Programming language

Overhead (engineering)

Fault tolerance

Block code

Set (abstract data type)

Code (set theory)

Quantum

Error detection and correction

Physics

Qubit

Quantum mechanics

Operating system

Computer science

Quantum computer

Algorithm

Distributed computing

Hamming code

Theoretical computer science

Quantum error correction

Decoding methods

Physical Review Letters

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.

Quantum Error Correction with Only Two Extra Qubits