It’s a bit of an overreach to assume that quantum computing can solve all problems. It’s not that I buy into the entire argument by Penrose but more that I think NP problems aren’t all going to be solved by mere parallelism. In fact, a significant part of what makes some problems NP is the fact they’re not decidable. Meaning they’re a question of “should I take this path or the other” and not a question of “which path is best” (technically it’s both but it’s really the former since the latter defines the condition of choosing). It’s why you have not only the Traveling Salesman Problem in the list of NP problems but also the Coloring Problem (these two oddly have related approximate algorithms, and boy are they hard to grasp).
Even if you have an infinite number of quantum computers via entanglement working together to collapse to the correct solution for some NP problems they’re still dealing with the same constraint of decidability that hampers them. It’s why problems like decryption with quantum computers seems feasible since most encryption schemes use prime numbers to create cipher text which means there exists some kind of algorithm that can use parallelism to find those prime numbers that are candidates for decryption whereas something like the coloring problem might not be something you can throw infinite quantum computers coloring all possible graphs (assuming we don’t put an upper bound on the graph size or vectors they contain which if we did then it’s something you could solve even with a classical computer given enough time). Basically, quantum computing is novel but not magic.
