A repetition code of 15 qubits (1709.00990v3)

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.

A Repetition Code of 15 Qubits

The paper by Wootton and Loss presents a paper on the implementation of a repetition code across 15 qubits using the IBM's 16-qubit device, ibmqx3, reflecting advancements in quantum error correction techniques and fault-tolerant quantum computing. This experimentation provides critical insights into the practical applicability of repetition codes and the behavior of quantum noise.

The repetition code implemented in their paper functions by storing classical information redundantly across multiple qubits, which enables detection and correction of errors through syndrome measurements. Specifically, the paper demonstrates a single round of syndrome measurements with ancilla qubits and controlled operations, thus capturing error data which allows decoding via a lookup table. The ability to observe the exponential decay of logical error rates through manipulation of code distance is a pivotal achievement, reinforcing the foundational assumptions of quantum error correction.

Several benchmarks of this device were investigated, including comparison to a single qubit memory and analysis of logical error probabilities across varying code distances. Logical error transparency was enhanced by contrasting full decoding—which takes into account information from both code and ancilla qubits—versus partial decoding using only code qubits. This comparison illustrated the importance of ancilla qubits and controlled operations, demonstrating superior effectiveness in error correction through full decoding.

The results support the hypothesis that, with increasing code distance, logical error probabilities decrease. The observed exponential decay conforms to theoretical expectations, though interesting deviations at specific distances offer further insight into device noise characteristics. The paper fits error data to a simple exponential decay model, revealing overall agreement despite finite size effects and biased noise causing deviations. Specifically, the tendency of noise driving qubits towards the state $\lvert0\rangle$ disproportionally affects systems designed to store $\lvert1\rangle$.

In terms of implications, the paper shows that current quantum technology is sufficiently advanced to execute repetition codes with considerable fidelity, crucial for error correction methodologies. The capability introduced by Wootton and Loss lays fundamental groundwork for progressing towards more complex quantum error correction schemes like the stabilizer codes or logical qubits with larger distances and deeper circuits—especially significant as the field moves towards realizing functional quantum processors with fault tolerance.

Future research could benefit from expanding on the limitations noted within this paper. Exploring devices with superior connectivity and larger qubit graphs would facilitate deeper error correction capabilities and further assess correlations in noise. Additionally, detailed analysis on biased and correlated noise impacts could hone our understanding of existing quantum system architectures and noise profiles, thus aiding in more robust engineering of quantum error correction codes.

Above all, this paper exemplifies a meaningful stride in quantum computing, not merely through theoretical verification, but through practical, empirical evaluation of quantum error correction protocols, highlighting both challenges and opportunities for future developments in the field of quantum information science.