A repetition code of 15 qubits

TL;DR

This paper demonstrates the implementation of repetition codes up to 15 qubits on a 16-qubit quantum device, showing exponential decay of logical error rate and providing insights into device noise.

Contribution

First experimental implementation of repetition codes up to 15 qubits on a real quantum device with syndrome measurement and lookup table decoding.

Findings

Logical error rate decays exponentially with code size

Provides insights into noise characteristics of the quantum device

Validates the effectiveness of repetition codes for quantum error correction

Abstract

The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most $15$ qubits on the $16$ qubit \emph{ibmqx3} device. Each experiment is run for a single round of syndrome measurements, achieved using the standard quantum technique of using ancilla qubits and controlled operations. The size of the final syndrome is small enough to allow for lookup table decoding using experimentally obtained data. The results show strong evidence that the logical error rate decays exponentially with code distance, as is expected and required for the development of fault-tolerant quantum computers. The results also give insight into the nature of noise in the device.