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I have been reading some papers related to surface codes, and I have a doubt regarding the cycle time of surface codes. Both of the papers I have been studying (How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits and Flexible layout of surface code computations using AutoCCZ states) assume that their surface codes have a code cycle time of 1 $\mu s$ independent to the distance of such codes. Specifically, they consider two different distances $17$ and $27$, and still consider that the cycle time is the same. Is there a reason for this to be like that? or is it just an assumption made by the authors?

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In a superconducting qubit quantum computer there are separate control lines going to each qubit, so they can all be operated in parallel. Adding more of them doesn't slow down the cycle. If you look at figure 1 of "Exponential suppression of bit or phase flip errors with repetitive error correction", which runs rep codes from distance 3 to distance 11 on a superconducting qubit chip, you can see it shows a fixed duration rep code cycle lasting 960ns (without any reference to the distance). The surface code cycle basically doubles the unitary part which is an extra 80ns roughly for a total of 1.04 microseconds. So, in superconducting qubits, I think a 1 microsecond cycle time is an extremely reasonable assumption. It's basically already demonstrated.

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For other types of quantum computers, where there is less parallelism or slower operations, a 1us cycle time would not be a reasonable assumption. For example, "Realization of real-time fault-tolerant quantum error correction" used an ion trap and achieved a cycle time of around 200 milliseconds. They did use a complex cycle involving flag qubits (see fig 7) but it was maybe 3x more complex than a raw surface code cycle; not 200000 times more complex. The time difference is due to the physical operations being fundamentally slower and to the stabilizers being measured one after the other instead of in parallel.

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