A first-order nearest-neighbor ZZ evolution scaffold expressed as CNOT–RZ–CNOT blocks.
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A first-order nearest-neighbor ZZ evolution scaffold expressed as CNOT–RZ–CNOT blocks. This 3-qubit record gives the repository a concrete, inspectable circuit at a known width rather than only a family-level description.
Derived from this entry's published gate sequence on every read, not authored alongside it. Depth is the longest serial run through the circuit, not the gate count: operations on disjoint qubits share a layer, and the terminal measurement is one layer of its own.
Estimated under a stated precision
This circuit's cost is dominated by arbitrary-angle rotations, which have no T-count until a synthesis precision is named. The figures below hold under the precision stated at the bottom of this panel and move with it.
This circuit does not have a cost; it has a cost per machine, and almost all of the difference is magic-state factories — hardware bought for speed, not asked for by the circuit. Neither end below was chosen by anyone: one factory is the fewest the estimator will cost a magic-state circuit on, and the other is the crossover, derived. Only the footprint and the wall-clock move between them; everything else on this page is a property of the circuit and reads the same on both.
The fewest factories this circuit can run on at all.
Past this count, the reaction time binds and more factories change nothing.
Architecture-independent. Nothing here mentions hardware.
The layers below cost the fastest useful machine — the right-hand column above. Factories are hardware bought for speed, not for the circuit. Cost them separately from the circuit's own patches — for a small circuit they are nearly the whole figure.
gidney-2025@v2+eps=1e-06
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.
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.
Takes a 3-qubit register, and this entry's published behaviour was measured from |0…0⟩. Putting another stage in front is a defined circuit and is no longer the thing this entry measured — the results on this page were not produced that way.
5 entries line up on shape, composition unverified. Named below.
Returns 3 classical bits. Nothing in this catalogue takes classical bits, so this end closes a pipeline rather than continuing one — what is worth having here is the measurement, not a register to pass on.
Nothing in the Atlas meets this end.
A whole program rather than a stage: it begins on |0…0⟩ and ends by measuring every qubit, so what it returns is classical bits. Nothing in this catalogue takes classical bits, so nothing follows it. See all 30 →
The widths and types line up. What is not established is everything a width does not carry — the basis convention, the normalisation, the state each was written to start from — so this is not a claim that the two compose.
The circuit is stored once as a framework-neutral ordered gate graph and converted lazily when a framework is selected. The converter preserves gate order, numeric angle expressions, qubit indices, and terminal all-qubit measurement for its bounded gate set. It intentionally does not claim that downstream compiler decompositions or device behavior are identical. The cited MQT Bench work motivates scalable, cross-level benchmark families; this particular circuit is a Leona Quantum-authored scaffold and should be compared by width, operation count, transpiled depth, two-qubit count, and measured output behavior.
from qiskit import QuantumCircuit
from numpy import pi
qc = QuantumCircuit(3)
qc.cx(0, 1)
qc.rz(1*pi/8, 1)
qc.cx(0, 1)
qc.cx(1, 2)
qc.rz(2*pi/8, 2)
qc.cx(1, 2)
qc.cx(2, 0)
qc.rz(3*pi/8, 0)
qc.cx(2, 0)
qc.measure_all()
FINAL_CIRCUIT = qcUse a classical state-vector or matrix simulation at the same width, precision, and measurement objective.
The quantum record demonstrates a state or operator behavior; it does not make classical simulation or communication costs disappear.
Compare fidelity, samples, gate depth, noise, memory, and the cost of preparing and reading the state.
Nobody has reviewed this record for gaps yet.
Defines a cross-level, scalable benchmark methodology; this entry is a Leona Quantum-authored portable scaffold, not a byte-for-byte upstream circuit.
arxiv.org/abs/2204.13719 ↗