Clifford brickwork benchmark · 3 qubits

Computed under

gidney-2025@v2+eps=1e-06

Rotation synthesis precision

ε = 1e-6

T gates per rotation

60

Magic states per Toffoli

8

Physical error rate

1e-3

Target failure probability

1e-2

Gidney, How to factor 2048 bit RSA integers with less than a million noisy qubits (arXiv:2505.15917), which states its hardware assumptions in one place: square nearest-neighbour grid, uniform 0.1% gate error, 1 us surface-code cycle, 10 us reaction time. It also states, in its Physical Costs section, the three values this model used to invent: 2(d+1)^2 physical qubits per logical patch, magic state factories covering a 3x4 area of patches, and 8T-to-CCZ distillation, so eight T states per Toffoli. threshold and logical_error_prefactor: the logical-error form this model uses, p_L = 0.1(100p)^((d+1)/2) with a 1% threshold, is Fowler and Gidney, Low overhead quantum computation using lattice surgery (arXiv:1808.06709) — quoted as equation (10) of Litinski's A Game of Surface Codes and equation (2) of Webber et al. (arXiv:2108.12371). The paper this set is named for does not use it: it picks a distance by reading a target error rate of 1e-15 per logical qubit round off simulated suppression curves (its figure 6), which is a shape this model has no field for. routing_factor: the leading term of Litinski's data blocks in A Game of Surface Codes (Quantum 3, 128, arXiv:1808.02892) — 2n+4 tiles for the intermediate block, 2n+sqrt(8n)+1 for the fast one, both 2n to leading order. arXiv:2505.15917 lays out a fixed 7x18 compute region with three columns of workspace rather than a multiplier on the data block, which is not a shape this field can hold. The constant term is dropped, so this is optimistic by a few patches. factory_cycles_per_state: the paper's own derivation — 14.7 rounds of magic state cultivation plus six lattice-surgery layers at 2d/3 rounds each, which is 14.7 + 4d rounds per CCZ state and reproduces its stated 114.7 at its own d = 25 — divided by the eight T states a CCZ costs here. The paper then rounds 114.7 up to 150 for slack and carries 150 forward, so this model is about 24% faster at distillation than the figure the paper reports. The derivation is taken rather than the rounded figure because it is the one that states how the cost moves with the code distance, which is the whole reason this field is not a constant. One distortion follows from spreading it over eight states and is worth knowing: the paper's factory delivers a CCZ state, not a bare T state, and its two terms are not alike — the 14.7 is cultivating the eight input T states (independently confirmed here: the paper's 30000 physical qubit-rounds per cultivated T state over a 12-patch factory at d = 25 is 1.85 rounds, which is 14.7/8), while the 4d is the 8T-to-CCZ distillation on top. This model has one magic-state currency, so a circuit whose states are plain T gates — every synthesised rotation in this catalogue — is charged a share of a distillation it never performs, and is pessimistic on factory time by roughly 3.4x at d = 9. A circuit of Toffolis is charged exactly the paper's 114.7. Pessimistic is the safe direction for a machine size, and splitting the two terms needs a factory model this record does not have. rotation_t_coefficient: Ross and Selinger, Optimal ancilla-free Clifford+T approximation of z-rotations (arXiv:1403.2975) — the leading term of 3*log2(1/eps) + O(log log 1/eps) for the T-count of an ancilla-free single-qubit z-rotation synthesis, which this field carries as the coefficient in t_per_rotation. Not from arXiv:2505.15917: that paper's circuit is Toffoli-only and states no rotation synthesis convention.

Two estimates may be compared only when this identity matches. Change the precision or the hardware set and every number above is a different claim.