Thank you so much. I just realized this!
Dear Zhenhuan, if the group only contains the identity, the channel only needs to purify the maximally mixed state (the unique state in the algebra spanned by the group). It achieves this by always outputting the maximally entangled state (regardless of the input state).
...(continued)Congratulations on the intersting result!
I was wondering the relationship between your result and Theorem 3 in [arXiv:2509.21111][1], which proves the exponential sample complexity lower bound of preparing a single purification state.
Your result seems to hold for all unitary groups. So if th
If you want to try it yourself Min's implementation of the beam search decoder is now available here: https://github.com/ionq-publications/BeamSearchDecoder
The term *light rectangle* was used [20 years ago by N. David Mermin with the same meaning](https://arxiv.org/pdf/gr-qc/0411069). Mermin also deduces the invariant interval from the area of a light rectangle drawn on the Euclidean plane.
...(continued)Hi Ben, thanks a lot for your kind words!
Whether "optimal" should be reserved only for results that are tight without logarithmic factors is, we think, still somewhat up for debate. 🙂
For example, one of the two concurrent seminal papers establishing quantum state tomography optimal up to logs w
It's great as a quantum-inspired algorithm, but what are the prospects of ever executing this on FTQC, given the scaling of the sampling cost of VQE? I mean, isn't the number of samples required to reach a decent accuracy prohibitively high above ~10 qubits?
...(continued)I fail to see a novel contribution in this pre-print. Since Shor put out his groundbreaking paper [[Shor94]](https://doi.org/10.1109/SFCS.1994.365700) [[Shor97]](https://doi.org/10.1137/S0097539795293172) back in 1994 many proposals for improvements have been published. Using divisors of the order $
...(continued)This is an excellent piece of work, congratulations on the result! I am particularly excited to see query complexity bounds established for general quantum channels, going beyond states and unitaries.
I just wanted to clarify one point. Would it be more appropriate to use the term *near-optimal l
...(continued)Congratulations on this nice paper! I have a small query regarding Algorithm 2 (Sliding-Window Decoding), specifically in lines 17 and 18. In the pseudo-code, m_com is passed to the inner DECODE function (line 17), while m_cvg is used to mask the error vector ê (line 18). However, based on the input
it might be interesting for you to know that somewhat related states were studied here from a different perspective (in particular using continuous groups)
https://arxiv.org/abs/2510.06602
Thanks for the reference!
Sadly, we were not aware of your work. The polygamous behaviour you describe is exactly of our interest. I'll look into that.
Congratulations on the results!
...(continued)It is always great to see more work exploring these important properties of non-locality. I wanted to highlight our work from earlier this year studying bipartite monogamy/polygamy. PRR : https://journals.aps.org/prresearch/abstract/10.1103/1m7q-rgrh. (ArXiv version: https://arxiv.org/abs/2405.20286
Link to the repo: https://github.com/QoroQuantum/maestro
...(continued)The work is interesting, but there are several major issues that make it difficult for me to fully trust the authors’ claims. Clarifying these points would greatly help my understanding.
1. It is unclear whether the experiments were actually conducted according to the definitions proposed in the
...(continued)Without having looked at this paper, the following comments. The fact that one has to use a different norm for errors (diamond norm) for FTQC to cover general errors has been known since Kitaevs papers "Quantum error correction with imperfect gates" and "Quantum computing: algorithms and error corre
...(continued)@Mingyu I suspect you made some mistake in the simulation, or were simulating a non-fault-tolerant construction (e.g. the output qubit being a single physical qubit). When I put 5-to-1 simulation into Quirk, I see the same qualitative "continuous perturbations become perturbations with pauses near t
...(continued)Lovely stuff - just wanted to signpost our paper which also considers these errors at the resource state level, applying it to a full architecture scirate.com/arxiv/2507.16152. I'd say our work is most closely aligned with what you talk about, since we don't use polarization encoding and do consider
Interesting. I have some old simulation for 5-to-1 distillation that says otherwise (coherent rotations before the MSD circuit is suppressed but not those after it). Thanks for correcting, I might check this out
...(continued)@Mingyu What? That's definitely false about the 15-to-1 distillation. One of the most common examples I show people when introducing them to Quirk is that if you put global continuous rotations at the end of the 15-to-1 distillation, and then look at the postselected output state, it rotates continu
Thanks, I'm glad that splitting-up helped!
...(continued)Hi Craig,
Thanks for the question! Yes, it's not known if A implies B! The problem is not limited to fault-tolerance but also is there in error correction. So let's say A' refers to "a family of error correcting code having error correcting threshold for stochastic noise" and "not B'" refers to "
...(continued)Right... maybe it's related to the difficulty of designing the entire FTQC architecture that works for both stochastic and coherent noise models, which this paper seems to do successfully. I can give you a really dumb example where typical protocols fail under the noise model where you have small an
...(continued)But in the context of scaling-with-distance-or-not-with-some-threshold, that distinction shouldn't matter... right? I might need a bigger distance or a stricter threshold to ensure the bound holds despite quadratic growth rather than linear growth, but qualitatively that detail shouldn't be able to
...(continued)I think the concern has been that in a stochastic error model, the error builds up linearly, but in a worst-case coherent error model where error is a sigma_z rotation by some angle theta, error builds up quadratically (p=sin^2(theta) then sin^2(n*theta) ~ n^2*p), so it has been hard to "translate"
I appreciate the splitting-up of 2408.05260 into two. It's a large paper with lots of results that could be missed. (At least, I missed some of them)
...(continued)I have a background question: are there any known examples where a circuit is known to be fault tolerant to stochastic noise (call this "A") but not fault tolerant to general noise (call this "not B")?
I ask because I was surprised to learn it wasn't known that the A implies B. My intuition is that
Hi Timo,
Thanks for your interest! I’m aware of your work; ultimately I decided to use a distinct name so readers wouldn’t get tripped up by the terminology.
Interesting work! Just wanting to point out that previously ACID was known as LSD in the community, see here: https://arxiv.org/abs/2406.18655
...(continued)Congratulations on your paper! It's really nice to see this dense packing simulated. I think there is a small mistake in your Figure 4, namely what constitutes a Z hook error should be parallel with the logical Z operator rather than perpindicular to it. Similarly in Figure 3 if the data qubits c an
...(continued)Very nice paper! In Section 5.2, you state that
> in lattice surgery each move costs one stabilizer measurement round, independent of distance.
However, if my understanding is correct, according to the [cited paper][1] a move takes $d$ stabilizer measurement rounds (for a distance $d$ surface
...(continued)It’s very helpful to see a careful re analysis of whether DESI DR2 really requires dynamical dark energy. A quick perspective from a framework where “Λ” actually has a controlled meaning.
In a recent series of notes I constructed a gauged constant‑vacuum (GCV) framework where the strictly spaceti
...(continued)These full shape DESI DR2 cosmological constraints are an important part of the current DE discussion. A quick perspective from a framework where “Λ” actually has a controlled meaning.
In a recent series of notes I constructed a gauged constant‑vacuum (GCV) framework where the strictly spacetime‑
...(continued)Thank you for this careful analysis of dynamical dark energy using DESI DR2 BAO. A quick perspective from a framework where “Λ” actually has a controlled meaning.
In a recent series of notes I constructed a gauged constant‑vacuum (GCV) framework where the strictly spacetime‑constant part of the m
想请教一下每个agent的具体的打分方式：如果用的自己训练的模型，是如何训练的呢
为什么agent增加之后有的指标掉的这么厉害呢；N-gram中的n是取多少呢，data_synthesizer是如何实现的呢，如何生成的呢，自动生成的么，
𝑅𝑠𝑡𝑒𝑝和Renhanced有啥区别么，有没有emb和rerank一起结合MARM进行对比评价的呢
...(continued)Thank you very much for your thoughtful and detailed comment. Let me clarify our perspective and address your concerns point by point:
About the effective trainable region:
Our construction does not restrict all training dynamics to the shallow $O(\log n)$-depth region near the gadget layer. As sho
...(continued)I have concerns about whether the proposed circuit construction actually addresses the problem. The idea of the construction can be described with an analog in classical machine learning:
Suppose I have a model M for, say, image generation. I create a new model M' which consists of the following:
Outstanding work!!
interesting paper! did you find any examples that give a stabilizer or CSS code; preferably with d>2
Thanks Tom!
welcome back
...(continued)> You say that the values $r_j$ are random guesses, but this directly contradicts the paper. The paper doesn't say "choose $r_j$ randomly", it says: "The values $r_j$ are trial orders, typically a list of hypothesized orders (or their multiples/divisors) that the true order r may belong to."
Per
...(continued)I don't want to complain too harshly about doing examples, because having examples is a huge improvement over not having any. But... an example case in the tens of millions is really not large enough to be convincing here. To quote Scott Aaronson:
> We’ve had decades of experience to tell us that
...(continued)> The values rj are trial orders, typically a list of hypothesized orders (or their multiples/divisors) that the true order r may belong to.
> Basically you will need to know the entire factorization of the period for this to work, but if you knew that then you would already know the period and s
And yet, despite this and many other retractions and BS papers "Nature" inexplicably continues to be treated as the pinnacle of scientific achievement...
I'm glad someone did the work of showing these representations should be safe. Solid stuff.
Thanks a lot for the reply! I'm looking forward to seeing what kind of codes you can obtain with these techniques.
...(continued)**An update on “Magic Tricycles: Efficient magic-state generation with finite block-length quantum LDPC codes”:**
We have made several major revisions to this work that are reflected in the current Arxiv version of the paper. In addition to correcting the technical issue with the original submissio
...(continued)Thank you both for your comments. I would like to see objections formulated more precisely: which part of the proof do You see as problematic? I am not sure that I understand what the comment "The N + 1 subspaces of operator space have nothing to do with the Hilbert space you start out with" really
Braneshop, and
the US National Science Foundation.
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