# Physical vs Logical Qubits A **physical qubit** is one real, noisy hardware device. A **logical qubit** is a single, robust qubit of information encoded across *many* physical qubits using [[Quantum Error Correction]]. ## First principles A physical qubit decoheres and its gates misfire — error rates of roughly $10^{-3}$ are typical. That is far too noisy for long algorithms. So you don't compute on physical qubits directly. Instead, you weave many of them together into an entangled block whose *collective* state stores one logical qubit. Errors on individual members are caught and repaired by [[Syndrome Extraction]] faster than they accumulate, so the logical qubit behaves as if it were far cleaner than any of its parts. $ \text{many noisy physical qubits} \;\xrightarrow{\text{encoding + correction}}\; \text{one reliable logical qubit} $ > [!intuition] A choir, not a soloist > One singer drifts off pitch. A large choir, constantly self-correcting, holds the note even as individuals waver. The logical qubit is the note the choir sustains. ## The cost: overhead Protection is expensive. Depending on the code and the target error rate, a single logical qubit can require tens, hundreds, or thousands of physical qubits. This **overhead** is the central engineering challenge of scaling — and the reason qubit *counts* race upward. > [!warning] Logical qubits ≠ logical operations per second > Having many logical qubits is not the same as being able to *operate* on them quickly. Slow physical [[Gate Fidelity|gates]] or hard [[Mid-Circuit Measurement]] can throttle the rate of logical operations even when the logical qubit count is high. ## Related - [[Quantum Error Correction]] - [[Code Distance and Threshold Theorem]] - [[Syndrome Extraction]] - [[Mid-Circuit Measurement]]