Logical qubit

A logical qubit is an error-corrected qubit encoded redundantly across many physical qubits so that errors can be detected and corrected faster than they accumulate. Physical qubits fail far too often for long algorithms; a logical qubit trades hardware for reliability, pushing effective error rates low enough to run the billions of operations that cryptanalysis requires.

#Surface code overhead

The leading error-correction scheme, the surface code, tiles physical qubits in a two-dimensional grid. Reaching useful logical error rates takes on the order of 1,000 physical qubits per logical qubit at realistic physical error rates, and the overhead shrinks as hardware improves.

#Why CRQC estimates are stated in logical qubits

Algorithm costs are hardware-independent when expressed in logical qubits and logical gates, so estimates for a cryptographically relevant quantum computer are quoted that way. Running Shor's algorithm against RSA-2048 needs a few thousand logical qubits; the physical translation has dropped from about 20 million noisy qubits in a 2019 estimate to under 1 million in a 2025 revision. That trend, rather than raw qubit counts, is what feeds serious Q-Day discussions.