Real-time quantum error correction beyond break-even | Hacker News Reader

Real-time quantum error correction beyond break-even

nature.com

88 pointsSLHamlet9 comments

They achieved an actual logical qubit for over a millisecond using error correction? Please correct me if I am wrong, but isn't this a huge breakthrough relative to previous progress?

Yes and no.

In true quantum form, it both is and isn't a breakthrough simultaneously.

My understanding of quantum computers hit a brick wall some time back, so please correct any errors:

Shor's algorithm requires not only the logical qubit to be stable (the superposition of 1 and 0, but also the phase -- in the remaining dimensions of the bloch sphere) of the qubit to be noise free to an extraordinary degree. There are rotations in very small angles many, many times in the computation.

This QEC algorithm trades phase for increase stability in the logical qubit.

So, if this QEC is used, doesn't that imply the resulting system could not execute Shor's algorithm. Could it be that it forgoes many of the algorithms that enable "quantum supremacy"?

Edit: Maybe I should have said real/imaginary parts of the Qubit? QEC seems to only worry about the real part, and trades the imaginary to keep the real stable?

QEC implies phase error correction (if you don't care about phase errors you could just use a classical error correction code). A 'logical qubit' refers to an abstraction layer that implements some sort of idealized qubit behaviour (including the phase) that is used as a qubit in computation without considering the underlying implementation. The underlying implementation of a single logical qubit may be something like 5 'physical qubits' using https://en.wikipedia.org/wiki/Five-qubit_error_correcting_co... or a entire structure of many physical qubits using something like a https://en.wikipedia.org/wiki/Toric_code

> Shor's algorithm requires not only the logical qubit to be stable (the superposition of 1 and 0, but also the phase [..] to be noise free to an extraordinary degree. There are rotations in very small angles many, many times in the computation.

This is wrong. Those rotations are not the hard part.

When Shor's algorithm is compiled using qubit recycling [0], factoring an n bit number uses 2n rotations that aren't a multiple of 45 degrees. For relevant number-to-factor sizes like 2048 bits, performing these rotations to a precision of ±0.0000000001° is more than sufficient. Rotations smaller than the required precision can simply be skipped. If you're asked to rotate by 0.00000000000000000001° ± 0.0000000001°, not rotating at all is within tolerance.

±0.0000000001° is more precise than would be reasonable with physical qubits, but it's achievable with logical qubits that can do 45 degree rotations. You decompose the arbitrary rotation into a sequence of a ~hundred 45 degree rotations that approximate the desired rotation [1].

It's also possible to replace all rotations by additions into a special re-usable "phase gradient state" [2][3]. When factoring a 2048 bit number, preparing a phase gradient state of sufficient quality only requires around a hundred non-multiple-of-45-degree-with-precision-±0.0000000001° rotations, instead of thousands.

If you count it all up, the precise rotations account for maybe a hundred thousand error corrected gates. The algorithm as a whole uses a billion to a trillion error corrected gates, depending on exactly which gates you count. The precise rotations are a negligible part of the difficulty; they make up less than 0.01% of the required work. From the perspective of superconducting qubits, the hard part is actually just idling a surface code qubit! All the operations are implemented using variations on idling.

0: https://arxiv.org/abs/quant-ph/0001066

1: https://www.mathstat.dal.ca/~selinger/newsynth/

2: https://arxiv.org/abs/1709.06648

3: https://arxiv.org/abs/1803.04933

"In this work, we used real-time error correction to real- ize a fully stabilized logical qubit whose lifetime is more than doubled compared to the best passive qubit encod- ing in the system, marking the transition of QEC from proof-of-principle studies to a practical tool for enhancing quantum memories."

https://arxiv.org/pdf/2211.09116.pdf

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