Creating a quantum computer is a massive scientific and engineering challenge. As of 2016, the largest general-purpose quantum computers have fewer than 10 qubits. Attacking Bitcoin keys would require around 1500 qubits. Humanity currently does not have the technology necessary to create a quantum computer large enough to attack Bitcoin keys. It is not known how quickly this technology will advance; however, cryptography standards such as ECRYPT II tend to say that Bitcoin's 256-bit ECDSA keys are secure until at least 2030-2040.
From the bitcoin wiki.
I wonder when Moore's will kick in for the quantum computer development. 1500 qubits might not be that far away with the current developments in nanotechnology.
I don't know what Moore's law has to do with QC
The law basically says that the number of transistors have been doubling every year since their invention (per unit of area). Obviously, you draw an analogy between qubits and transistors. But qubits are not transistors, and they wouldn't necessarily follow this law at all. In other words, today we may have only 10 qubits while in a year we might have 100 (or the same 10 qubits). Further, this field of research is heavily classified so we don't really know how many qubits the most advanced countries and research centers are already operating