of quantum computation. Optimism about improvements in basic gate fidelity and error correction aside, is there anything I am missing about errors in entangled states that gives rise to these predictions? To state this more precisely, is there any theoretical effect or algorithm that can be exploited to limit the error probability in entangled systems to be polynomial or at least subexponential in the size of the system?
More bits without the ability to produce larger entangled states seem to have a limited advantage, because it would be practically equivalent to using two computers or executing in sequences. Most interesting algorithmic building blocks, like the QFT, require entanglement between all of the involved bits. It looks like building large systems of the same fidelity becomes exponentially harder, and just scaling an existing design will result in a system with exponentially lower fidelity. The probability of error grows exponentially, if $x < 1.0$, which is of course true for all practical systems.ĮCCs mitigate this to some extent, but also just by a polynomial factor and require even more bits.
Given a fidelity where $P = x$ means no error occurs on bit $i$ with probability $x$, it would seem to me that an entangled system of size $n$ would have probability $P = x^n$. Naively, I would assume that bigger systems are much harder to engineer, especially if one wanted to be able to entangle all of their bits, because only the undisturbed outcome is correct. seem to imply a linear/exponential growth in the size of their quantum computers. I am quite stumped by the fact that the roadmaps for quantum computers as given by IBM, Google, IonQ, etc.
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