My understanding is that this simulation of random quantum circuits is already known to be hard in a theoretical sense[1], and there is no argument that a class

My understanding is that this simulation of random quantum circuits is already known to be hard in a theoretical sense[1], and there is no argument that a classical computer could compete with a quantum computer much bigger than 50-60ish qubits. And that arguments against those previous papers has more to do with classical optimizations such as using disk w/ RAM rather than just RAM alone. For example, take this line from IBM's refutation of Google's Quantum Supremacy experiment: "64 PiB of disk space are required for 53-qubit circuits, and 128 PiB for 54-qubit circuits. Both fit within the 250 PiB available on Summit."[2] If you have to use over 50% of the total disk space on one of the world's strongest supercomputers, you're probably going to run into some major issues once we start hitting the 55, 56, 57, 58, etc. qubit territory. And although this is a moving goalpost, the supercomputers clearly aren't going to get better faster than adding single qubits onto the current chips. Already Rigetti is announcing an 80-qubit quantum computer, and IBM is making an 127-qubit computer.[3] So, IMHO we are far past the point where quantum computers have to prove themselves superior to classical ones, at least on designed tasks. I don't think we should compare failed P vs NP proofs (which, IMHO is a problem we're anywhere from 5 to 10000 years out from solving). All this being said, I do have to agree with IBM on the value of the term "Quantum Advantage" versus "Quantum Supremacy". Quantum computers have not yet demonstrated a significant advantage in terms of cost on any problem, but I'm optimistic they will in about a decade. Probably in problems that are already naturally fit to quantum computers, like studying interactions between particles in quantum physics. Also for the record I'm a layperson with just an unusual interest in this field, so it's easily possible I've missed some incredibly important central problem that everyone is being quiet about. [1] https://arxiv.org/abs/2007.07872 https://arxiv.org/abs/2007.07872 [2] https://arxiv.org/pdf/1910.09534.pdf https://arxiv.org/pdf/1910.09534.pdf [3] https://arstechnica.com/science/2021/06/quantum-computing-startup-rigetti-to-offer-modular-processors/ https://arstechnica.com/science/2021/06/quantum-computing-st...