...(continued)I just wanted to point out a possible typo in the no-distillation proof that would slightly change the exponential scaling required in the number of copies (but of course not its consequence).
If I'm not mistaken, the definition of $m_j $ (D11) implies $\sum_j m_j = d$, leading to $\sum_i \delta_i^
Nice use (and mention) of ChatGPT in research work :)
...(continued)Hi Stergios, Mark and Joschka,
Thanks for the response! Empirically Tesseract does have polynomial scaling - here is a log-log plot showing that Tesseract has comparable runtime to belief propagation (without LSD) for SI1000 superdense color code circuits:
![Runtime of BP+LSD, BP, Teseract an
...(continued)Where do the default algorithmic scalings for quantum algorithms in your calculator come from? I cannot find any references for most of these in your paper, or in the tool itself. For example, the runtime for exact quantum chemistry calculations is listed simple as "n^5" and for quantum acceleration
Hi Stergios,
Thanks for your reply! Glad to hear that you are planning to share the code soon.
Cheers,
Seok-Hyung
...(continued)Hi Oscar. Thanks for your interest in our new decoder. We stand by our claim that VibeLSD is the first *practical* decoder for colour codes that brings performance on par with the surface code. We absolutely agree that there are more accurate decoders. However, these decoders prioritise accuracy at
...(continued)Congratulations on this very nice paper! It's very exciting to see BP-based decoding doing so well on color codes, and VibeLSD seems like a very useful and general decoder. I had a few comments/questions:
1) I wanted to point out the neural network decoding of the color code experiment in this pape
...(continued)Just to be perfectly clear, in case anyone is still confused: the main text of this article demonstrates that the "brilliant" experiment, in the form originally proposed and analyzed by Wang et al, (i) does not exhibit Bell violation with unentangled photons (contrary to its title); (ii) is perfectl
...(continued)Hi Seok-Hyung, thank you for your interest and questions.
1. BP scheduling: Thanks for your feedback on this! We will separate parallel and serial pseudo-code (i.e. two algorithms) in V2 of the paper to make this important point clearer.
2. Runtime Analysis: Our decoder has worst-case cubic
...(continued)Congrats on your paper! Really interesting results, and I'm very excited to see colour code performance finally reaching on par with surface codes.
I have a few minor questions.
1. It seems the current serial schedule algorithm in Appendix A appears to behave the same as the parallel schedule
...(continued)Hi Craig, I think John and I are describing the same procedure. If you replace the measurement in your circuit by a CNOT onto a fresh qubit, the resulting unitary will map |psi,0,0> to T|psi> \otimes |somefixedstate>. Therefore running the circuit in reverse will map |phi> \otimes |somefixedstate> t
...(continued)Congratulations on the new paper! I just wanted to point out earlier work have already defined Gowers norms for quantum states ([arxiv2408.06289][1], [arxiv2305.10277][2]), given properties of the Gowers-3 norm, and several papers have shown testing of stabilizer states via Gowers-3 norm of quantum
...(continued)You're missing that the final state of the measured qubits can be complex. For example, try inverting this T gate gadget and see if it still does a T gate: https://algassert.com/quirk#circuit=%7B%22cols%22%3A%5B%5B1%2C%22H%22%5D%2C%5B1%2C%22Z%5E%C2%BC%22%5D%2C%5B%22%E2%80%A2%22%2C%22X%22%5D%2C%5B1%2
Best title of the year
...(continued)Thank you for your interest Noah.
We used BP-OSD, which gives better LEPs than MWPM (we didn't include that comparison in the paper, but we obtained data with vanilla MWPM). We haven't compared correlated matching to BP-OSD. Maybe comparing with Tesseract would be a good comparison, that would rea
...(continued)Shortly after posting this preprint, we became aware of an important issue with our results on the ability of the codes presented in this paper to host transversal CCZ circuits. Unfortunately, the set of conditions we impose on our codes (equations 22-25 in Appendix B of our work) is not sufficient
Thanks for the comment Tom! Also, we have updated a nomenclature table to this paper, which the first posting to arxiv missed.
Have not read much of this yet, but just wanted to say that the "Reader's Guide" section at the start of this paper is incredibly useful and I would love to see something like this become standard practice in papers of this length.
Interesting. I am curious if the improvement would persist if better decoders were used for the surface (i.e. rotated planar) code. E.g., correlated matching decoding.
...(continued)Just writing here to point out that we’ve updated our paper on arXiv. It now includes improved results for bivariate bicycle codes, including a timing analysis of our implementation of the proposed decoder. Furthermore, we include new results for surface codes, comparing the BP+BP+OTF decoder with b
I think this might be correct. I have some minor worries that |g> might still be entangled with (U |psi>), due something like irrelevant global phases becoming relevant relative phases when purifying the measurements by adding the ancillary system.
...(continued)If the original circuit implements a unitary, the extended circuit will always prepare a fixed pure state on the ancillas (unentangled from the original qubits), so you can prepare this state by running the forward circuit on an arbitrary input. (This is what I meant with the second paragraph of my
...(continued)Hi Craig
Right, this is a good point. Let's assume we're happy to defer the mid-circuit measurements to the end. In this case, an algorithm simulating a unitary U can be modeled as a unitary V s.t.
V * |psi> |0^a> = (U * |psi>) |0^a>,
where |0^a> is the ancilla register. This is the case i
...(continued)I disagree, because the circuit construction you are describing when run forwards has the ancilla qubits in an easily prepared state (all 0), but when run backwards needs the ancilla qubits prepared into non-trivial states in other for the inserted circuit to correctly map the output state back to t
...(continued)Given a general circuit, you should be able to automatically generate an isometric circuit that has the same effect when one ignores the added ancillas (e.g. each measurement gate gets replaced by a CNOT onto a fresh ancilla). This new circuit can be inverted gate by gate.
In particular you can d
Oh I see, sorry. I misunderstood the model. I thought it would be fine to measure a qubit, collect the outcome classically and then apply a correction on that same qubit (based on that classical outcome).
...(continued)I don't think this is unitary as written, you'd need to do measurements in the X basis (not just reset) and some classically controlled corrections depending on the measurement outcomes, right? E.g take f(x)=x, then this is just a teleportation protocol, and the corrections are obvious (conversely i
...(continued)Assuming one-way permutations exist, I think it should be in general hard to invert unitary-effect operations that involve measurements/feedback (this is similar to the examples you mentioned). Let f be a OWP. Then the mapping |x> -> |f(x)> is unitary, since it's just a permutation unitary. Given th
...(continued)Very interesting paper. Somewhat tangentially, in the introduction you mention
> Our standard rationale for being given access to both X and X† is as follows: we imagine that X is given as a quantum circuit on a scalable quantum computer, in which case X† can be performed by simply inverting the qu
...(continued)the 2D families in the paper referenced in the comment look to be exactly the same codes as the ones in the paper; the new angle seems to be constructing them as GB codes (with simple polynomials at that) which is pretty interesting. It would also be interesting to see if this can be extended to th
How does your result relate to the construction in https://arxiv.org/abs/2505.10403? They seem to share similar parameters.
Thanks for pointing this out! It is indeed helpful for us to see that this concept of global stationarity is important in other contexts, as our Lemma 3 derives global stationarity from the perspective of relational equilibrium (i.e. local subsystems being invariant).
...(continued)Coincidentally, the global stationarity given by Eq. (7) is also what I assumed to derive an unambiguous notion of time reversal for open quantum systems (in the context of time-reversal symmetry and detailed balance) in Proposition D.1 in https://arxiv.org/abs/2403.12896. Really cool to see it in w
...(continued)Interesting work! I'd like to shamelessly promote some earlier work of ours that studies the same problem of quantum metrology with environmental measurements, albeit using a larger-Hilbert-space approach:
Mankei Tsang, Howard M. Wiseman, and Carlton M. Caves, "Fundamental Quantum Limit to Wavefo
It seems that this now completely resolves our conjecture in https://arxiv.org/pdf/1608.05317, which already showed the "easy" direction of the bound.
...(continued)Yeah, I agree that with this setup the efficiency is likely too low.
That said... if you somehow have reliable storage, then efficiency stops being an issue for violating the inequality. The entanglement generation doesn't need to be spacelike separated, only the entanglement consumption. So you
...(continued)Sure, I'm no stranger to the usefulness of post-selection. As you point out, SPDC plus heralding is still the best way to get hold of single photons in quantum optics!
However, if you are going to use post-selection, you have to take into account the reduced efficiency. Otherwise, one would not
...(continued)I wouldn't be so hard on post-selection. It's very possible to analyze it in confusing ways, but I think it will ultimately be extremely useful for building larger systems.
For example, quantum networks will need to distribute entanglement across their links. The quality of that entanglement can be
...(continued)Just wanted to point out that (up to cyclic shifts) the polynomials for your [[12,2,3]] code are equivalent to (1+y) and (1+xy). These are the same polynomials used to generate the twisted torus in [Breuckmann and Eberhardt, 10.1109/TIT.2021.3097347, Figure 8] with the same code parameters. These 2
...(continued)I'm surprised to see so few comments. It is well-known that separable states cannot demonstrate any kind of non-locality, given the accepted definitions of these terms. See for instance the classic reviews on "Quantum Enganglement" by the Horodeckis (arxiv.org/abs/quant-ph/0702225) and "Bell nonloca
...(continued)I think a better title for this paper would be "producing entanglement by frustrated interference and mode measurements". The title's current claim that the state isn't entangled seems clearly disproven by equation 15 (the superposition before measurement). The state described in that equation is en
...(continued)Woke up to an email pointing out that a lot of this work overlaps with Appendix C of https://scirate.com/arxiv/2402.02185.
What is still unique to my paper?
- Showing this circuit increases the timelike distance
- Making the circuit remove leakageWill update the paper with a note credi
This very clear to me now. Thank you!
...(continued)Thank you for your question. In fusion-based quantum computation (FBQC), a quantum computation is executed by repeatedly generating copies of entangled few-qubit resource states and performing fusions (entangling two-qubit measurements) between pairs of resource states, as well as single-qubit measu
Figure 17 displays a `[[4, 2, 2]]` code where a `T` measurement is performed on the first qubit, a `Z` measurement on the second qubit, and `X` measurements on the third and fourth qubits.
How does the state injection work if all the states are collapsed at the beginning of the protocol?
It's been difficult verifying your results (figure 3). Do you have additional information that you can share on the circuit noise models you used for the two syndrome extraction methods?
> No other equations are affected.
Glad to know! Cheers :)
...(continued)Ah, you are correct! That equation should be equal to a sum over x and tilde x that are stabilizations, and not just permutations of one another. Many apologies, we expanded this section of the proof at a later stage for readability, and introduced this error.
This does not change any later steps
...(continued)Hi, and thanks for this very nice paper! I'm still reading it, but there's something I'm not sure to understand, and I hoped you could clarify it for me.
On page 22, below Equation (57), you write:
> When averaged, the global random phase $F$ enforces that $\tilde{x}$ and $x$ are related by a perm
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