Last week the Google team reported in Nature the exponential suppression of errors using quantum error correction. I heard about this first from all the media coverage, so I won't bother summarising the entire paper, but will just note a few thoughts on this publication:
1. Even small-scale error-corrected quantum computing is still a LONG way away. The demonstration of exponential error suppression was based on a 1D error-correcting code, which only corrects for one of the two dominant error sources on the device. The measured error rates in the proof-of-concept demonstration of the 2D surface code (able to correct both types of errors) are close to, but not yet at the threshold where logic error rate is reduced by adding more qubits. Moreover, to reach a "practical" error rate at which only 1000 physical qubits are required to encode a single logical qubit will require noise rates to be reduced by more than a factor of 10.
2. Error correction is slow. Each round of error correction requires read-out of the ancilla qubits, which on Google's device takes about 1 microsecond. Moreover, this time is limited by the slowest readout time among all of the ancilla qubits. Therefore, efforts will need to be devoted towards reducing both this time, and the variability of the read-out times from qubit to qubit.
3. Fig. 2d illustrates large scale-correlated noise observed in the device, likely due to cosmic rays. This affects about 0.4% of the measurements, which were removed via post-selection. Running useful quantum algorithms such as Shor's algorithm will require hours or days, and therefore schemes to minimize or mitigate these cosmic ray-induced correlated errors will be required.
4. The peer review file for this paper is available and makes for an interesting read, not only for the expert referees' perspectives, but also because the Google team mentions some of their ongoing research directions in their rebuttal letter.
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