Physical-to-Logical Qubit Ratio

The Physical-to-Logical Qubit Ratio is the number of physical qubits needed to build one error-corrected logical qubit, the overhead cost of fault-tolerant quantum computation. It follows from the surface code distance: a larger distance protects against more errors but needs more physical qubits, and because the ratio grows with the square of the distance, the book describes the resulting requirement as thousands of physical qubits per logical qubit. This quadratic scaling is the central trade-off between error protection and resource requirements in the book's treatment of physical qubit scaling and error correction for substrate architectures. R⚛/ℹ = 2 × d² ≈ (1000–10000), where R⚛/ℹ is the physical-to-logical qubit ratio, 2 is a multiplication factor, d is the surface code distance parameter, and 1000 and 10000 are the lower and upper bound estimates. All quantities are dimensionless, [∅]. It depends directly on the Surface Code Distance and belongs with Quantum Error Correction, Fault-Tolerant Quantum Computation, Effective Qubit Count and Qubit Count Scaling.