Advances in quantum error correction

This month has seen a few different groups report implementation of quantum error correcting codes using superconducting quantum processors:

Logical-qubit operations in an error-detecting surface code

This article published in Nature Physics on 16th December by a Dutch team and collaborators implements a distance-2 surface code, encoding a single logical qubit in a 2D lattice of 7 physical qubits. They demonstrate state initialization and single-qubit gates on their logical qubit.

Realizing repeated quantum error correction in a distance-three surface code

This arXiv preprint posted on 7th December by a Swiss team and collaborators reports implementation of the surface code on a 17 qubit processor, yielding a single logical qubit protected against both bit flip and phase errors using a 1.1us error correction cycle.

Realizing an error-correcting surface code with superconducting qubits

This arXiv preprint by the USTC team was posted on 27th December. They similarly implement the distance 3 surface code using a 17 physical qubit grid selected from their 66-qubit superconducting quantum processor. Their error correction cycle is also on the order of microseconds, but seems a little longer than the Swiss team's because they use a slower readout scheme to reduce the error rate.

 

Points to note 

• Improvements in gate fidelity are still needed for the logical error rate for superconducting qubits to be less than the 2-qubit gate errors, such that the error correction algorithm beats the physical error rate. Ion trap quantum processors have on the other hand already reached this break-even point.
  
• At this stage the error correction is still done off-line, i.e. as a correction to the measured data. The ultimate goal is on-the-fly error correction, which will require integration of fast digital processing, feedback, and qubit resetting. Doing so without increasing the physical error rate will likely be challenging. Again, ion traps have the lead.
  
• Current experiments involve post-selection, with leakage states discarded. Leakage states are measurements not correctable via the error-correction scheme, e.g. due to too many or correlated errors, one source of which is cosmic rays. Without mitigation schemes, correlated errors may hinder large scale error correction, as highlighted by a recent paper by the Google team.