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Please excuse the broad nature of the question. I am interested in understanding recent developments by various hardware companies and their approaches towards quantum error correction.

My knowledge right now is fragmented and I see a lot of papers/blogs/press releases by Google, IBM, QuEra, Alice&Bob around hardware improvements that claim to bring quantum error correction and fault-tolerant quantum computing within reach in the next decade or so.

Assuming this not just hype, is there a good resource/review paper to get an overview of what has changed recently that has made fault-tolerant quantum computing more realistic than before? Do we have better error correction codes or better qubits or something else that allowed multiple companies to achieve this feat?

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This kind of thing is why:

enter image description here

(That's just the easiest image I could find with a google search. It's from https://twitter.com/jjgarciaripoll/status/1295752348124553217 . Don't know what paper, but coherence times have definitely increased by orders of magnitude over the years.)

Everything has been getting gradually better. Things have become good enough that error correction is essentially starting to work. Five years ago physical qubits were obviously better. Now it's kind of even. Probably in five years the logical qubits will be obviously better.

Technically there's error correction papers going back 25 years showing it "working", but the number of caveats on what "working" means has been going down. For example, a major difference between recent QEC experiments and early QEC experiments is now we do multi-round experiments. Computations span many rounds, so single-round experiments were always unrealistic. But multi-round experiments are much more demanding, requiring mid-cycle measurements and higher fidelities across the board.

Examples of important caveats are:

  • Single round instead of multiple rounds
  • Repetition code instead of quantum code
  • Error detection instead of error correction
  • Postselection of correlated error mechanisms like leakage or cosmic rays

From https://arxiv.org/abs/2207.06431 :

enter image description here

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