Quantum computing is a very active and rapidly expanding field of research. Many companies and research institutes are spending a lot on this futuristic and potentially game-changing technology. Some even built toy models for a quantum computer in the lab. For instance, see IBM's 50-qubit quantum computer.

However, some scientists are not that optimistic when it comes to the predicted potential advantages of quantum computers in comparison with the classical ones. They believe there are *theoretical obstacles* and *fundamental limitations* that significantly reduce the efficiency of quantum computing.

One mathematical argument against quantum computing (and the only one that I am aware of) is based on the Gil Kalai's idea concerning the sensitivity of the quantum computation process to noise, which he believes may essentially affect the computational efficiency of quantum computers.

Question.I look for some references on similar theoretical (rather than practical) mathematical arguments against quantum computing — if there are any. Papers and lectures on potential theoretical flaws of quantum computing as a concept are welcome.

**Remark.** The theoretical arguments against quantum computing may remind the so-called *Goedelian arguments* against the artificial intelligence, particularly the famous Lucas-Penrose's idea based on the Goedel's incompleteness theorems. Maybe there could be some connections (and common flaws) between these two subjects, particularly when one considers the recent innovations in QAI such as the Quantum Artificial Intelligence Lab.

`quantum-computation`

tag exists, and I added it (at the expense of the`computer-science`

tag, because there is a limit of 5). $\endgroup$ – Carlo Beenakker Jun 11 '18 at 6:36