open-standards/wai/wai-quantum/docs/published-architectures.md

Published architectures, re-estimated

This page puts published fault-tolerant resource estimates through this crate's estimators. For each quantity it gives the published figure, ours, the delta between them, and why they differ. Each estimator gets the source's stated assumptions (its code, distances, error rates, cycle and reaction times, factories and logical counts). Nothing is fitted to the figures it is compared with, with one exception its row names: which end of the line the Ising program's T factory sits at, which the source does not print.

Every row has one of six classes:

• agrees: equal to the digits the source prints;
• assumption: we were given, or chose, a different assumption, and the row states it;
• their model: the source models it differently, and the row says how;
• their numbers: the source's own figures disagree with each other or with the method it states, and the row says where;
• our limit: our estimator does not model this, and the row says what it leaves out;
• open: not resolved, and the row says what is known.

The published figures are kept apart from the code that computes ours, in tests/data/published_figures.tsv: each with where it is printed, as printed, its value and its rule. A row that agrees agrees to the digits the source prints: exactly, to the nearest printed unit, rounded up or down where the source rounds so, or, for a figure ours takes from the source's fits, within the range the fits' printed parameters allow. Every other row carries a guard, our figure to four digits. A test holds every row to its rule, and another holds the rows below to the example's output, so a change to an estimator that moves a figure fails until its guard, its reason and this page are updated together. The resource-estimation workflow runs them in a release build.

cargo run --release --example published_architectures --features full                 # columns
cargo run --release --example published_architectures --features full -- --markdown   # this page's rows
cargo run --release --example published_architectures --features full -- --guards     # ours, for the guards

The sources

A row's source names the section, table or figure where its published figure is printed. source files means the figure is quoted from the paper's arXiv source (its TeX tables and plot data), which keeps more digits than its PDF prints; every other figure is quoted with the digits the PDF prints.

• The bicycle architecture, arXiv:2506.03094 (2025): the gross [[144,12,12]] and two-gross [[288,12,18]] codes, its Tables 1–3, 5, 6, 9 and 10, §§1.2, 3.2 and 4, Fig. 9, Fig. 10, Fig. 17 and Appendices A.1, A.2, A.7 and A.10. Our model of it is quantum_bicycle. Beside it, the same codes' memory figures in arXiv:2308.07915, Table 1. Its authors' compiler is released as bicycle_compiler, bicycle_cliffords and bicycle_common on crates.io (0.1.0 of 2025-07-31); one row below cites its source.
• RSA-2048 on the surface code, arXiv:1905.09749 (Quantum 5, 433, 2021): its Tables 1 and 3, §§2.10–2.14, and the cost script in its ancillary files. Our model of it is quantum_arch::windowed_factoring_estimate, and its counts go through the estimate job as well.
• FeMoCo on the surface code, arXiv:2011.03494 (PRX Quantum 2, 030305, 2021): its Table III, §IV.C and Fig. 10, on the same factory and clock.
• RSA-2048 on yoked surface codes, arXiv:2505.15917 (2025): §3.2, through quantum_arch::factoring_estimate.
• The planar model's own source, arXiv:2211.07629 (2022): Appendix F, through quantum_resource.

What it finds

The bicycle architecture. Our model reproduces the paper's physical- and logical-qubit counts exactly, the 24 fitted rates of its Table 10 (each within the range its fits' printed parameters allow), every failure probability of its Table 10 from its instruction counts, and its error-rate bounds for the Ising program. Its other differences are explained in their rows:

• Its four mean compile costs (Fig. 9) come out to every printed digit when a shift's action is taken as A on X̄ and A⁻¹ on Z̄, on both halves of a module. That is what its authors' released compiler did in bicycle_cliffords 0.1.0 (src/measurement.rs). A CNOT circuit |x⟩ → |Ax⟩ takes Z̄ by A⁻ᵀ, which is how the operators move, and ours follows the operators; its version 0.2.1 takes X̄ by A⁻¹ and Z̄ by Aᵀ, a consistent pair. (On the printed basis a shift acts as A on the first half and Aᵀ on the second, where the paper says A on both; taken as the paper says, with Z̄ by A⁻ᵀ, every cost comes out as ours.)
• Its idle and shift rates are the simulated circuit's failure, undivided, where its text says they are divided by the circuit's C cycles. Ours divides, as the text says, and that choice is about a third of a point of the gross capability at 10⁻³ (its own row).
• Its Ising program takes 15,542,400 T gates in its tables and 19,036,800 in its text and Fig. 1. pygridsynth 1.0.1, the version it cites, gives the 15,542,400 exactly. Our synthesiser also searches the rotations one global phase away and takes 6.1% fewer, and no more than pygridsynth on any of the angles and precisions its tests compare.
• Its gross Ising machine of 4,817 qubits takes the adapter of the 10⁻³ factory beside the 10⁻⁴ factory it names (4,801).
• The Ising program's inter-module measurements match its 946,800 with the factory after the last module; before the first, 781,200. The paper prints neither: this is the one choice here made to fit a published figure.

Two differences are open. Its gross capabilities at 10⁻⁴ need a failure per rotation of 8.3·10⁻⁷ that does not depend on the machine's size, where its factory's printed error is 4·10⁻⁸; its released compiler's capability estimate at those machines would settle it, and this check does not run third-party code. And the earlier paper's memory rate for the same codes, arXiv:2308.07915, is about 1,250 times the later's fit at the same p: their decoders, circuits and fitting differ, and which accounts for it is not found here.

RSA-2048 (2021). The re-run of its cost script reproduces every row of its Table 3 to the digits it prints, which it takes up to two, and its Table 1's Toffoli count. Its title's 8 hours is the re-run's 7.31 hours expected across retries, taken up to one digit. Its hand-worked §2.14 (23 million qubits) rounds as it goes and says so. Its §2.12 reads a 6.4% distillation error from an earlier paper's spreadsheet where its own script's formula gives 0.6%. Our estimate job, given the same counts, finds the same code distance on its default step clock, three logical steps of d cycles a Toffoli as the planar model of arXiv:2211.07629 has it, and takes 12 times as long. On its reaction-limited clock at the paper's 10 µs, the rule quantum_arch takes, it takes 7.50 hours at d = 25: every Toffoli after the one before. The paper does not run them so, and counts alone do not carry how it does (our limit): its 5.1 hours and its §2.11 "approximately 7 hours" are one parallel basis, 37 ms a lookup addition, with its two runway pieces' additions side by side and its lookups at half a beat an entry. §2.11 reaches 7 by rounding its lookup additions up to 0.1·n_e·n and then 3.7·n_e·n ms up to 4·n_e·n; 37 ms on the unrounded count is 5.18 hours. The paper prints no serial figure. Its equations, at 10 µs a Toffoli one after another, give 7.3 hours, a figure of ours, not the paper's. The job's 20.05 million qubits are near the paper's 20 million by chance: 129 T factories at d = 25, not its CCZ factories at d = 27.

FeMoCo. Its floorplan, factory, Toffoli rate and 3 days come back on the same clock; its §IV.C.5 says 3.5 days where §IV.C.4 says 3. The estimate job runs at the beat on its step clock; on its reaction-limited clock it keeps enough T factories to tick at 10 µs, 0.78 days on 10.8 million qubits, where the paper's four CCZ factories set its pace at 38.75 µs. Most of that factory count is the kind of factory, not the tick: at the paper's 38.75 µs the job keeps 41 of its 15-to-1 units, each about ten times slower to a CCZ state than the paper's.

RSA-2048 (2025). As quantum_arch documents: its stated durations give 10.6 hours a shot where it prints 12.07, its hot-storage counts disagree with its own formula, and so on. Its Toffoli count comes back.

The planar model's source comes back whole.

What this does not do

• The estimate job runs every Toffoli after the one before. On either clock it reads no Toffoli depth, so a program whose Toffolis run side by side takes less time than it gives.
• The bicycle machine is not scheduled. A rotation's time is the mean of its parts, a few percent under the paper's compiled critical path, and repeated in-module measurements are not removed.
• The bicycle rates are the paper's. No decoder here has run its instructions; its fits extrapolate far below what any simulation reaches, and its two-gross measurement rates are assumed without data.
• No third-party code runs here. The paper's released compiler would settle the open gross rows.

The rows

The bicycle machine: its parts

Quantity	Source	Published	Ours	Delta	Class	Why
gross: code block c, by 2n	arXiv:2506.03094 Table 1	288	288	0	agrees
gross: processing unit u, as tallied	arXiv:2506.03094 Table 1	90	90	0	agrees
gross: adapter a, by 2(d−1)	arXiv:2506.03094 Table 1	22	22	0	agrees
two-gross: code block c, by 2n	arXiv:2506.03094 Table 1	576	576	0	agrees
two-gross: processing unit u, as tallied	arXiv:2506.03094 Table 1	158	158	0	agrees
two-gross: adapter a, by 2(d−1)	arXiv:2506.03094 Table 1	34	34	0	agrees
10⁻³ gross factory: adapter a′, by 2d−1	arXiv:2506.03094 Table 3	29	29	0	agrees
10⁻³ two-gross factory: adapter a′, by 2d−1	arXiv:2506.03094 Table 3	29	29	0	agrees
10⁻⁴ gross factory: adapter a′, by 2d−1	arXiv:2506.03094 Table 3	13	13	0	agrees
10⁻⁴ two-gross factory: adapter a′, by 2d−1	arXiv:2506.03094 Table 3	49	49	0	agrees
logical qubits in 5,000 physical qubits, gross, p = 10⁻³	arXiv:2506.03094 Fig. 10(a)	121	121	0	agrees
logical qubits in 50,000 physical qubits, two-gross, p = 10⁻³	arXiv:2506.03094 Fig. 10(a)	704	704	0	agrees
logical qubits in 5,000 physical qubits, gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a)	110	110	0	agrees
logical qubits in 50,000 physical qubits, gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a)	1,342	1,342	0	agrees
logical qubits in 50,000 physical qubits, two-gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a)	440	440	0	agrees
logical qubits in 500,000 physical qubits, two-gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a)	6,886	6,886	0	agrees

The bicycle machine: logical error rates

Quantity	Source	Published	Ours	Delta	Class	Why
gross P_I at p = 10⁻³	arXiv:2506.03094 Table 10	1.6·10⁻⁹	1.61e-9	+0.36%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_U at p = 10⁻³	arXiv:2506.03094 Table 10	4.0·10⁻⁷	4.01e-7	+0.22%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_M at p = 10⁻³	arXiv:2506.03094 Table 10	1.1·10⁻⁵	1.11e-5	+0.72%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_C at p = 10⁻³	arXiv:2506.03094 Table 10	2.0·10⁻³	2.01e-3	+0.66%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_I at p = 10⁻⁴	arXiv:2506.03094 Table 10	1.4·10⁻¹⁵	1.44e-15	+2.93%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_U at p = 10⁻⁴	arXiv:2506.03094 Table 10	6.1·10⁻¹³	6.07e-13	-0.45%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_M at p = 10⁻⁴	arXiv:2506.03094 Table 10	1.0·10⁻⁹	1.01e-9	+1.43%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_C at p = 10⁻⁴	arXiv:2506.03094 Table 10	4.8·10⁻⁸	4.81e-8	+0.24%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_I at p = 5·10⁻⁵	arXiv:2506.03094 Table 10	4.5·10⁻¹⁷	4.46e-17	-0.99%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_U at p = 5·10⁻⁵	arXiv:2506.03094 Table 10	2.2·10⁻¹⁴	2.16e-14	-1.63%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_M at p = 5·10⁻⁵	arXiv:2506.03094 Table 10	5.7·10⁻¹¹	5.74e-11	+0.70%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_C at p = 5·10⁻⁵	arXiv:2506.03094 Table 10	2.8·10⁻⁹	2.79e-9	-0.41%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_I at p = 3·10⁻⁵	arXiv:2506.03094 Table 10	3.5·10⁻¹⁸	3.54e-18	+1.02%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_U at p = 3·10⁻⁵	arXiv:2506.03094 Table 10	1.9·10⁻¹⁵	1.92e-15	+0.92%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_M at p = 3·10⁻⁵	arXiv:2506.03094 Table 10	5.9·10⁻¹²	5.90e-12	+0.07%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_C at p = 3·10⁻⁵	arXiv:2506.03094 Table 10	3.2·10⁻¹⁰	3.18e-10	-0.73%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_I at p = 10⁻⁵	arXiv:2506.03094 Table 10	1.5·10⁻²⁰	1.51e-20	+0.62%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_U at p = 10⁻⁵	arXiv:2506.03094 Table 10	9.5·10⁻¹⁸	9.53e-18	+0.29%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_M at p = 10⁻⁵	arXiv:2506.03094 Table 10	3.3·10⁻¹⁴	3.29e-14	-0.28%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross P_C at p = 10⁻⁵	arXiv:2506.03094 Table 10	2.1·10⁻¹²	2.10e-12	+0.03%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
two-gross P_I at p = 10⁻³	arXiv:2506.03094 Table 10	8.2·10⁻²¹	8.13e-21	-0.84%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
two-gross P_U at p = 10⁻³	arXiv:2506.03094 Table 10	3.3·10⁻¹⁵	3.24e-15	-1.71%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
two-gross P_I at p = 10⁻⁴	arXiv:2506.03094 Table 10	5.4·10⁻³⁹	5.39e-39	-0.23%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
two-gross P_U at p = 10⁻⁴	arXiv:2506.03094 Table 10	1.3·10⁻³⁷	1.34e-37	+3.07%	agrees	Ours evaluates Table 6's fits by Eq. (83); the band is ours with their parameters at the ends of their last printed digit.
gross idle, one syndrome cycle, p = 10⁻³	arXiv:2506.03094 §A.7 against Table 2	10^−8.8	1.61e-10	×0.101	their numbers	§A.7 says an idle's or a shift's rate is the simulated circuit's failure divided by its C cycles. Table 2 and Table 10 print the circuit's failure undivided: Table 6's fits give them so. Ours divides, as the text says, and is lower by C (10 for gross, 18 for two-gross).
two-gross idle, one syndrome cycle, p = 10⁻³	arXiv:2506.03094 §A.7 against Table 2	10^−20.1	4.52e-22	×0.057	their numbers	§A.7 says an idle's or a shift's rate is the simulated circuit's failure divided by its C cycles. Table 2 and Table 10 print the circuit's failure undivided: Table 6's fits give them so. Ours divides, as the text says, and is lower by C (10 for gross, 18 for two-gross).
gross automorphism, p = 10⁻³	arXiv:2506.03094 §A.7 against Table 2	10^−6.4	4.01e-8	×0.101	their numbers	§A.7 says an idle's or a shift's rate is the simulated circuit's failure divided by its C cycles. Table 2 and Table 10 print the circuit's failure undivided: Table 6's fits give them so. Ours divides, as the text says, and is lower by C (10 for gross, 18 for two-gross).
gross memory per cycle, p = 10⁻³	arXiv:2308.07915 Table 1, against arXiv:2506.03094 §A.7	2·10⁻⁷	1.61e-10	×8.0e-4	open	Two papers on the same code at the same p. The earlier (decoded by BP-OSD) measures 2·10⁻⁷ a syndrome cycle for the gross code at 10⁻³; the later's fits (Relay-BP) give a circuit of C idle cycles, divided by C as its text says, 1.61e-10: a factor of about 1,246 (about 125 undivided). Their decoders, circuits and fitting differ, and which accounts for the factor is not found here. Ours takes the later's fits.
gross memory per cycle, p = 10⁻⁴	arXiv:2308.07915 Table 1, against arXiv:2506.03094 §A.7	8·10⁻¹³	1.44e-16	×1.8e-4	open	Two papers on the same code at the same p. The earlier (decoded by BP-OSD) measures 2·10⁻⁷ a syndrome cycle for the gross code at 10⁻³; the later's fits (Relay-BP) give a circuit of C idle cycles, divided by C as its text says, 1.61e-10: a factor of about 1,246 (about 125 undivided). Their decoders, circuits and fitting differ, and which accounts for the factor is not found here. Ours takes the later's fits.
two-gross memory per cycle, p = 10⁻³	arXiv:2308.07915 Table 1, against arXiv:2506.03094 §A.7	2·10⁻¹²	4.52e-22	×2.3e-10	open	Two papers on the same code at the same p. The earlier (decoded by BP-OSD) measures 2·10⁻⁷ a syndrome cycle for the gross code at 10⁻³; the later's fits (Relay-BP) give a circuit of C idle cycles, divided by C as its text says, 1.61e-10: a factor of about 1,246 (about 125 undivided). Their decoders, circuits and fitting differ, and which accounts for the factor is not found here. Ours takes the later's fits.
two-gross memory per cycle, p = 10⁻⁴	arXiv:2308.07915 Table 1, against arXiv:2506.03094 §A.7	1·10⁻²²	2.99e-40	×3.0e-18	open	Two papers on the same code at the same p. The earlier (decoded by BP-OSD) measures 2·10⁻⁷ a syndrome cycle for the gross code at 10⁻³; the later's fits (Relay-BP) give a circuit of C idle cycles, divided by C as its text says, 1.61e-10: a factor of about 1,246 (about 125 undivided). Their decoders, circuits and fitting differ, and which accounts for the factor is not found here. Ours takes the later's fits.

The bicycle machine: the compile

Quantity	Source	Published	Ours	Delta	Class	Why
native measurements	arXiv:2506.03094 §3.2	540	540	0	agrees
any shift, in generators, at most	arXiv:2506.03094 §1.2	2	2	0	agrees
native rotations	arXiv:2506.03094 §3.2	510	245	×0.480	their numbers	§3.2 defines a native rotation by a native measurement Q ⊗ R with Q one of X, Y, Z on the pivot: there are 245 such R. Over all the native measurements there are 510 distinct R ≠ I: 284 occur with Q = I, 19 of them also with Q ≠ I. That its 510 counts those is our inference from the matching count. Fig. 9's first bin holds 245.
mean in-module measurements per Pauli, pivot basis chosen, gross	arXiv:2506.03094 Fig. 9 caption, right	18.48	18.526	+0.25%	their numbers	Our search runs from the printed polynomials, basis and native set, over the 4¹¹ − 1 Paulis (4¹² − 1 with the pivot fixed). The authors' released compiler, bicycle_cliffords 0.1.0 (crates.io, 2025-07-31), takes a shift's action in src/measurement.rs as A on X̄ and A⁻¹ on Z̄, on both halves of a module; taken so, our search gives the source's four means to every printed digit (a test in quantum_bicycle holds this). A CNOT circuit
the same, two-gross	arXiv:2506.03094 Fig. 9 caption, right	18.58	18.482	-0.53%	their numbers	Our search runs from the printed polynomials, basis and native set, over the 4¹¹ − 1 Paulis (4¹² − 1 with the pivot fixed). The authors' released compiler, bicycle_cliffords 0.1.0 (crates.io, 2025-07-31), takes a shift's action in src/measurement.rs as A on X̄ and A⁻¹ on Z̄, on both halves of a module; taken so, our search gives the source's four means to every printed digit (a test in quantum_bicycle holds this). A CNOT circuit
mean in-module measurements per Pauli, pivot basis fixed, gross	arXiv:2506.03094 Fig. 9 caption, left	18.55	18.593	+0.23%	their numbers	Our search runs from the printed polynomials, basis and native set, over the 4¹¹ − 1 Paulis (4¹² − 1 with the pivot fixed). The authors' released compiler, bicycle_cliffords 0.1.0 (crates.io, 2025-07-31), takes a shift's action in src/measurement.rs as A on X̄ and A⁻¹ on Z̄, on both halves of a module; taken so, our search gives the source's four means to every printed digit (a test in quantum_bicycle holds this). A CNOT circuit
the same, two-gross	arXiv:2506.03094 Fig. 9 caption, left	18.67	18.561	-0.58%	their numbers	Our search runs from the printed polynomials, basis and native set, over the 4¹¹ − 1 Paulis (4¹² − 1 with the pivot fixed). The authors' released compiler, bicycle_cliffords 0.1.0 (crates.io, 2025-07-31), takes a shift's action in src/measurement.rs as A on X̄ and A⁻¹ on Z̄, on both halves of a module; taken so, our search gives the source's four means to every printed digit (a test in quantum_bicycle holds this). A CNOT circuit

The bicycle machine: what a machine of a given size can run

Quantity	Source	Published	Ours	Delta	Class	Why
T count at failure ⅓, 5,000 physical qubits, gross, p = 10⁻³	arXiv:2506.03094 Fig. 10(a), source files	13.5958	1.365e1	+0.42%	assumption	Ours divides P_I and P_U by C, as §A.7's text says (the rates section); with them undivided, as Table 10 prints them, ours is 1.361e1 (next row). That choice is +0.30% of the difference, and the sampling below +0.12%.
the same, P_I and P_U undivided, as Table 10 prints them, 5,000 physical qubits, gross, p = 10⁻³	arXiv:2506.03094 Fig. 10(a), source files	13.5958	1.361e1	+0.12%	their model	Theirs samples eight random circuits of up to 10⁵ rotations and extends a straight-line fit (Fig. 17); ours is the expected count, at the rates as the tables print them.
timesteps per T, 5,000 physical qubits, gross, p = 10⁻³	arXiv:2506.03094 Fig. 10(a), source files	3367.15	3190.77	-5.24%	our limit	Theirs is the critical path of a compiled schedule; ours adds the mean time of a rotation's parts, with no scheduling. Ours runs a few percent low, more where a compiler takes more shifts than the fewest.
T count at failure ⅓, 50,000 physical qubits, two-gross, p = 10⁻³	arXiv:2506.03094 Fig. 10(a), source files	3.4712·10⁶	3.478e6	+0.21%	their model	Theirs samples eight random circuits of up to 10⁵ rotations and extends a straight-line fit (Fig. 17); ours is the expected count, at the rates as the tables print them. Our division of P_I and P_U by C, as §A.7's text says, is +0.00% of it (next row: undivided).
the same, P_I and P_U undivided, as Table 10 prints them, 50,000 physical qubits, two-gross, p = 10⁻³	arXiv:2506.03094 Fig. 10(a), source files	3.4712·10⁶	3.478e6	+0.20%	their model	Theirs samples eight random circuits of up to 10⁵ rotations and extends a straight-line fit (Fig. 17); ours is the expected count, at the rates as the tables print them.
timesteps per T, 50,000 physical qubits, two-gross, p = 10⁻³	arXiv:2506.03094 Fig. 10(a), source files	7057.34	7060.97	+0.05%	our limit	Theirs is the critical path of a compiled schedule; ours adds the mean time of a rotation's parts, with no scheduling. Ours runs a few percent low, more where a compiler takes more shifts than the fewest.
T count at failure ⅓, 5,000 physical qubits, gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), source files	2.2209·10⁵	4.701e5	×2.117	open	Its two gross rows at this p need a failure per rotation of 6.70·10⁻⁸ per module (ours: 6.69·10⁻⁸) plus 8.3·10⁻⁷ whatever the machine's size. Ours has 4·10⁻⁸ there: Table 3's factory, an injection's inter-module measurement and one link fewer. Nothing the paper prints accounts for the other 7.9·10⁻⁷. Its authors' compiler is released (bicycle_compiler 0.1.0 on crates.io): its capability estimate at these two machines would settle it; this check does not run it.
the same, P_I and P_U undivided, as Table 10 prints them, 5,000 physical qubits, gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), source files	2.2209·10⁵	4.700e5	×2.116	open	Its two gross rows at this p need a failure per rotation of 6.70·10⁻⁸ per module (ours: 6.69·10⁻⁸) plus 8.3·10⁻⁷ whatever the machine's size. Ours has 4·10⁻⁸ there: Table 3's factory, an injection's inter-module measurement and one link fewer. Nothing the paper prints accounts for the other 7.9·10⁻⁷. Its authors' compiler is released (bicycle_compiler 0.1.0 on crates.io): its capability estimate at these two machines would settle it; this check does not run it.
timesteps per T, 5,000 physical qubits, gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), source files	3090.55	2912.77	-5.75%	our limit	Theirs is the critical path of a compiled schedule; ours adds the mean time of a rotation's parts, with no scheduling. Ours runs a few percent low, more where a compiler takes more shifts than the fewest.
T count at failure ⅓, 50,000 physical qubits, gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), source files	3.7033·10⁴	4.064e4	+9.73%	open	Its two gross rows at this p need a failure per rotation of 6.70·10⁻⁸ per module (ours: 6.69·10⁻⁸) plus 8.3·10⁻⁷ whatever the machine's size. Ours has 4·10⁻⁸ there: Table 3's factory, an injection's inter-module measurement and one link fewer. Nothing the paper prints accounts for the other 7.9·10⁻⁷. Its authors' compiler is released (bicycle_compiler 0.1.0 on crates.io): its capability estimate at these two machines would settle it; this check does not run it.
the same, P_I and P_U undivided, as Table 10 prints them, 50,000 physical qubits, gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), source files	3.7033·10⁴	4.063e4	+9.71%	open	Its two gross rows at this p need a failure per rotation of 6.70·10⁻⁸ per module (ours: 6.69·10⁻⁸) plus 8.3·10⁻⁷ whatever the machine's size. Ours has 4·10⁻⁸ there: Table 3's factory, an injection's inter-module measurement and one link fewer. Nothing the paper prints accounts for the other 7.9·10⁻⁷. Its authors' compiler is released (bicycle_compiler 0.1.0 on crates.io): its capability estimate at these two machines would settle it; this check does not run it.
timesteps per T, 50,000 physical qubits, gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), source files	3135.16	2912.77	-7.09%	our limit	Theirs is the critical path of a compiled schedule; ours adds the mean time of a rotation's parts, with no scheduling. Ours runs a few percent low, more where a compiler takes more shifts than the fewest.
T count at failure ⅓, 50,000 physical qubits, two-gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), source files	7.0154·10¹⁵	7.033e15	+0.26%	their model	Theirs samples eight random circuits of up to 10⁵ rotations and extends a straight-line fit (Fig. 17); ours is the expected count, at the rates as the tables print them. Our division of P_I and P_U by C, as §A.7's text says, is +0.00% of it (next row: undivided).
the same, P_I and P_U undivided, as Table 10 prints them, 50,000 physical qubits, two-gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), source files	7.0154·10¹⁵	7.033e15	+0.26%	their model	Theirs samples eight random circuits of up to 10⁵ rotations and extends a straight-line fit (Fig. 17); ours is the expected count, at the rates as the tables print them.
timesteps per T, 50,000 physical qubits, two-gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), source files	5435.87	5300.97	-2.48%	our limit	Theirs is the critical path of a compiled schedule; ours adds the mean time of a rotation's parts, with no scheduling. Ours runs a few percent low, more where a compiler takes more shifts than the fewest.
T count at failure ⅓, 500,000 physical qubits, two-gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), source files	4.4830·10¹⁴	4.494e14	+0.25%	their model	Theirs samples eight random circuits of up to 10⁵ rotations and extends a straight-line fit (Fig. 17); ours is the expected count, at the rates as the tables print them. Our division of P_I and P_U by C, as §A.7's text says, is +0.00% of it (next row: undivided).
the same, P_I and P_U undivided, as Table 10 prints them, 500,000 physical qubits, two-gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), source files	4.4830·10¹⁴	4.494e14	+0.25%	their model	Theirs samples eight random circuits of up to 10⁵ rotations and extends a straight-line fit (Fig. 17); ours is the expected count, at the rates as the tables print them.
timesteps per T, 500,000 physical qubits, two-gross, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), source files	5436.91	5300.97	-2.50%	our limit	Theirs is the critical path of a compiled schedule; ours adds the mean time of a rotation's parts, with no scheduling. Ours runs a few percent low, more where a compiler takes more shifts than the fewest.
surface code: logical qubits, 5,000 qubits, p = 10⁻³	arXiv:2506.03094 Fig. 10(a), §A.10	45	45	0	agrees
surface code: T count, its formula, 5,000 qubits, p = 10⁻³	arXiv:2506.03094 Fig. 10(a), §A.10	7	7	0	agrees	§A.10's formula for the surface-code row, evaluated as it states it: the largest whole T count.
surface code: T count, our code model, 5,000 qubits, p = 10⁻³	arXiv:2506.03094 Fig. 10(a), §A.10	7	1.23e2	×17.637	their model	Our planar model takes 0.03·(p/p*)^((d+1)/2) per patch per d cycles, as arXiv:2211.07629 does. §A.10 takes 0.03·(p/p*)^(d/2) per cycle, times d cycles: higher by d·√(p*/p).
surface code: timesteps per T, 5,000 qubits, p = 10⁻³	arXiv:2506.03094 Fig. 10(a)	381	381	0	agrees	§A.10: the factory's timesteps (Table 3) and the lattice surgery's 6d.
surface code: logical qubits, 50,000 qubits, p = 10⁻³	arXiv:2506.03094 Fig. 10(a), §A.10	42	42	0	agrees
surface code: T count, its formula, 50,000 qubits, p = 10⁻³	arXiv:2506.03094 Fig. 10(a), §A.10	2.5·10⁶	2.46e6	-1.58%	agrees	§A.10's formula for the surface-code row, evaluated as it states it: the largest whole T count.
surface code: T count, our code model, 50,000 qubits, p = 10⁻³	arXiv:2506.03094 Fig. 10(a), §A.10	2.5·10⁶	1.32e8	×52.910	their model	Our planar model takes 0.03·(p/p*)^((d+1)/2) per patch per d cycles, as arXiv:2211.07629 does. §A.10 takes 0.03·(p/p*)^(d/2) per cycle, times d cycles: higher by d·√(p*/p).
surface code: timesteps per T, 50,000 qubits, p = 10⁻³	arXiv:2506.03094 Fig. 10(a)	2,269	2,269	0	agrees	§A.10: the factory's timesteps (Table 3) and the lattice surgery's 6d.
surface code: logical qubits, 5,000 qubits, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), §A.10	21	21	0	agrees
surface code: T count, its formula, 5,000 qubits, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), §A.10	377,928	377,928	0	agrees	§A.10's formula for the surface-code row, evaluated as it states it: the largest whole T count.
surface code: T count, our code model, 5,000 qubits, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a), §A.10	377,928	2.65e7	×70.000	their model	Our planar model takes 0.03·(p/p*)^((d+1)/2) per patch per d cycles, as arXiv:2211.07629 does. §A.10 takes 0.03·(p/p*)^(d/2) per cycle, times d cycles: higher by d·√(p*/p).
surface code: timesteps per T, 5,000 qubits, p = 10⁻⁴	arXiv:2506.03094 Fig. 10(a)	115	115	0	agrees	§A.10: the factory's timesteps (Table 3) and the lattice surgery's 6d.
surface code: logical qubits, 50,000 qubits, p = 10⁻⁴, d = 7	arXiv:2506.03094 Fig. 10(a), §A.10	250	250	0	agrees
surface code: T count, its formula, 50,000 qubits, p = 10⁻⁴, d = 7	arXiv:2506.03094 Fig. 10(a), §A.10	31,746	31,746	0	agrees	§A.10's formula for the surface-code row, evaluated as it states it: the largest whole T count.
surface code: T count, our code model, 50,000 qubits, p = 10⁻⁴, d = 7	arXiv:2506.03094 Fig. 10(a), §A.10	31,746	2.22e6	×70.000	their model	Our planar model takes 0.03·(p/p*)^((d+1)/2) per patch per d cycles, as arXiv:2211.07629 does. §A.10 takes 0.03·(p/p*)^(d/2) per cycle, times d cycles: higher by d·√(p*/p).
surface code: timesteps per T, 50,000 qubits, p = 10⁻⁴, d = 7	arXiv:2506.03094 Fig. 10(a)	115	115	0	agrees	§A.10: the factory's timesteps (Table 3) and the lattice surgery's 6d.
surface code: logical qubits, 50,000 qubits, p = 10⁻⁴, d = 17	arXiv:2506.03094 Fig. 10(a), §A.10	27	27	0	agrees
surface code: T count, its formula, 50,000 qubits, p = 10⁻⁴, d = 17	arXiv:2506.03094 Fig. 10(a), §A.10	1.2·10¹⁵	1.21e15	+0.86%	agrees	§A.10's formula for the surface-code row, evaluated as it states it: the largest whole T count.
surface code: T count, our code model, 50,000 qubits, p = 10⁻⁴, d = 17	arXiv:2506.03094 Fig. 10(a), §A.10	1.2·10¹⁵	2.06e17	×1.7e2	their model	Our planar model takes 0.03·(p/p*)^((d+1)/2) per patch per d cycles, as arXiv:2211.07629 does. §A.10 takes 0.03·(p/p*)^(d/2) per cycle, times d cycles: higher by d·√(p*/p).
surface code: timesteps per T, 50,000 qubits, p = 10⁻⁴, d = 17	arXiv:2506.03094 Fig. 10(a)	509	509	0	agrees	§A.10: the factory's timesteps (Table 3) and the lattice surgery's 6d.
surface code: logical qubits, 500,000 qubits, p = 10⁻⁴, d = 17	arXiv:2506.03094 Fig. 10(a), §A.10	416	416	0	agrees
surface code: T count, its formula, 500,000 qubits, p = 10⁻⁴, d = 17	arXiv:2506.03094 Fig. 10(a), §A.10	7.9·10¹³	7.86e13	-0.56%	agrees	§A.10's formula for the surface-code row, evaluated as it states it: the largest whole T count.
surface code: T count, our code model, 500,000 qubits, p = 10⁻⁴, d = 17	arXiv:2506.03094 Fig. 10(a), §A.10	7.9·10¹³	1.34e16	×1.7e2	their model	Our planar model takes 0.03·(p/p*)^((d+1)/2) per patch per d cycles, as arXiv:2211.07629 does. §A.10 takes 0.03·(p/p*)^(d/2) per cycle, times d cycles: higher by d·√(p*/p).
surface code: timesteps per T, 500,000 qubits, p = 10⁻⁴, d = 17	arXiv:2506.03094 Fig. 10(a)	509	509	0	agrees	§A.10: the factory's timesteps (Table 3) and the lattice surgery's 6d.

The bicycle machine: the 10 × 10 Ising model

Quantity	Source	Published	Ours	Delta	Class	Why
physical qubits, two-gross	arXiv:2506.03094 §4	8,138	8,138	0	agrees
physical qubits, gross	arXiv:2506.03094 §4	4,817	4,801	-0.33%	their numbers	§4 names the 10⁻⁴ gross factory, whose adapter is 13 qubits (Table 3). 4,817 takes the 29 of the 10⁻³ factory.
rotations	arXiv:2506.03094 §A.10	184,000	184,000	0	agrees
inter-module measurements N_C, gross	arXiv:2506.03094 Table 9	9.4680·10⁵	946,800	0	assumption	Sites in order and the factory after the last module give the paper's count; before the first module, 781,200. The paper prints neither, and this is the end chosen to match it: the one choice in this check made to fit a published figure.
the same on two-gross	arXiv:2506.03094 Table 9	9.4680·10⁵	946,800	0	assumption	Sites in order and the factory after the last module give the paper's count; before the first module, 781,200. The paper prints neither, and this is the end chosen to match it: the one choice in this check made to fit a published figure.
in-module measurements N_M, gross	arXiv:2506.03094 Table 9, source files	4,215,240	4,283,200	+1.61%	our limit	Ours removes no repeated in-module measurement, which theirs does (§4), and takes sites in order, which it does not print. Its counts also carry the compile section's action of a shift on Z̄, which puts its gross below its two-gross; ours has them the other way round.
in-module measurements N_M, two-gross	arXiv:2506.03094 Table 9, source files	4,238,828	4,148,800	-2.12%	our limit	Ours removes no repeated in-module measurement, which theirs does (§4), and takes sites in order, which it does not print. Its counts also carry the compile section's action of a shift on Z̄, which puts its gross below its two-gross; ours has them the other way round.
automorphisms N_U, gross	arXiv:2506.03094 Table 9, source files	2,270,400	2,728,800	+20.19%	our limit	Ours takes the fewest shifts on a path of fewest measurements, and merges none; theirs is a compiler's.
automorphisms N_U, two-gross	arXiv:2506.03094 Table 9, source files	2,294,400	2,368,000	+3.21%	our limit	Ours takes the fewest shifts on a path of fewest measurements, and merges none; theirs is a compiler's.
T injections N_T	arXiv:2506.03094 Table 9, source files	15,542,400	14,592,000	-6.11%	their model	pygridsynth 1.0.1, the version the source cites, run on the program's four angles at ε = 5·10⁻⁹, gives 86, 80, 84 and 82 T gates, which make 15,542,400 exactly; it approximates the rotation itself. Ours, the same Ross–Selinger method, gives 79, 80, 79 and 82: it also searches the class one global phase e^(iπ/8) away, which a rotation of the pivot allows, and of the solver's solution of the norm equation and its unit multiples it keeps the one whose operator takes the fewest T gates. It takes no more than the reference on any of 1,192 angles and precisions (engine::synth::rz's tests).
T injections as §4 and Fig. 1(b) state	arXiv:2506.03094 §4; Fig. 1(b), source files	1.9·10⁷ (Fig. 1(b): 19,036,800)	14,592,000	-23.35%	their numbers	§4 says N_T = 1.9·10⁷ and Fig. 1(b) plots 19,036,800. Table 9 and every failure probability of Table 10 take 15,542,400, which the row above compares ours with.
idles N_I, two-gross, from its N_T	arXiv:2506.03094 Table 9, source files	41,636,714,298	42,100,476,000	+1.11%	our limit	Ours: every module idles while the factory works, and otherwise never. Theirs counts the idles of its schedule.
failure probability, gross, p = 10⁻³, its counts	arXiv:2506.03094 Table 10	3.33·10⁴	3.331e4	+0.03%	agrees	Table 9's counts at our evaluation of Table 6's fits (Eq. (26)); the band moves the fits' parameters by their last printed digit.
failure probability, gross, p = 10⁻⁴, its counts	arXiv:2506.03094 Table 10	7.97·10⁻¹	7.977e-1	+0.09%	agrees	Table 9's counts at our evaluation of Table 6's fits (Eq. (26)); the band moves the fits' parameters by their last printed digit.
failure probability, gross, p = 5·10⁻⁵, its counts	arXiv:2506.03094 Table 10	4.62·10⁻²	4.622e-2	+0.05%	agrees	Table 9's counts at our evaluation of Table 6's fits (Eq. (26)); the band moves the fits' parameters by their last printed digit.
failure probability, gross, p = 3·10⁻⁵, its counts	arXiv:2506.03094 Table 10	5.27·10⁻³	5.263e-3	-0.14%	agrees	Table 9's counts at our evaluation of Table 6's fits (Eq. (26)); the band moves the fits' parameters by their last printed digit.
failure probability, gross, p = 10⁻⁵, its counts	arXiv:2506.03094 Table 10	3.48·10⁻⁵	3.478e-5	-0.07%	agrees	Table 9's counts at our evaluation of Table 6's fits (Eq. (26)); the band moves the fits' parameters by their last printed digit.
failure probability, two-gross, p = 10⁻³, its counts	arXiv:2506.03094 Table 10	1.65·10⁻²	1.653e-2	+0.19%	agrees	Table 9's counts at our evaluation of Table 6's fits (Eq. (26)); the band moves the fits' parameters by their last printed digit.
failure probability, two-gross, p = 10⁻⁴, its counts	arXiv:2506.03094 Table 10	1.65·10⁻¹¹	1.653e-11	+0.19%	agrees	Table 9's counts at our evaluation of Table 6's fits (Eq. (26)); the band moves the fits' parameters by their last printed digit.
failure probability, two-gross, p = 10⁻³, a T injection at its factory	arXiv:2506.03094 Table 10	1.65·10⁻²	3.274e-1	×19.841	their model	Table 10 sets P_T = P_C ("the T factory can be chosen to distill states of sufficient fidelity") and §4 neglects the factory. At the factory it allocates, Table 3's 2·10⁻⁸, the T injections alone fail with 0.31.
physical error rate for failure 10⁻³, two-gross	arXiv:2506.03094 §A.10	7.32·10⁻⁴	7.322e-4	+0.03%	agrees	Its power law through two of its points of Table 10, solved for a failure of 10⁻³; the band moves the fits' parameters by their last printed digit.
physical error rate for failure 10⁻³, gross	arXiv:2506.03094 §A.10	2.09·10⁻⁵	2.086e-5	-0.20%	agrees	Its power law through two of its points of Table 10, solved for a failure of 10⁻³; the band moves the fits' parameters by their last printed digit.
surface code, d = 9: physical error rate, Eq. (96)	arXiv:2506.03094 §A.10, Eq. (96)	5.48·10⁻⁵	5.476e-5	-0.07%	agrees	With §4's N_T of 19,036,800. §4 prints it truncated to two digits.
surface code, d = 9: physical error rate, our code model	arXiv:2506.03094 §A.10, Eq. (96)	5.48·10⁻⁵	1.430e-4	×2.610	their model	As in the capability section: a patch's error per d cycles, not a cycle's times d, and (d+1)/2.
surface code, d = 9: physical qubits	arXiv:2506.03094 §4, Fig. 10(b)	17,010	33,210	+95.24%	their numbers	§4 and Fig. 10(b) count 2d² a logical qubit. Eq. (96) puts 2n patches in each rotation, and §A.10's capability comparison reserves half the patches for routing: 4d². Ours is 4d².
surface code, d = 17: physical error rate, Eq. (96)	arXiv:2506.03094 §A.10, Eq. (96)	5.89·10⁻⁴	5.892e-4	+0.03%	agrees	With §4's N_T of 19,036,800. §4 prints it truncated to two digits.
surface code, d = 17: physical error rate, our code model	arXiv:2506.03094 §A.10, Eq. (96)	5.89·10⁻⁴	9.446e-4	+60.38%	their model	As in the capability section: a patch's error per d cycles, not a cycle's times d, and (d+1)/2.
surface code, d = 17: physical qubits	arXiv:2506.03094 §4, Fig. 10(b)	58,263	116,063	+99.21%	their numbers	§4 and Fig. 10(b) count 2d² a logical qubit. Eq. (96) puts 2n patches in each rotation, and §A.10's capability comparison reserves half the patches for routing: 4d². Ours is 4d².
surface code, d = 19: physical error rate, Eq. (96)	arXiv:2506.03094 §A.10, Eq. (96)	7.85·10⁻⁴	7.845e-4	-0.06%	agrees	With §4's N_T of 19,036,800. §4 prints it truncated to two digits.
surface code, d = 19: physical error rate, our code model	arXiv:2506.03094 §A.10, Eq. (96)	7.85·10⁻⁴	1.196e-3	+52.36%	their model	As in the capability section: a patch's error per d cycles, not a cycle's times d, and (d+1)/2.
surface code, d = 19: physical qubits	arXiv:2506.03094 §4, Fig. 10(b)	72,663	144,863	+99.36%	their numbers	§4 and Fig. 10(b) count 2d² a logical qubit. Eq. (96) puts 2n patches in each rotation, and §A.10's capability comparison reserves half the patches for routing: 4d². Ours is 4d².

RSA-2048 on the surface code (arXiv:1905.09749, Quantum 5, 433, 2021)

Quantity	Source	Published	Ours	Delta	Class	Why
physical qubits, re-run on its layout	arXiv:1905.09749 Table 3	20 (megaqubits)	19,248,768	-3.76%	agrees	Its script takes each figure up to two digits.
hours per run, re-run	arXiv:1905.09749 Table 3	5.1	5.05	-1.06%	agrees	Its script takes each figure up to two digits.
retry risk, re-run	arXiv:1905.09749 Table 3	31%	0.3098	-0.08%	agrees	Its script takes it up to a whole percent.
megaqubit-days per run, re-run	arXiv:1905.09749 Table 3	4.1	4.05	-1.29%	agrees	Its script takes each figure up to two digits.
Toffolis, re-run	arXiv:1905.09749 Table 1	2.7 (billions)	2.698e9	-0.06%	agrees
factories in each piece, re-run	arXiv:1905.09749 §2.10	14	14	0	agrees
hours, expected across retries	arXiv:1905.09749 title	8 hours	7.31	-8.62%	agrees	The re-run's 5.05 hours a run at its 30.98% retry risk is 7.31 hours expected; the title takes that up to one digit.
physical qubits, its worked case, level-1 distance 17	arXiv:1905.09749 §2.14	"approximately 23 million"	21,616,448	-6.02%	their numbers	That section rounds as it goes, and says so: 226 × 63 patches, where the script's layout at these distances has 226 × 61.
distillation error of 3·10⁹ CCZ states, distances 17 and 27	arXiv:1905.09749 §2.12	6.4%	0.0060	×0.094	their numbers	That section reads a spreadsheet of an earlier paper. Its own script's formula, which produced its tables, gives 0.6%.
code distance, job, assumed code model	arXiv:1905.09749 §2.13 (d = 27); its counts in the estimate job	27	27	0	agrees
code distance, job, code model fitted to our decoders	arXiv:1905.09749 §2.13 (d = 27); its counts in the estimate job	27	27	0	agrees	Our fit is a = 0.0233, p* = 0.01004, extrapolated from p = 0.002–0.005.
physical qubits, job, assumed code model	arXiv:1905.09749 Table 3; its counts in the estimate job	20 (megaqubits)	18,906,836	-5.47%	our limit	The job lays out 2N + √(8N) + 1 tiles of 2d² qubits and T factories from 15-to-1; the source a board of 2(d+1)²-qubit patches and CCZ factories, placed by hand.
physical qubits, job, fitted code model	arXiv:1905.09749 Table 3; its counts in the estimate job	20 (megaqubits)	18,906,836	-5.47%	our limit	The job lays out 2N + √(8N) + 1 tiles of 2d² qubits and T factories from 15-to-1; the source a board of 2(d+1)²-qubit patches and CCZ factories, placed by hand.
physical qubits, the planar model on the source's patch and error rule	arXiv:1905.09749 Table 3; its counts in the estimate job	20 (megaqubits)	27,571,456	+37.86%	our limit	The job lays out 2N + √(8N) + 1 tiles of 2d² qubits and T factories from 15-to-1; the source a board of 2(d+1)²-qubit patches and CCZ factories, placed by hand.
hours per run, job, assumed code model	arXiv:1905.09749 Table 3; its counts in the estimate job	5.1	60.71	×11.904	assumption	On its default step clock the estimate job prices the planar architecture of arXiv:2211.07629: three logical steps of d cycles for each Toffoli. The source teleports a Toffoli's fixups away and runs it in one tick; the job does so on its reaction-limited clock (the rows below).
hours per run, the planar model on the source's patch and error rule	arXiv:1905.09749 Table 3; its counts in the estimate job	5.1	69.71	×13.668	assumption	On its default step clock the estimate job prices the planar architecture of arXiv:2211.07629: three logical steps of d cycles for each Toffoli. The source teleports a Toffoli's fixups away and runs it in one tick; the job does so on its reaction-limited clock (the rows below).
code distance, job, reaction-limited clock at 10 µs	arXiv:1905.09749 §2.13 (d = 27); its counts in the estimate job	27	25	-7.41%	our limit	The tiles wait out 7.50 hours here and 60.71 on the step clock, so a smaller distance meets the same budget.
hours per run, job, reaction-limited clock at 10 µs	arXiv:1905.09749 Table 3; its counts in the estimate job	5.1	7.50	+46.97%	our limit	The job runs each Toffoli in one 10 µs tick, all of them one after another, as its layout runs every step; the source does not, and counts alone do not carry how it does. Its 5.1 hours and its §2.11 "approximately 7 hours" are one parallel basis, 37 ms a lookup addition, with the two runway pieces' additions side by side and the lookups at half a beat an entry. §2.11 reaches 7 by rounding: eq. (1)'s 503,808 lookup additions as 0.1·n_e·n, then 3.7·n_e·n ms as 4·n_e·n, which is 6.99 hours; 37 ms on the unrounded count is 5.18. The source prints no serial figure. 5,207 Toffolis a lookup addition at 10 µs each would be 7.3 hours: that is our derivation from its equations, not its figure.
physical qubits, job, reaction-limited clock at 10 µs	arXiv:1905.09749 Table 3; its counts in the estimate job	20 (megaqubits)	20,050,780	+0.25%	our limit	The job lays out 2N + √(8N) + 1 tiles of 2d² qubits and T factories from 15-to-1; the source a board of 2(d+1)²-qubit patches and CCZ factories, placed by hand. On this clock the job keeps enough factories (129) that a CCZ state comes every tick, at d = 25: near the source's count by chance, a different machine from its d = 27 and CCZ factories.
factories, job	arXiv:1905.09749 §2.10; its counts in the estimate job	14 CCZ per piece, 28 in all	16 T factories	—	our limit	A CCZ state costs four T states in the planar model.
1024 bits: megaqubits, re-run	arXiv:1905.09749 Table 3	9.7	9.62	-0.78%	agrees	Its script takes each figure up to two digits.
1024 bits: hours per run, re-run	arXiv:1905.09749 Table 3	1.3	1.26	-2.79%	agrees	Its script takes each figure up to two digits.
3072 bits: megaqubits, re-run	arXiv:1905.09749 Table 3	38	37.90	-0.27%	agrees	Its script takes each figure up to two digits.
3072 bits: hours per run, re-run	arXiv:1905.09749 Table 3	12	11.61	-3.28%	agrees	Its script takes each figure up to two digits.
4096 bits: megaqubits, re-run	arXiv:1905.09749 Table 3	55	54.62	-0.70%	agrees	Its script takes each figure up to two digits.
4096 bits: hours per run, re-run	arXiv:1905.09749 Table 3	22	21.08	-4.20%	agrees	Its script takes each figure up to two digits.
8192 bits: megaqubits, re-run	arXiv:1905.09749 Table 3	140	133.32	-4.77%	agrees	Its script takes each figure up to two digits.
8192 bits: hours per run, re-run	arXiv:1905.09749 Table 3	86	85.54	-0.53%	agrees	Its script takes each figure up to two digits.
12288 bits: megaqubits, re-run	arXiv:1905.09749 Table 3	200	199.98	-0.01%	agrees	Its script takes each figure up to two digits.
12288 bits: hours per run, re-run	arXiv:1905.09749 Table 3	200	192.47	-3.76%	agrees	Its script takes each figure up to two digits.
16384 bits: megaqubits, re-run	arXiv:1905.09749 Table 3	270	266.64	-1.25%	agrees	Its script takes each figure up to two digits.
16384 bits: hours per run, re-run	arXiv:1905.09749 Table 3	350	342.54	-2.13%	agrees	Its script takes each figure up to two digits.

FeMoCo on the surface code (arXiv:2011.03494, PRX Quantum 2, 030305, 2021)

Quantity	Source	Published	Ours	Delta	Class	Why
physical qubits, p = 10⁻³, its floorplan	arXiv:2011.03494 Fig. 10	≈ 4·10⁶	3,907,584	-2.31%	agrees	53 × 36 = 1,908 patches of 2(d+1)², as its caption works out.
days, p = 10⁻³, re-run on our clock	arXiv:2011.03494 §IV.C.4	3	3.01	+0.22%	agrees
what sets the pace, p = 10⁻³	arXiv:2011.03494 §IV.C.4	the factories (a "tick" limit)	MagicStates	—	agrees
Toffoli rate, kHz	arXiv:2011.03494 §IV.C.4	25	25.81	+3.23%	agrees	Four factories each finish a CCZ state every 5·31 cycles: 25.8 kHz, printed as 25.
distillation failure over 10¹⁰ Toffolis	arXiv:2011.03494 §IV.C.4	"roughly 0.1%"	0.00103	+2.85%	agrees
physical qubits, p = 10⁻⁴	arXiv:2011.03494 §IV.C.5	"one million"	976,896	-2.31%	agrees
days, p = 10⁻⁴, re-run on our clock	arXiv:2011.03494 §IV.C.5	1.5	1.45	-3.01%	agrees
days at p = 10⁻³, as §IV.C.5 states	arXiv:2011.03494 §IV.C.5	3.5	3.01	-14.09%	their numbers	§IV.C.4 says 3 days; §IV.C.5 scales "3.5 days" by 15/31 and gets 1.5, which is 3 days scaled. Its abstract says under four.
Toffolis, Table III against its layout	arXiv:2011.03494 Table III against §IV.C.4	5.3·10⁹ (Table III); 6.7·10⁹ (§IV.C.4)	—	—	their numbers	The paper's own two figures: Table III costs the algorithm with its own QROM choices; the layout takes an output expansion factor of 1 for the select reads (§IV.C.2), which holds fewer qubits and takes more Toffolis. Ours takes each in turn below.
logical qubits, Table III against its layout's data	arXiv:2011.03494 Table III against §IV.C.4	2,142 (Table III); under 700 data qubits (§IV.C.4)	—	—	their numbers	The paper's own two figures: Table III costs the algorithm with its own QROM choices; the layout takes an output expansion factor of 1 for the select reads (§IV.C.2), which holds fewer qubits and takes more Toffolis. Ours takes each in turn below.
code distance, its layout's counts	arXiv:2011.03494 §IV.C.4; its counts in the estimate job	31	29	-6.45%	assumption	Its rule is 0.1·(100p)^((d+1)/2) a cycle (§IV.C.5: "Λ of 10"); the planar model's 0.03·(p/0.01)^((d+1)/2) a step of d cycles, lower by d/0.3, one step of distance at this size.
physical qubits, job, Table III's counts	arXiv:2011.03494 §IV.C.4; its counts in the estimate job	≈ 4·10⁶	8,419,152	×2.105	our limit	The job lays out 2N + √(8N) + 1 tiles of 2d² qubits and T factories from 15-to-1; the source a board of 2(d+1)²-qubit patches and CCZ factories, placed by hand.
physical qubits, job, its layout's counts	arXiv:2011.03494 §IV.C.4; its counts in the estimate job	≈ 4·10⁶	3,529,152	-11.77%	our limit	The job lays out 2N + √(8N) + 1 tiles of 2d² qubits and T factories from 15-to-1; the source a board of 2(d+1)²-qubit patches and CCZ factories, placed by hand.
days, job, Table III's counts	arXiv:2011.03494 §IV.C.4; its counts in the estimate job	3	5.34	+77.89%	assumption	On its default step clock the estimate job prices the planar architecture of arXiv:2211.07629: three logical steps of d cycles for each Toffoli. The source teleports a Toffoli's fixups away and runs it in one tick; the job does so on its reaction-limited clock (the rows below).
days, job, its layout's counts	arXiv:2011.03494 §IV.C.4; its counts in the estimate job	3	6.75	×2.250	assumption	On its default step clock the estimate job prices the planar architecture of arXiv:2211.07629: three logical steps of d cycles for each Toffoli. The source teleports a Toffoli's fixups away and runs it in one tick; the job does so on its reaction-limited clock (the rows below).
physical qubits, job, p = 10⁻⁴	arXiv:2011.03494 §IV.C.5; its counts in the estimate job	"one million"	968,200	-3.18%	our limit	The job lays out 2N + √(8N) + 1 tiles of 2d² qubits and T factories from 15-to-1; the source a board of 2(d+1)²-qubit patches and CCZ factories, placed by hand.
days, job, p = 10⁻⁴	arXiv:2011.03494 §IV.C.5; its counts in the estimate job	1.5	3.49	×2.328	assumption	On its default step clock the estimate job prices the planar architecture of arXiv:2211.07629: three logical steps of d cycles for each Toffoli. The source teleports a Toffoli's fixups away and runs it in one tick; the job does so on its reaction-limited clock (the rows below).
days, job, its layout's counts, reaction-limited clock at 10 µs	arXiv:2011.03494 §IV.C.4; its counts in the estimate job	3	0.78	×0.259	assumption	The job ticks at 10 µs where the source's four CCZ factories set a pace of 38.75 µs (25 kHz), and that ratio is this delta. It keeps 157 T factories to do so, and the two counts are different machines: each of the job's is a 15-to-1 unit taking 1,568 µs a CCZ state, each of the source's 155. At the source's own 38.75 µs the job keeps 41, so of the ×39 against four the tick is ×3.8 and the kind of factory ×10. The job's frontier slows the ticks to need fewer.
physical qubits, job, its layout's counts, reaction-limited clock at 10 µs	arXiv:2011.03494 §IV.C.4; its counts in the estimate job	≈ 4·10⁶	10,799,568	×2.700	assumption	The job lays out 2N + √(8N) + 1 tiles of 2d² qubits and T factories from 15-to-1; the source a board of 2(d+1)²-qubit patches and CCZ factories, placed by hand. As above: most of this is the T factories that keep up with the tick; at the source's own 38.75 µs the job needs 4,410,288 qubits.

RSA-2048 on yoked surface codes (arXiv:2505.15917, 2025)

Quantity	Source	Published	Ours	Delta	Class	Why
physical qubits	arXiv:2505.15917 §3.2	897,864	958,480	+6.75%	their numbers	Ours keeps 152 logical qubits hot by its peak formula and buys whole grid blocks; its count keeps 131 and a fractional block. At its 131 and 430 qubits a logical qubit, our arithmetic gives its 897,864.
hours per shot	arXiv:2505.15917 §3.2	12.07	10.58	-12.36%	their numbers	Its tallies at its stated durations give 10.62 hours, and its clock at whole milliseconds 10.58.
days per factoring	arXiv:2505.15917 §3.2	4.96	4.31	-13.20%	their numbers	From the hours per shot above; it also multiplies by 9.1 shots where its table gives 9.2. It rounds 4.96 up to "less than a week".
logical qubits	arXiv:2505.15917 §3.2	1,409	1,432	+1.63%	their numbers	§3.2 prints 1,409 for its peak formula m + 3f + 2ℓ + len m, which evaluates to 1,432; its Table 4 gives 1,399.
Toffolis per factoring, by its counting rule	arXiv:2505.15917 §3.2	"6.5 billion"	6.50e9	-0.04%	agrees

The planar model's own source (arXiv:2211.07629, 2022)

Quantity	Source	Published	Ours	Delta	Class	Why
code distance, RSA-2048, (ns, 10⁻⁴)	arXiv:2211.07629 Appendix F	13	13	0	agrees
factories	arXiv:2211.07629 Appendix F	18	18	0	agrees
physical qubits	arXiv:2211.07629 Appendix F	8.72M	8,716,258	-0.04%	agrees
run time, hours	arXiv:2211.07629 Appendix F	17 hours 43 mins	17.723	+0.04%	agrees	Table IV prints 18 hours.