Four Hundred Forty One

In the standard surface code, a logical qubit at code distance dd uses

nq=(2d−1)2n_q = (2d - 1)^2

data plus measurement qubits, and corrects any error pattern of weight up to (d−1)/2(d-1)/2. Below the per-step threshold of about 0.57%, the logical error rate falls off sharply as dd grows.

A team builds one logical qubit at d=11d = 11. How many physical qubits, and how many simultaneous errors can it correct?

A

22 physical qubits, correcting up to 10 errors

B

441 physical qubits, correcting up to 5 errors

C

121 physical qubits, correcting up to 5 errors

D

441 physical qubits, correcting up to 11 errors