Shor's algorithm can be used to break elliptic curve cryptography by computing discrete logarithms on a hypothetical quantum computer. The latest quantum resource estimates for breaking a curve with a 256-bit modulus (128-bit security level) are 2330 qubits and 126 billion Toffoli gates.
Link to resource?
Read
https://www.reddit.com/r/Bitcoin/comments/6is19z/new_estimate_quantum_computers_require_at_most/ , an x-post of your resource:
blk0 72 points 4 years ago
In all fairness, I have to state that the 2330 qubits refer to ideal, fault-tolerant, logical qubits, whereas the 17 qubits currently achieved by IBM's quantum processor are raw, imperfect qubits which could be used to encode 7 logical qubits. Yet, quantum error-correction of even a single fault-tolerant qubit has not been achieved in experiments today.
World's most powerful quantum computer as of today can do
66 qubits.
And *it's* research paper says this:
In conclusion, we have reported the design, fabrication, measurement, and benchmarking of a state-of-the-art 66- qubit superconducting quantum processor that is fully programmable through electric control. ...... We note that the performance of the whole system behaves as predicted when system size grows from small to large, confirming our high fidelity quantum operations and low correlated errors on the Zuchongzhi processor. The quantum processor has a scalable architecture that is compatible with surface-code error correction, which can act as the test-bed for fault-tolerant quantum computing.
In other words, you still have a long shot to make even 66 *logical* (fault-free) Qbits.
So wake me up when you get anywhere near 2000 logical ones.