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.