Dynamical codes for hardware with noisy readouts

Alex Townsend-Teague; Benjamin J. Brown; Jens Eisert; Markus S. Kesselring; Oscar Higgott; Peter-Jan H.S. Derks

REVIEW 3 major objections 5 minor 22 references

Dynamical codes for hardware with noisy readouts

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Repeating measurements in a dynamical quantum error-correcting code shrinks its spacetime cost when readout noise dominates, but not otherwise.

desk verdict Useful, honest numerical study of DCCC schedule tailoring; the teraquop-volume ordering rests on extrapolation and should be read as provisional. read the letter →

arxiv 2505.07658 v2 pith:3LYNKDEO submitted 2025-05-12 quant-ph

Peter-Jan H.S. Derks , Alex Townsend-Teague , Jens Eisert , Markus S. Kesselring , Oscar Higgott , Benjamin J. Brown This is my paper · ORCID

classification quant-ph

keywords dynamicallycondensedcolourcodesteraquopvolumehoneycombcodebeliefmatchingminimum-weightperfectmeasurement-biasednoiseschedule-inducedgauge-fixinglatticesurgery

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks how to choose the measurement schedule of a dynamically condensed colour code, a family of dynamical stabilizer codes that can serve as the basic block of a lattice-surgery quantum computer, when the hardware's weak point is noisy readout. To answer it, the authors introduce the teraquop volume: the number of qubits times the number of measurement rounds needed to bring the logical error probability below $10^{-12}$. They find that repeating measurements in the schedule improves the volume substantially when the noise is biased toward measurement errors, but has negligible effect for unbiased or Z-biased noise. They also find that the choice of decoder matters as much as the choice of code: belief matching makes the X1Y1Z1 code the best performer while minimum-weight perfect matching makes it the worst.

What carries the argument

The central object is the measurement schedule of a dynamically condensed colour code, specified by how many consecutive rounds of XX, YY, and ZZ edge measurements are performed, giving XaYbZc or XaZb codes. Repeating measurements is schedule-induced gauge-fixing: it creates two-measurement edge detectors that catch measurement errors directly, at the cost of lengthening the face detectors and worsening timelike distances for data-qubit errors. The paper's performance metric is the teraquop volume, the product of qubit count and measurement rounds needed to reach a $10^{-12}$ logical error rate. The comparison tool is the decoding graph, where measurement errors that violate four detectors become hyperedges; belief matching pre-processes these hyperedge probabilities before minimum-weight matching, recovering information that ordinary MWPM throws away.

What would settle it

Run the same memory and stability experiments at substantially larger distances, say distance 24 or 32 for phenomenological noise, and check whether logical error rates continue the exponential decay that the line fits assume. A second check is to simulate the X1Z1 code with planar boundaries and compare its logical error rate to the toric result; if planar performance differs markedly, the volume rankings built on toric simulations would need revisiting.

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Extended reading notes

Core claim

The paper's central claim is that the optimal DCCC measurement schedule is not intrinsic to the code but is co-determined by noise bias and decoder. In all three phenomenological noise models studied, the X1Y1Z1 code under belief matching has the smallest teraquop volume, while the same code under MWPM has the largest; the effect grows with measurement bias. Repeating measurements, a form of schedule-induced gauge-fixing that creates two-measurement edge detectors, improves the teraquop volumes of both the XaZb and XaYbZc code families under both decoders when the noise is measurement-biased, but is negligible otherwise, contrary to the authors' initial expectations. At the circuit level, the superconducting-inspired noise bias is not strong enough to make repetition worthwhile, while under entangling-measurement noise the X2Z2 code wins with MWPM. Across most of the parameter sweep, performance differences come primarily from the number of measurement rounds required rather than the number of qubits, which is why the volume metric matters.

Load-bearing premise

The teraquop volumes are extrapolated from logical error rates at small code distances down to $10^{-12}$ by assuming exponential decay in one code dimension and linear dependence on the others; if error rates bend at larger sizes, the reported volumes and rankings could change. The simulations also assume a torus, and planar performance for the X1Z1 code has not been verified.

Editorial extensions

If this is right

Lattice-surgery resource estimates that use only the teraquop footprint will miss most of the difference between codes, since the gaps come primarily from the number of measurement rounds.
Hardware with measurement-dominated noise should use schedules with repeated measurements; hardware with unbiased or Z-biased noise gains little from repetition.
Decoder choice should be made jointly with code choice, because belief matching can turn a worst-performing code into the best-performing one under the same noise model.
Under entangling-measurement noise and MWPM, the X2Z2 schedule wins, showing that the optimal schedule also depends on how the multi-qubit measurement is physically implemented.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

For a readout-limited device, the practical recipe suggested by these results is a measurement-repeated X1Y1Z1 schedule decoded with belief matching; the paper does not spell this out as a single recommendation, but it follows from the per-bias best-code tables.
The teraquop volume metric could be used to benchmark other spacetime codes against DCCCs, but this paper only compares codes within the DCCC family.
At Z bias beyond 16, asymmetric repetition schedules that spend more time in detectors sensitive to Z errors may begin to pay off; the paper's parameter sweep stops too early to see this.
The reported ranking may be sensitive to the assumption that timelike E and M errors occur equally often in a lattice-surgery computation; if one type dominates, the optimal height differs from the averaged value used here.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Punchline: this is a well-executed numerical paper that will be useful to people working on Floquet/dynamical codes, but the headline rankings are extrapolated from small lattices to 10^-12 error rates, so I would take the precise ordering as provisional.

The genuinely new content is the systematic sweep: the teraquop volume (a natural spacetime extension of teraquop footprint), the application of schedule-induced gauge fixing (repeating measurements) to DCCCs, and the demonstration that under measurement-biased noise repeating helps while under Z-bias or unbiased it doesn't. The decoder story is also clean: all measurement errors in the X1Y1Z1 code are hyperedges, which is bad for MWPM and good for belief matching, and the numerics bear that out. The paper ships code and uses the standard Stim/Sinter/PyMatching/BeliefMatching stack, so the numbers are reproducible in principle. Self-citations to prior constructions are appropriate.

Soft spots: the teraquop volumes are not measured but extrapolated. The fits use d=4,8,12,16 (d=2,4,6,8 for EM noise) and assume exponential decay in distance stays straight to 10^-12. The rankings sometimes differ by factors of 2-10 in block height, so a slope change or curvature term could reorder codes. The stress-test point about belief matching using only 10^4 shots is fair: at the largest distances, that gives maybe 100 expected errors at p_L ~ 10^-2, and at lower rates you can get zero observed errors, which makes line fitting delicate. I don't think this invalidates the qualitative conclusions; the effects are large and consistent. But I wouldn't anchor on the exact volume numbers. Also, all simulations are on a torus; the authors note planar X1Z1 performance is unverified. That's an acknowledged limitation, not a hidden one.

Who is this for? People choosing between DCCC schedules for a specific hardware noise model, and anyone citing resource metrics. It deserves a serious referee; the referee should ask for a sensitivity check on the extrapolation (e.g., fit with and without the largest distance, or report where slopes change), but I would not desk-reject it.

Verdict: accept with revisions.

Referee Report

3 major / 5 minor

Summary. The paper studies dynamically condensed colour codes (DCCCs) under noise models with tunable measurement bias and Z bias, and introduces the teraquop volume as a spacetime generalization of the teraquop footprint. Using Stim/Sinter with PyMatching (MWPM) and BeliefMatching, it simulates XaYbZc and XaZb codes on a torus for phenomenological, standard depolarizing, superconducting-inspired, and entangling-measurement noise. It reports that (i) MWPM favors XaZb schedules while belief matching favors XaYbZc schedules, (ii) differences in volume are dominated by the number of measurement rounds rather than qubit count, and (iii) repeating measurements helps mainly under strong measurement bias. The paper also provides analytic distance and hyperedge-likelihood tables and makes the simulation code publicly available.

Significance. If the reported teraquop-volume rankings are correct, the paper gives a concrete, decoder- and hardware-aware rule for choosing DCCC schedules, and the teraquop volume is a useful metric for comparing spacetime overhead. The strengths are the use of a standard, externally benchmarked simulation pipeline (Stim/Sinter/PyMatching/BeliefMatching) with explicit noise models and error bars; the public code for full reproducibility; and the transparent analytic tables (Tables 3, 4, and 6) that separate distance effects from decoder-dependent hyperedge effects. The central caveat is that the headline volumes and orderings are extrapolated from small simulated distances, so the quantitative ranking is less secure than the qualitative trends. The finding that volume differences come predominantly from measurement rounds rather than footprint is an important caution for metric choice in QEC resource estimation.

major comments (3)

[Section 3.1] The headline volumes and rankings are extrapolated, not directly simulated. The fits use distances d=4,8,12,16 (d=2,4,6,8 for EM noise) and assume log p_L is linear in d with linear dependence on the other two dimensions, then extend to 10^-12. Figure 16 validates the linear-in-nM and linear-in-h dependence only for E memory experiments under MWPM for the X1Z1 and X1Y1Z1 codes; no equivalent check is shown for belief matching or for repeated codes. The belief-matching fits use 10^4 shots per point (Appendix A), so at the largest d a run may have zero or very few logical errors, making the fitted slope and intercept carry large relative uncertainty. Since the ranking differences in Key points 4.5 and 5.7 are factors of a few in the teraquop height, a modest change in slope or a bend at d>16 could reorder the codes. Please add data at larger distances or provide a bounded extrapolation analysis, report the number of logical errors per point for the belief-matching fits, and state whether the linear-dependence assumption has been checked for the repeated schedules and for belief matching.
[Definition 3.1] The definition requires the probability of any spacelike or timelike logical error to be at most 10^-12, but the estimation procedure minimizes each of nE, nM, hE, and hM separately from four different experiments and then forms the product nE * nM * (hE+hM)/2. The text does not give a union bound or an independence justification for combining the four channels. If the four logical error channels are positively correlated or simply additive, the quoted volume can underestimate the volume needed for the total logical error probability to reach 10^-12. Please state the approximation being made and estimate its effect on the reported volumes.
[Section 2.9] All simulations are on a torus, and the section explicitly says the authors have not verified the planar X1Z1 code, while the planar X1Y1Z1 code was shown in Ref. [GNM22] to perform essentially as well. Because the motivation is hardware and lattice surgery, the transfer of the torus results to planar surface-code blocks is load-bearing for the practical conclusions. Please either add planar boundary simulations for the key comparisons (at least X1Z1 and X1Y1Z1 under the relevant noise models and decoders) or explicitly restrict the central claims to the torus case.

minor comments (5)

[Figure 10 caption] The caption contains the typo 'mesurements'; it should be 'measurements'.
[Sections 3.1 and 3.3] There are typos 'teraqoup' and 'necesarrilly' in the text; please correct them.
[Figure 15 caption] The caption and axis labels use the placeholder '10□12' instead of typeset superscripts; please fix the rendering.
[Section 5.2] The text refers to '(nM,mE,h r)-block' where the second dimension should be nE, not mE; please correct the typo.
[Key point 1.4 and Figure 3 caption] Key point 1.4 says repeating measurements is not worthwhile under SI noise, while the Figure 3 caption notes a possible improvement for X1Y1Z1 in SI noise; please reconcile the wording to avoid an apparent contradiction.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the teraquop-volume ranking is an extrapolated simulation output, not a fitted target or a self-citation chain.

full rationale

The paper's central results (Key points 4.5 and 5.7) are numerical teraquop volumes obtained by simulating memory and stability experiments with Stim, PyMatching, and BeliefMatching, then extrapolating logical error rates to 10^-12 (Section 3.1, Appendix A). The teraquop volume (Definition 3.1) is defined independently of any code ranking: it is the minimal spacetime volume at which the logical error probability is 10^-12, and the reported volumes follow from the simulations rather than being imposed as fit targets. The distance-dependent linear fits in log(p_L) versus d are standard threshold extrapolations; the extrapolation quality is explicitly checked for MWPM in Figure 16, and its limitations are acknowledged in Section 3.3 (equal space/time weighting, schedule and patch effects) and Section 2.9 (planar X1Z1 performance not verified). Prior-work citations ([KdlFT+24] for DCCC definitions, [HB21] for SIGF, [GNFB21]/[GNM22] for noise models and the footprint metric) supply constructions and benchmarks but do not determine the measured error rates or the resulting ranking; the belief-matching decoder is independently implemented in Refs. [HBK+23]/[Hig23]. No equation in the paper defines a prediction in terms of the fitted quantities, and no load-bearing claim rests on a self-citation chain. The stated extrapolation and torus-to-planar caveats are correctness risks, not circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claims depend on the chosen noise models, the extrapolation of simulated error rates to 10^-12, and the torus-to-planar transferability assumption. No target quantity is fitted from data; the noise parameters are benchmark inputs.

free parameters (3)

Total physical error rate, phenomenological noise = 10^-3
Chosen by hand in Eq. (3) to keep the physical error rate fixed while varying bias; conclusions are reported at this rate, not fitted.
Circuit-level physical error rates (SD, SI, EM) = 5e-4, 2.5e-4, 2.5e-3
Chosen to be below threshold and comparable to prior literature; not fitted to the results.
Bias grid (eta_m, eta_Z) = {1,4,8,16} x {1,4,8,16}
Simulation grid defining the scope; Z-bias conclusions are limited to eta_Z <= 16, as acknowledged in Section 5.4.

assumptions (5)

standard math Stabilizer formalism and detector error model definitions from prior literature are correct for DCCCs.
Used throughout Section 2; central to constructing decoding graphs and logical error labels.
domain assumption The three noise models (phenomenological, SI, SD, EM) accurately model relevant hardware with measurement-biased noise.
Table 2 and Section 2.3; the claims are conditioned on these choices.
domain assumption Logical error rates decay exponentially in the tailored distance and linearly in other dimensions, so independent optimization and line extrapolation to 10^-12 are valid.
Section 3.1 and Figure 16; underpins every teraquop volume estimate.
domain assumption Toric simulations are a valid proxy for planar surface-code blocks.
Section 2.9 states planar X1Z1 performance is not verified; torus is used for fair comparisons.
domain assumption Timelike E and M errors occur roughly equally often in lattice surgery, justifying h = (hE+hM)/2.
Section 3.1; affects the reported teraquop heights.

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Cite this review

Pith. "Pith review of Dynamical codes for hardware with noisy readouts." pith.science (2026). https://pith.science/paper/3LYNKDEO

@misc{pith2026250507658,
  author       = {Pith},
  title        = {Pith review of: Dynamical codes for hardware with noisy readouts},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3LYNKDEO}},
  note         = {Machine review of arXiv:2505.07658}
}

abstract

Dynamical stabilizer codes may offer a practical route to large-scale quantum computation. Such codes are defined by a schedule of error-detecting measurements, which allows for flexibility in their construction. In this work, we ask how best to optimise the measurement schedule of dynamically condensed colour codes in various limits of noise bias. We take a particular focus on the setting where measurements introduce more noise than unitary and idling operations - a noise model relevant to some hardware proposals. For measurement-biased noise models, we improve code performance by strategically repeating measurements within the schedule. For unbiased or $Z$-biased noise models, we find repeating measurements offers little improvement - somewhat contrary to our expectations - and investigate why this is. To perform this analysis, we generalise a metric called the teraquop footprint to the teraquop volume. This is the product of the number of qubits and number of rounds of measurements required such that the probability of a spacelike or timelike logical error occurring is less than $10^{-12}$. In most cases, we find differences in performance are primarily due to the number of rounds of measurements required, rather than the number of qubits - emphasising the importance of using the teraquop volume in the analysis. Additionally, our results provide another example of the importance of making use of correlated errors when decoding, in that using belief matching rather than minimum-weight perfect matching can turn a worst-performing code under a given noise model into a best-performing code.

Figures

Figures reproduced from arXiv: 2505.07658 by the authors.

**Figure 1.** Squares in the top patchwork plot are red (green) if the code with the smallest teraquop volume is an XaZ b code (XaZ bY c code). A darker shade indicates a higher volume. The four bar plots show the footprints of the 10 best codes at the four limits of the simulated biases. The error bars are explained in Appendix A. Decoding is performed using MWPM. For all noise models investigated here, the XaZ b code outperform… view at source ↗

**Figure 2.** Same plot as in [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Teraquop volumes of XaY bZ c and XaZ b codes for three circuit-level noise models; standard depolarizing noise with p = 0.0005, superconducting inspired noise with p = 0.00025, and entangling measurement noise with p = 0.0025. Decoding is performed using MWPM. In each case, the code with the best teraquop volume is from the XaZ b family, though the difference is small. Repeating measurements broadly has negligible e… view at source ↗

Figures from the paper (27 more)

**Figure 4.** Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: (a) A Y ⊗2 yellow edge operator ey,Y . (b) An X⊗6 magenta face operator fm,X. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

**Figure 6.** Figure 6: For a subset of qubits, we show the sequence of measurements defining the X1Y 1Z 1 (middle) and X1Z 1 (right) honeycomb codes. This figure uses the ZX-calculus [CD11], a rigorous graphical language for quantum mechanics. For those unfamiliar with the ZX-calculus, a cra…

**Figure 7.** Figure 7: Representatives of logical E and M operators for the X1Y 1Z 1 (left) and X1Z 1 (right) honeycomb codes at timesteps t mod 6. Timestep 0 mod 6 is the top left subfigure in each cycle. Boundaries are periodic, forming a torus. Throughout this work we say a DCCC encodes o…

**Figure 8.** Figure 8: Subfigures (a), (b) and (c) show the non-identity Pauli gates as ZX-diagrams. Subfigures (d) and (e) show examples of errors in a phenomenological noise model. Specifically, (d) shows an X error occuring before an eκ,X measurement, while (e) shows a measurement error o…

**Figure 9.** Figure 9: Subfigures (a), (b) and (c) show the |+⟩ state, X measurement and CX gate respectively as ZX-diagrams. Subfigures (d) and (e) show examples of errors in a circuit-level noise model, where two-qubit gates and a single-qubit measurement are used to measure eκ,X. Specifi…

**Figure 10.** Figure 10: A subset of detectors of the X1Y 1Z 1 code (left) and the X1Z 1 code (right). Certain wires in this ZX-diagram are highlighted red, green or blue; they constitute a Pauli web, which we go into in more detail in Appendix B. In essence, one can think of a Pauli web as t…

**Figure 11.** Figure 11: An em,Y measurement error in the X1Y 1Z 1 honeycomb code, which violates four detectors. In the top left subfigure, we show the error as a ZX-diagram. Since it violates four detectors, it corresponds to a hyperedge in the decoding graph (top middle). This hyperedge th…

**Figure 12.** Figure 12: On the left we show five timesteps from the X1Y 1Z 1 code. Areas coloured cyan, magenta and yellow denote detectors, though to make the diagram simpler we have not drawn the Pauli webs that define them (see Appendix C for a detector cheat sheet). On the right we show …

**Figure 13.** Figure 13: On a subset of qubits, we show a spacelike (left) and timelike (right) logical error in the XYZ honeycomb code consisting only of data qubit errors. The spacelike and the timelike logical errors in Crumble [Gid23a], a prototype tool for Clifford circuit exploration. 2…

**Figure 14.** Figure 14: Schematic explaining how the teraquop volume of a DCCC is estimated. We perform E-memory experiments to estimate the number of columns n˜M of hexagons in any DCCC that reaches the teraquop regime. Then M-memory experiments estimate the number of rows n˜E required, and…

**Figure 15.** Figure 15: Plots showing line-fits to determine the minimal value of nE, nM hE, and hM such that the probability of any logical error occuring is 10−12. The value of the x-axis wherever a dotted line would first cross the line y = 10−12 is the value used for the corresponding te…

**Figure 16.** Figure 16: Plots showing the logical error rate of E memory experiments with varying nM and h. Decoding is performed with MWPM. The plots confirm that the probability of a spacelike logical E error occurring depends linearly on nM and h. depend on the specific choice of DCCC, as…

**Figure 17.** Figure 17: Comparison of n˜E, n˜M, h˜E, h˜M, and teraquop volume of the X1Y 1Z 1 and X1Z 1 code decoded using MWPM and belief matching for unbiased, Z-biased, and measurement-biased phenomenological noise. In all cases, using belief matching rather than MWPM turns the X1Y 1Z 1 c…

**Figure 18.** Figure 18: Comparison of n˜E, n˜M, h˜E, h˜M, and teraquop volume of the X1Y 1Z 1 and X1Z 1 code decoded using MWPM and belief matching for three circuit level noise models; standard depolarizing noise with p = 0.0005, superconducting inspired noise with p = 0.00025, and entangl…

**Figure 19.** Figure 19: Left: a detector in the X1Y 1Z 1 code with volume 6 · 4 = 24 consisting of 12 measurements (as can be read off from the Pauli web – see [PITH_FULL_IMAGE:figures/full_fig_p032_19.png]

**Figure 20.** Figure 20: Top: a spacelike logical error in the X1Y 1Z 1 code consisting entirely of measurement errors. Bottom: the analogous spacelike logical error in the X2Y 2Z 2 code. This again consists entirely of measurement errors, but there are twice as many of them as before, becaus…

**Figure 21.** Figure 21: Left: a subset of a timelike logical error in the X1Y 1Z 1 code consisting entirely of data qubit errors. Middle: the analogous timelike logical error in the X2Y 2Z 2 code, with half (E or M) of the face detectors indicated. Right: the same logical error but with the …

**Figure 22.** Figure 22: (a) A measurement error in the X2Y 2Z 2 code. (b) The ordinary edge it corresponds to in the decoding graph. (c, d) The E detectors the error violates, drawn as Pauli webs. (e, f) The M detectors the error sits on but does not violate, drawn as Pauli webs. Compare thi…

**Figure 23.** Figure 23: (a) Five timesteps of the X3Y 3Z 3 code, centered on a yellow face. The shaded yellow areas denote a face detector and 12 edge detectors. (b) The edges between the face detector and the 12 edge detectors in the decoding graph. The face detector has 12 further edges (u…

**Figure 24.** Figure 24: Teraquop volumes of the XaY bZ c code for phenomenological noise with measurement bias 16, and an increasing number a + b + c of repeated rounds of measurements. As predicted by Difference 5.5, using belief matching rather than MWPM initially makes a huge difference t…

**Figure 25.** Figure 25: Comparison of n˜E, n˜M, h˜E, h˜M, and teraquop volume of the X1Z 1 and X3Z 3 code decoded using MWPM and belief matching for unbiased, Z-biased, and measurement-biased phenomenological noise. Based on Difference 5.3, we expected that repeating measurements would redu…

**Figure 26.** Figure 26: Plots showing the timelike distances of (nE, nM, h)-blocks of XaY bZ c and XaZ b codes under different noise models as a fraction of the block height h. Since standard depolarizing noise and superconducting-inspired noise differ only in the probabilites of the certain…

**Figure 27.** Figure 27: E (left) and M (right) detectors of the X1Y 1Z 1 code. 51 [PITH_FULL_IMAGE:figures/full_fig_p051_27.png]

**Figure 28.** Figure 28: E (left) and M (right) detectors of the X1Z 1 code. 52 [PITH_FULL_IMAGE:figures/full_fig_p052_28.png]

**Figure 29.** Figure 29: E (left) and M (right) detectors of the X2Y 2Z 2 code. 53 [PITH_FULL_IMAGE:figures/full_fig_p053_29.png]

**Figure 30.** Figure 30: E (left) and M (right) detectors of the X2Z 2 code. 54 [PITH_FULL_IMAGE:figures/full_fig_p054_30.png]

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2025 arXiv
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How to factor 2048 bit rsa integers in 8 hours using 20 million noisy qubits.Quantum, 5:433,

[GE21] Craig Gidney and Martin Ekerå. How to factor 2048 bit rsa integers in 8 hours using 20 million noisy qubits.Quantum, 5:433,
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[AMC+24] Hany Ali, Jorge Marques, Ophelia Crawford, Joonas Majaniemi, Marc Serra-Peralta, DavidByfield, BorisVarbanov, BarbaraM.Terhal, Leonardo DiCarlo, and Earl T

Ac- cessed: 2025-03-13. [AMC+24] Hany Ali, Jorge Marques, Ophelia Crawford, Joonas Majaniemi, Marc Serra-Peralta, DavidByfield, BorisVarbanov, BarbaraM.Terhal, Leonardo DiCarlo, and Earl T. Campbell. Reducing the error rate of a supercon- ducting logical qubit using analog rea...

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[KB25] Gilad Kishony and Erez Berg

Accessed: 2025-05-09. [KB25] Gilad Kishony and Erez Berg. Increasing the distance of topological codes with time vortex defects.arXiv preprint arXiv:2502.12236,

2025

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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[BTHG25] Noah Berthusen, Shi J. S. Tan, Eric Huang, and Daniel Gottesman. Adap- tive syndrome extraction.arXiv preprint arXiv:2502.14835,

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[DTTBE24] Peter-Jan H. S. Derks, Alex Townsend-Teague, Ansgar G. Burchards, and Jens Eisert. Designing fault-tolerant circuits using detector error models. arXiv preprint arXiv:2407.13826,

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Less bacon more threshold.arXiv preprint arXiv:2305.12046,

[GB23] Craig Gidney and Dave Bacon. Less bacon more threshold.arXiv preprint arXiv:2305.12046,

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Stim: Command line usage documentation

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[Gid23a] Craig Gidney

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Surviving as a quantum computer in a classical world - 2024 draft,

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Using detector likelihood for benchmarking quantum error correction

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Improved quantum circuits for elliptic curve discrete log- arithms

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