...(continued)Congrats on the nice cultivation results, Jahan! I also wanna bring your attention to the work that first realized logical Hadamard on $RP^2$ surface code: https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.5.020360, which is the type of gate that can be measured for your cultivatio
...(continued)Hi Jahan, using three pi/3 phase states we can produce a |W> state. So it looks like with the pi/6 states that protocol produces you could construct a |W> state using 6 of them (though there might be a smarter way than just combining two pi/6 together to get a pi/3).
Though I don't have the details
I, the author, have found out some bugs regarding figures that should be fixed in the next version soon.
Good to know 😌. Thanks!
...(continued)I think it's wrong.
Shor's algorithm produces states that have exponentially huge numbers of likely outputs. Small subsections of the output will be exponentially close to uniformly random. So sampling small parts of the output is equivalent to sampling a uniformly randomly generated number. The
...(continued)I agree! Being able to (even probabilistically) produce a $|CCZ\rangle$ state or similar with $|C_{XYZ}\rangle$ states would basically solve the problem.
I started out restricting to $CX$ gates and $e^{i\pi Z/12}$ rotations (done probabilistically with $|C_{XYZ}\rangle$ states as specified in Br
...(continued)The main reason to expect the X+Y+Z magic state to be good is that it reaches further outside of the stabilizer octohedron compared to the X+Y magic state. It is "more magical". But conversions between different forms of magic are often lossy... so it could still be that it ends up more expensive to
...(continued)Using this space to advertise a question I have: are $|C_{XYZ}\rangle$ magic states (i.e., eigenstates of $(X+Y+Z)$) useful? Because while $|T\rangle$ states are kind of hard to cultivate on the surface code, $|C_{XYZ}\rangle$ states are quite easy, see [my thread here][1].
But just because they
@craig-gidney Thoughts?
We have updated the paper
with two new cultivation types.
Hope you'll enjoy.
More interestingly, the first author "Scited" **every single paper** listed here on Scirate but did not "cite" in their paper : P
...(continued)Hi, Alex
We thank you for pointing out the references. Indeed, we find Theorem 1.2 of https://arxiv.org/pdf/2505.16715 to be identical to our result; however, the proof differs somewhat, particularly in its dependence on the operator norm and accuracy.
Regarding the second paper, the BQP-hard
...(continued)To the authors,
Since last year, there has been substantial progress on trace estimation of quantum state powers, and I have been following this ongoing line of research with interest.
I have a few concerns regarding your manuscript. First, your main result, Theorem 1, is **completely identica
Congrats on your paper! Is your data available? Would you consider making your source code public?
...(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
Braneshop, and
the US National Science Foundation.
SciRate