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I am currently reading the papers about the QEC (quantum error-correction) experiments of 2023 and while they are impressive (!), I would like to better understand what are their limitations. My goal is to better grasp the state of the art of the experimental side in QEC.

I am in particular focusing, the Google's one, and the Harvard's one (Bluvstein's paper).

Google experiment:

In Google's paper, they only looked at a quantum memory. They showed that for sufficiently low physical error-rates, increasing code distance of the surface code from $d=3$ to $d=5$ reduced the logical error-rate of the quantum memory.

[A] Am I correct to understand that while this effect occured, the logical error-rate of the quantum memory was still higher than the physical error rates of the gates used.

For instance in Fig 3 of the main text, their error-rate can get close to $1-0.97=3 \%$. Yet, the typical error-rate for their physical gates is always below $3 \%$ (see for instance S4 c) for the error-rate of CZ gates in the supplemental) (and an identity gate, which is the good gate to be compared to, for a physical clock cycle would likely have much lower error-rate than that).

Harvard experiment:

Among other things, in Harvard's experiment they create a logical Bell state between two logical qubit (by implementing a cNOT on an initial state $|+\rangle |0\rangle$. They measure the Bell stabilizers $X_1 X_2$ and $Z_1 Z_2$ and show that when the code distance increases from $d=3$ to $d=5$, the error-rate decreases.

My understanding is that there are two limitations:

[B] Like in Google I am (not sure?) that their logical error rate is lower than the physical ones

[C] They only do a single round of syndrome extraction, which from my understanding of the surface code is not sufficient to guarantee fault-tolerance if a sequence of logical gate is implemented in the algorithm (they would have need to show this improvement even if $d$ rounds of QEC are performed).

My questions in summary:

  1. Do you agree with the limitations I pointed out (specifically, my points [A], [B], [C])
  2. In Harvard paper they insist on the fact they do a "projective measurement" to measure the stabilizers. What do they exactly mean by that? Is it that they measure all the physical qubits in $X$ or $Z$ basis (hence they destroy the logical state).
  3. Are there any other important limitation in these experiments?
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  1. Yes.
  2. Sounds right. Assembling stabilizers by destructively measuring the state is typically less noisy. They're certainly working on extending to multiple rounds of syndrome extraction. Probably first with a reservoir of ancilla qubits, and then later with continuous reloading.
  3. Of course. For neutral atoms, they're running out of atoms as the experiment goes on. For superconductors, real-time decoding, ensuring that leakage isn't growing, fixing cosmic rays, etc.

Both really good papers getting signatures of QEC working though. Totally personally, I think the rep code stuff down to $10^{-7}$ error rates is also very compelling.

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  • $\begingroup$ Thank you very much, very useful. For point 2: do you know where it is explicitly said in Harvard's paper (i.e. the place where they explain that for them "projective measurement" means measuring all the physical data qubits in $X$ or $Z$ basis)? I did not find the place. $\endgroup$ Jan 16 at 9:57

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