Universal quantum computing is still gated behind a technology known as a "magic state". Maintaining coherence is but one technical challenge to the implementat

Universal quantum computing is still gated behind a technology known as a "magic state". Maintaining coherence is but one technical challenge to the implementation of a quantum computer, and while we have not solved it, I think it is likely to be the lesser of the two hurdles. The main problem with magic states is that the larger our computation needs to be, the more pure our magic state needs to be. The claim is that we can take many "copies" of impure magic states, and leverage QEC to produce a single "copy" of a purer magic state. Fortunately, given this, the number of copies we need in order scale our computation to n qubits for n operations is polynomial in n. The big caveat, however, is that in order for this scheme to work, the impure copies need to have no entanglement between them. These are partial measurements of a larger quantum system which are by definition not maximally mixed, and as far as I know, no one has come up with a compelling physical or mathematical argument why it should be easy to find n separable mixed states like this. In fact, I think the more natural claim would be that this is hard to do, since separable pure states are a measure zero subset of pure states.