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I think IBM didn't elaborate because it is kind of obvious if you are into this, and if you are not, linearly scaling graph from 10 to 30 is more than good enough. But since we have niche audience here, let's elaborate. Quantum supremacy is O(n) claim. Then what is n? The answer is that there are two parameters, not one. In Google paper, n is number of qubits and m is circuit depth. n is well known to be difficult to increase. m is not easy either, because if your qubit isn't stable enough, you can't run deep circuit. What Google did is to run n=53 and m=20. Then, why do you need n=53 and m=20? After all, you could see whether it's exponential by, say, trying n and m from 10 to 15, it doesn't need to take days and years. The answer is that there is time-space tradeoff available and if your n is constant, exp(n) space (but still constant space, since n is constant) poly(m) time algorithm is available, and if your m is constant, exp(m) space (but still constant space, since m is constant) poly(n) time algorithm is available. So if you want to show exponential speedup, you need to be able to exclude these algorithms by increasing n or m enough such that exp(n) or exp(m) space is not realizable. Google chose n=53 such that exp(n) is not realizable, and ran scaling experiment on m. This is what they mean whey they say in the paper "Up to 43 qubits, we use a Schrödinger algorithm, which simulates the evolution of the full quantum state... Above this size, there is not enough random access memory (RAM) to store the quantum state". Now what IBM is saying is becoming clear. There is not enough RAM, but there is enough disk, so exp(n) where n=53 is realizable, and simulation runs linear in m. It's not a new algorithm, it's exactly the same algorithm Google ran up to n=43. So 43 qubits clearly can't demonstrate quantum supremacy. For the same reason, 53 qubits can't either. |