When discussing the capability of quantum computers to break encryption systems like RSA or elliptic curve encryption, the focus is often on the number of qubits we need. People say that it takes 4,000 qubits to break RSA encryption and 2,500 qubits to break elliptic curve encryption. However, these figures refer to logical qubits and do not account for the necessity of quantum error correction.
Quantum error correction is a crucial aspect often overlooked in these discussions. To maintain the integrity of quantum computations and correct errors that occur naturally in quantum systems, a significantly larger number of physical qubits are required beyond the logical ones. According to some estimates, the number of physical qubits needed for quantum error correction could range from 2 to 10 million. This vast difference underscores the complexity and current technological challenges in building a quantum computer capable of breaking these encryption systems.
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