How many physical qubits does one logical qubit need?
As of March 2026, one error-corrected logical qubit costs about 31.5 physical qubits with the most efficient demonstrated qLDPC code (the [[144, 12, 12]]: 144 data + 144 check + 90 logic-unit qubits per 12-logical-qubit block), and 1,011–3,747 physical qubits with the standard surface code at distances 13–25 (formula: 3·(2d²−1), including routing overhead).
Why the range is so wide
Overhead depends on the code, the code distance d (which must grow as the target error rate shrinks), and what is counted. The surface-code figure includes a ×3 routing/overhead multiplier; the qLDPC figure counts the full computational footprint (data + syndrome ancillas + logic-processing unit) but no routing multiplier, so cross-code comparisons are tilted up to ~3× in the qLDPC direction, an asymmetry stated here because it is stated in the model's own caveats.
Compared like-for-like (routing multiplier excluded from both sides), the Gross code ([[144, 12, 12]], Bravyi et al., Nature 2024 (IBM)) needs ~10.7× fewer qubits per logical qubit than a distance-13 surface-code patch, consistent with the paper's own "10× fewer qubits" claim, reproduced from first principles.
Compute it yourself
Every number on this page is computed from the same open model that powers the interactive calculator and the MCP server for AI assistants.
GET https://www.quantum-expectations.com/api/expectation?qubitErrorRate=0.001&numQubits=12&compDepth=100&useErrorCorrection=true&errorCorrectionCode=bb-144-12-12