Quantum computers have a long way to go before they are a real threat to breaking classical computer algorithms including elliptic curve discrete log problem.
Both classical and quantum computers require gates to perform computation. Classical computers have transistors which make gates and quantum computers have qubits and rotation transforms to form gates.
In each case billions of gates are needed to perform algorithms to break elliptic curve cryptography. At the present doubling rate of 1 year it will be 30 years before quantum computers can break today's cryptographic algorithms.
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