A rotated surface code of code distance d uses, for one logical qubit, d² physical data qubits and d² − 1 physical measurement qubits that check for errors. For d = 15, how many physical qubits does one logical qubit need?

Answer: C. 449

There are 15² = 225 data qubits and 225 − 1 = 224 measurement qubits, a total of 2d² − 1 = 449. A code of distance d can correct up to (d − 1)/2 errors, so d = 15 can handle up to 7 errors. Estimates suggest that with physical error rates of about 0.1%, reaching the logical error rates needed for practical computations requires d of roughly 15 to 25, which means several hundred to about 1,500 physical qubits per logical qubit. Because the surface code works with operations only between neighboring qubits on a two-dimensional grid, it suits superconducting qubit chips well.

• A. This is 2d − 1. The number of qubits in a surface code grows in proportion to the square of d.
• B. This counts only the d² data qubits and leaves out the measurement qubits.
• C. Correct. 225 + 224 = 449.