More on quantum error correction

Hot on the heels of the Google team's recent demonstration of quantum error correction, last week Quantinuum released a heavily-promoted preprint: Implementing Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code. This work studies the performance of quantum error correcting codes using trapped ion quantum processors.

The authors compare the performance of logical gates implemented using two different error-correcting codes (5 qubit code and the colour code), without running error correction cycles. Logical CNOT gates were performed with higher fidelity compared to physical CNOT gates, however "the inclusion of QEC cycles along with more careful measurements will be crucial components in a “fair” comparison between the performance of physical and logical qubits."

Error rates are still too high for the 5 qubit code to be useful; even with a 1000-fold reduction in the physical two-qubit gate errors, simulations indicate the error correction using the 5 qubit code will not give an improvement compared to non error-corrected circuits! The authors speculate that this code might still be useful as a quantum memory.

On the other hand, "the color code CNOT with an added FT QEC cycle should eventually outperform the standalone gate, but requires somewhat lower error rates than we currently achieve. In contrast, adding a non-FT QEC to the end of the gate operation causes the simulated logical gate to always perform worse than the physical operation in the error regimes we probed." 

One challenge with the ion trap architecture is that adding additional qubits (ions) generally reduces the gate fidelities due to effects such as cross-talk. 

Another challenge identified in this work is that different error correction codes can have different performance depending on the quantum computing platform used and relative strengths of different noise sources. "It is currently difficult to predict which codes and implementations of those codes may perform the best in general scenarios, and when considering anything but the simplest error models, one is usually forced to resort to numerical studies. Additionally, the exploration space is vast."

Useful error-corrected quantum circuits are still a long way off, requiring difficult improvements to the performance of physical gates.