Revisiting the hopes for scalable quantum computation

The hopes for scalable quantum computing rely on the “threshold theorem”: once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based on a number of assumptions, which are supposed to be satisfied exactly, like axioms, e.g. zero undesired interactions between qubits, etc. However, in the physical world no continuous quantity can be exactly zero, it can only be more or less small. Thus the “error per qubit per gate” threshold must be complemented by the required precision with which each assumption should be fulfilled. In the absence of this crucial information, the prospects of scalable quantum computing remain uncertain.