Logical Qubit

A logical qubit is a single error-corrected qubit formed by encoding quantum information across many physical (noisy) qubits. The encoding protects against physical errors: if a few physical qubits in the logical qubit suffer errors, the quantum information is preserved and errors can be detected and corrected without measuring the logical qubit directly. The surface code — the most popular quantum error correction code — typically requires ~1,000 physical qubits per logical qubit at current error rates. A fault-tolerant quantum computer capable of breaking RSA-2048 would need ~4,000 logical qubits, requiring roughly 4 million physical qubits. Current NISQ devices have 0 logical qubits in the fault-tolerant sense (some partial demonstrations exist). Quantinuum demonstrated 48 logical qubits in a restricted sense using their H-Series hardware (2023).