Quantum Error Correction with Only Two Extra Qubits

TLDR

Noise rates in quantum computing experiments have dropped dramatically, but reliable qubits remain precious, making fault‑tolerance schemes with minimal qubit overhead essential. We introduce fault‑tolerant error‑correction procedures that use only two extra qubits. The procedures add flags to detect faults that cause correlated errors, enabling fault‑tolerant error correction with only two extra qubits. The scheme works for distance‑three codes, enabling testing of the ⟦5,1,3⟧ code with seven qubits and protecting seven encoded qubits using only 17 physical qubits for ⟦7,1,3⟧ and ⟦15,7,3⟧ Hamming codes.

Abstract

Noise rates in quantum computing experiments have dropped dramatically, but reliable qubits remain precious. Fault-tolerance schemes with minimal qubit overhead are therefore essential. We introduce fault-tolerant error-correction procedures that use only two extra qubits. The procedures are based on adding "flags" to catch the faults that can lead to correlated errors on the data. They work for various distance-three codes. In particular, our scheme allows one to test the ⟦5,1,3⟧ code, the smallest error-correcting code, using only seven qubits total. Our techniques also apply to the ⟦7,1,3⟧ and ⟦15,7,3⟧ Hamming codes, thus allowing us to protect seven encoded qubits on a device with only 17 physical qubits.