The noise models

How a compiled QCCD program becomes a logical error rate. The program is replayed on the device, which says where every ion is, how hot it is and how long everything takes. Each operation becomes its gate in a stim circuit, and each clause of the model below puts its Pauli noise before or after what it names, with the probability its term computes from the replay and the device's physics. The model IS this text: the grader reads it, and the Evaluation page explains every word of it. The circuit's detectors come from the memory experiment's circuit, so an experiment means the same thing whichever compiler compiled it. A board names its model; changing the physics makes a new model, never an edit to an old one.

qccd-noise@2

It prices what the schedule does, not only the gates. An ion loses memory for every instruction that does not operate on it, whether it idles, rides a rotation or is shuttled, linearly in time and coherently over each idle stretch. A readout disturbs the ions beside it, and every gate starts from the motion cooling leaves behind. Every number is a published measurement on trapped-ion hardware. A per-shuttle error is left out because no experiment reports one: transport is charged through its time and its heating instead. Ion loss is left out too, because no vendor reports a number and it is not a Pauli channel. A Z-basis memory cannot see dephasing, so the boards under this model measure an X and a Z memory together. Used by Surface code memory, distance 5, both bases, Surface code memory, distance 3, both bases, Surface code memory, distance 7, both bases, Steane code memory, both bases, Shor code memory, both bases, Repetition code memory, distance 3, both bases, Repetition code memory, distance 5, both bases, Bivariate bicycle code [[18,4,4]] memory, both bases, Bivariate bicycle code [[72,12,6]] memory, both bases, Bivariate bicycle code [[90,8,10]] memory, both bases.

The clauses, as the text writes them (the whole text; digest sha256:08b78aad27ca):

after p in preparations:
  X_ERROR(min(1 / 2, scale * primitive("reset", "error"))) on ions(p) counted as reset

before o in qubit_operations, i in ions(o):
  Z_ERROR(min(1 / 2, scale * pow(sin(pi * coherent_rate * waited(i, o) * 1e-6), 2))) on i

before m in measurements where basis(m) = "Z":
  X_ERROR(min(1 / 2, scale * (1 - primitive("measure", "fidelity")))) on ions(m) counted as measure

before m in measurements where basis(m) = "X":
  Z_ERROR(min(1 / 2, scale * (1 - primitive("measure", "fidelity")))) on ions(m) counted as measure

after g in two_qubit_gates:
  DEPOLARIZE2(min(15 / 16, scale * ms_error(gate_heat(g), gate_length(g)))) on ions(g)
    counted as ms_base = ms_error(0, 2),
               ms_heating = ms_error(gate_heat(g), 2) - ms_error(0, 2),
               ms_chain = ms_error(gate_heat(g), gate_length(g)) - ms_error(gate_heat(g), 2)

after g in single_qubit_gates where gate(g) != "VZ" and gate(g) != "I":
  DEPOLARIZE1(min(3 / 4, scale * (1 - primitive("1q_gate", "fidelity")))) on ions(g)

after r in resets:
  X_ERROR(min(1 / 2, scale * primitive("reset", "error"))) on ions(r)

after k in steps where kind(k) = "measure":
  DEPOLARIZE1(min(3 / 4, scale * crosstalk_near)) on near(k)

after k in steps where kind(k) = "measure":
  DEPOLARIZE1(min(3 / 4, scale * crosstalk_far)) on far(k)

after k in steps where kind(k) = "reset":
  DEPOLARIZE1(min(3 / 4, scale * crosstalk_reset)) on far(k) counted as crosstalk_global

after k in steps where duration(k) > 0:
  Z_ERROR(min(1 / 2, scale * memory_rate * duration(k) * 1e-6)) on {i for i in ions where i not in operated(k)}

The physics it is graded under: qccd-physics@2

A ¹³⁷Ba⁺ QCCD with ¹⁷¹Yb⁺ coolant. Its gate, readout and memory errors are Helios's (Quantinuum, arXiv:2511.05465), and its transport times are Quantinuum's published primitives, in the operating-point table quantinuum. One segment of a design is one zone pitch, 375 µm. A design entered on a board with this physics takes it unless it set its own.

qccd-noise@1

Gates, readout, reset and a T₂ dephasing on every ion, priced from the device's own physics block; the first preparation is noiseless, and no crosstalk is charged. Used by Repetition code memory, distance 5, Surface code memory, distance 3.

The clauses, as the text writes them (the whole text; digest sha256:e46c03f06242):

before m in measurements where basis(m) = "Z":
  X_ERROR(min(1 / 2, scale * (1 - primitive("measure", "fidelity")))) on ions(m) counted as measure

before m in measurements where basis(m) = "X":
  Z_ERROR(min(1 / 2, scale * (1 - primitive("measure", "fidelity")))) on ions(m) counted as measure

after g in two_qubit_gates:
  DEPOLARIZE2(min(15 / 16, scale * ms_error(gate_heat(g), gate_length(g)))) on ions(g)
    counted as ms_base = ms_error(0, 2),
               ms_heating = ms_error(gate_heat(g), 2) - ms_error(0, 2),
               ms_chain = ms_error(gate_heat(g), gate_length(g)) - ms_error(gate_heat(g), 2)

after g in single_qubit_gates where gate(g) != "VZ" and gate(g) != "I":
  DEPOLARIZE1(min(3 / 4, scale * (1 - primitive("1q_gate", "fidelity")))) on ions(g)

after r in resets:
  X_ERROR(min(1 / 2, scale * primitive("reset", "error"))) on ions(r)

after k in steps + readout where idle and duration(k) > 0 and t2 != none:
  Z_ERROR(min(1 / 2, scale * ((1 - exp(-duration(k) * 1e-6 / t2)) / 2))) on ions

What counts as running the experiment

Before any sampling, the noiseless circuit is checked. Every detector and observable must be deterministic, and must have the parity the source circuit gives it. The second half matters: a program that implements a gate with the opposite sign (an MS pulse of −π/2 for +π/2) keeps every detector deterministic but flips its value, and is caught only there.

The memory experiments

The data readout after the last round is added by the grader, where the ions are, with the device's measurement error; an XZ experiment reads each patch in its own basis. The reference compiler's rotation cannot measure an ion that rides the loop. This is an approximation: the readout's own transport is not charged.