Crate deep_causality_quantum

Expand description

Quantum causal models on the causal monad.

This crate carries the quantum-information layer of DeepCausality: the QuantumGates/QuantumOps traits and gate kernels migrated out of deep_causality_physics, with HilbertState (the pure-state ket) staying in deep_causality_multivector as the foundational carrier.

Two quantum senses share this crate but are kept strictly apart by modality: the verifiable path (deterministic simulated Choi–Jamiołkowski operators, checked at the freeze boundary) is the default build and the target of the Lean proofs; the emergent path (a physical QPU call as a monadic effect) is a seam only.

All metric signatures come from deep_causality_metric, the single source of truth; this crate defines no metric type of its own.

Structs§

Abstraction: A downward abstraction from a low-level model L to a high-level model H.
Adjudication: What adjudicate examined and concluded.
AlignmentEntry: One aligned type: high-level wires, the low-level wires they abstract, the channel and its section.
AlignmentStructure: What check_alignment_structure computed.
BoundaryWarrant: What a boundary check certifies: the measured hypothesis and the bound it buys.
CausalStructure: A causal structure: a bipartite influence relation between input systems and output systems. contains(i, o) holds when input i influences output o.
Channel: A quantum channel, CPTP-checked once, at construction.
Check: One decision: a measured quantity against a threshold, with the margin and the verdict.
CheckReport: The records of one decision, with the count of what it examined.
CircuitModel: A compositional model in QC. See the module documentation.
CircuitSubject: A compositional model in QC: the circuit is the stored object, and its dilation is what the structural stages screen. The one subject that can enter an abstraction.
ClassInvariance: What a class-invariance check examined and concluded.
CliffordAction: What a Clifford-action check examined and concluded.
CodeAbstraction: A CSS code as an abstraction. See the module documentation.
CodeSubject: A chain complex, evaluated exactly. No probes, no evidence.
CommutatorCheck: One recorded commutator check (the shared B1(c)/Q-TOL telemetry).
CommutatorTolerance: The depth-aware, condition-driven commutator tolerance (Q-TOL): an incremental first-order forward-error budget over the real unit roundoff u. The pair test accepts [ρ_j, ρ_k] = 0 iff ‖[ρ_j,ρ_k]‖_F ≤ C · (‖ρ_j‖·budget_k + ‖ρ_k‖·budget_j + 2·γ_n·‖ρ_j‖·‖ρ_k‖) with γ_n = n·u/(1−n·u) and C the safety factor. Per-node budgets default to u·‖ρ‖_F; deeper/nested models can supply larger budgets that grew through their construction.
Config: A built configuration: a subject that passed its preconditions, and what the stages share.
ConfigBuilder: A configuration under construction.
Control: The control stage: observe, gate, fork, predict, compare, design, adjudicate. Failure is sticky and is carried out by finalize as the structured error.
ControlReport: The report control finalizes into: the root ledger, every world’s ledger side by side, the plan and the adjudication.
ControlWorld: One live world after fork: a candidate, the plant under it, and its own ledger.
CountHistogram: The concrete outcome-count histogram returned by the in-process simulator.
CssCode: A CSS code read off a chain complex: n qubits from the 1-cells, k logical qubits from β₁ over 𝔽₂, and the two check families as the raw columns of ∂₂ and δ₀.
DensityMatrix: A validated density matrix: Hermitian, positive semidefinite (checked via the dense Hermitian eigendecomposition), and unit trace — every constructor enforces the invariants and returns a typed QuantumError on violation.
DesignPlan: What design returns: the ordered experiments, their total cost, what each resolves, what no experiment resolves, and the separation report over every pair examined.
DiagonalPhase: A diagonal logical gate: exp(2πi · Q(a(γ)) / M) with M a power of two.
DiamondBound: The two-sided bound a Frobenius residual on Choi operators places on the diamond distance.
Dilated: A dilated circuit: the factorization, its supports, the default instruments and the wiring.
Draw: One draw against a budget: the shots granted and the seed they are drawn at.
EnvironmentalPrep: A read-only handle to the environmental preparation ρ_A. Cloneable and comparable, but never mutable: the only way to obtain one is Self::new, and it exposes no write methods, keeping the simulated-CJ model in the verifiable region.
Evidence: What a configuration declares: how many shots, at which seed.
ExactNaturality: The exact naturality check of a code abstraction over its gates.
ExactProgram: A program the exact semantics can evaluate.
Experiment: An experiment a plan may choose: its cost, the shots it would take, and the read-out each hypothesis predicts for it.
FactorSupports: The Hilbert support of each factor: the ordered leg-ids it acts on (ascending, the row-major factor layout) plus each leg’s dimension. For the flat QCM the leg-id of a single-system node is the node index itself, and support(Aᵢ) = {Aᵢ} ∪ Pa(Aᵢ).
Fault: One fault: a Pauli error on distinct wires, inserted after a node of the low-level circuit or, with no node named, before its first box.
FaultRecord: One fault’s verdict.
FaultSet: A finite signature of fault queries over the low-level model.
FaultToleranceReport: The fault-tolerance report of one gate or one abstraction under a fault set.
GateNaturality: One gate’s exact naturality verdict.
GaugeFieldGate: A diagonal gate in the algebra of its blocks’ logical Z̄s. See the module documentation.
HarunaFilter: The Haruna filter: which Table 1 gates of a code tolerate every weight-one Pauli fault.
Hypothesis: A structural or mechanism candidate.
IdealRecovery: The isometry and the recovery of a code.
InducedDag: The open DAG a compositional model induces (Lorenz & Tull, arXiv:2602.16612, Example 61): one vertex per node of the model’s grouping, one edge per wire leaving one node and entering another. Derived, never stored beside the model.
InvarianceWitness: The basis state that witnessed a class-invariance failure.
LdpcWeights: What check_ldpc_weights examined and concluded.
Ledger: The threaded state of a run: what was spent on the device, and what was only computed.
LogicalBasis: The logical operators of a CSS code at one grade: a basis of H_k and one of H^k.
LogicalPauli: A Pauli operator on the physical qubits, in symplectic form.
LogicalProgram: A logical gate as a physical-gate program, with the global phase the construction carries.
Marginalised: What a marginalisation returns when its warrant holds.
Mechanisms: Marker: the plant’s candidates are mechanisms, which carry no structural claim.
MinCostCover: The objective design solves: cover every hypothesis pair at floor_bits of separation at least cost, refusing above max_hypotheses.
ModelSubject: A Choi–Jamiołkowski factorization over a frozen graph: the degenerate plant with one structural candidate and no evidence, and what the shipped freeze_quantum callers map onto.
NaturalityReport: What check_naturality examined and concluded.
NoCandidates: Marker: the plant has no candidates yet.
NoSubject: The builder before a subject is named.
NodeLeg: One node’s leg: its wires ascending, their dimensions, and the node dimension d.
NumericCaps: The two caps of the numeric semantics, both counted and refused before allocating.
Observable: A named projector carrying its own read-out.
PlanEntry: One chosen experiment and the pairs it resolves.
PlantSubject: A system that evolves and is measured, with the observables it exposes and its candidates.
ProcessFactors: The node-keyed store of CJ factors. Keys are intrinsic graph node indices (never enumeration/insertion order); an absent key denotes a node with no operator factor. This is an external parameter to the freeze, mirroring LambdaEdges<V>; it is never carried on the runtime arity-5 STATE channel.
Projection: A projection (Hermitian idempotent) on a fixed D-dimensional Hilbert space. The type-level dimension is what lets Verdict::bottom/top (which take no arguments) know the space they live in.
ProjectionFold: The projection lattice’s fold of a commuting family: the meet and the join of every verdict.
Propagated: A Pauli pushed through an exact program: the Pauli it became and the diagonal remainder the non-Clifford layers left, U P U† = pauli · remainder up to the remainder’s own phases.
QcMorphism: A morphism of QC carried at the Kraus level: for each pair of classical input values x and classical output values y, a family of Kraus operators d_out × d_in, the completely positive map f(y | x) of Lorenz & Tull’s Example 57. The Choi operator of a block is formed only when asked for, under the entry cap.
QclBuilder: The one origin of every configuration, and the entry to each stage.
QpuParams: The requested-parameter summary routed to the STATE channel by qpu_effect.
QuantumCircuit: A storable circuit: a num_qubits register, an ordered gate program, and a computational-basis measurement over a subset of qubits. Clone + Debug + PartialEq; carries no amplitudes.
QuantumError: The crate-local quantum error: an outer newtype over QuantumErrorEnum, mirroring the repo convention (CausalityError(CausalityErrorEnum::…)).
QuantumMarkovReport: The instrumented report of a Markov check: one entry per intersecting-support factor pair.
QuantumPlant: A sealed, validated state that evolves by operation.
QubitOperator: A single-qubit unitary, built by name and owning its shape.
QuerySignature: A set of queries validated against the DAG they will be asked of.
QueryType: The wires a query’s morphism runs between, in the order the morphism’s legs take them: quantum wires ascending, classical wires in declaration order.
Screened: What validate terminates in: the config, the admitted candidates, and the report.
ShotBudget: The ledger of a shot budget: what remains, what was spent, and the run seed.
ShotEstimate: A Bernoulli point estimate from a histogram, with its standard error and the shots behind it.
SimCalibration: The calibration surfaced to the context channel by qpu_effect.
SimQpu: A deterministic dense state-vector simulator. Amplitudes never leave the simulator — sample returns only a classical CountHistogram.
Structural: Marker: the plant’s candidates are structural, and must be screened before control.
Survivor: The hypothesis that survived, and how far it stood from its nearest rival.
TypeAlignment: The type alignment of an abstraction. See the module documentation.
Validate: The validate stage: checks accumulate, the first failure is sticky, and finalize terminates in a Screened or carries the structured error out.
World: One live world after a fork: the hypothesis it ran under, the verdict it came back with, and the read-out the verdict was taken from.

Enums§

AlignmentSide: Which side of a query’s type an entry aligns. A query has an input type and an output type (Lorenz & Tull, footnote 19), and a code’s low-level model in the shape of Example 58, encoder then gate, aligns its logical inputs by the identity and its physical outputs by the decoder.
Ambiguity: Why no single hypothesis survived.
Axis: The axis of a single-qubit rotation.
CheckItem: What one Check examined: the identifier the decision form is generic over.
CheckMatrix: Which check matrix an LDPC item came from.
CheckVerdict: The three states a report can be in. Vacuous is an acceptance that examined nothing.
CircuitBox: One box of a CircuitModel: a morphism of QC (Lorenz & Tull, arXiv:2602.16612, Figure 2) on the wires it names.
ExactLayer: One layer of an exact program.
Factorization: Where the factors a Markov report certifies came from.
FaultOrigin: Which constructor produced a fault set.
GateOp: A single reified gate over the migrated gate alphabet. Plain data — no function pointers, no amplitudes.
LdpcItem: Whether an LDPC item is a column, one check, or a row, one qubit.
LogicalGate: A logical gate of Table 1 on the code’s logical qubits, by index.
PauliKind: A single-qubit Pauli error.
QuantumErrorEnum: Detailed classification of quantum errors. Typed variants name the exact failure; a String payload carries the operation-specific context.
Query: A query on a compositional model, Lorenz & Tull, arXiv:2602.16612, §3.2 and §7.2.
ScreenOrigin: Where a screened subject’s factorization came from.
ScreenStatus: Why a screened report is or is not current.
SemanticsPath: Which semantics decided a value derived from a CircuitModel.
Spec: A real-valued specification a read-out is judged against.
StructureScope: What the predicates license.
Tolerance: The tolerance family: the policies the crate’s checks derive their thresholds from, named.
WireSource: Where a wire enters a node from.
WireType: The type of a wire in the category QC (Lorenz & Tull, arXiv:2602.16612, Example 57): a finite-dimensional Hilbert space, drawn thick, or a finite set of classical outcomes, drawn thin.
WorldVerdict: The verdict a forked world came back with. Verdicts are extracted at the measurement boundary, so there is no constructor from an operator: a world that reaches adjudicate carrying an operator no observe turned into a verdict has nothing to fold.

Constants§

ATOM_ENUMERATION_CAP: The largest block-occupancy enumeration check_class_invariance will attempt per shift.
DEFAULT_MAX_HYPOTHESES: The default cap on the hypotheses design will cover exactly. 2^C(7,2) = 2^21 subsets.
DILATION_ENTRY_CAP: The most entries one factor is allowed to occupy: a factor on legs of dimension d² each is dense on their product, and three two-qubit nodes already reach 2^24.
FAULT_SET_CAP: The default cap on the number of faults a set may enumerate.
FROBENIUS_ON_CHOI: The norm a naturality report measured in.
IDEAL_RECOVERY_MAX_QUBITS: The widest register the dense construction takes.
MAX_GATE_QUBITS: The widest gate a unitary is formed for: a 2^12 × 2^12 matrix is the numeric semantics’ default entry cap, and a wider Cmz would allocate before any cap could refuse it.
MAX_GAUGE_BLOCKS: The most blocks one gate carries, so the phase table stays 2^m ≤ 2^16 entries.
TUPLE_ENUMERATION_CAP: The largest tuple enumeration logical_t and logical_multi_cz attempt by default. About a million tuples: under it, a weight-180 T̄; over it, the cost is reported rather than paid.

Traits§

BuildSubject: What build() checks of a subject before any stage runs.
ControlSource: What may enter control: a plant config whose candidates are mechanisms, or a screen. A plant config with structural candidates has no implementation, which is the compiler saying that structural candidates enter control only through validate.
QcModel: A compositional model in QC that can answer queries: the low-level or high-level side of an Abstraction. Static dispatch: each model type implements it directly.
QpuSampler: The generic sampler seam. Implementations return measurement shots as classical ShotHistogram data at the Kleisli cut; no concrete vendor adapter is shipped by this crate. Used only as a bound S: QpuSampler.
QuantumGates: Standard Quantum Gates interface.
QuantumOps: Core Quantum State Operations (Dirac Notation), parameterized over the underlying real field $R$ so the operations can be carried out at f32, f64, f128, or any other real-field precision.
ShotHistogram: A classical measurement histogram: outcome bitstrings (packed LSB-first over the circuit’s measured qubits) to shot counts. Never exposes amplitudes.
SubjectOrigin: The origin a subject type reports.

Functions§

adjudicate: Fold the worlds’ verdicts under the verdict law, and separate the survivor from its rivals.
apply_choi: Applies a channel to a state through its Choi operator: E(ρ)[j,l] = Σ_{ik} ρ[i,k] · J[(i,j),(k,l)].
apply_gate: Causal wrapper for mechanics::apply_gate_kernel.
apply_gate_kernel: Applies a quantum gate to a state: $|\psi’\rangle = U |\psi\rangle$.
apply_kraus: Applies a channel to a state through its Kraus family: E(ρ) = Σ K ρ Kᴴ.
bhattacharyya_bits_per_shot: The per-shot Bhattacharyya distance between two Bernoulli distributions, in bits: −log₂(√(pq) + √((1−p)(1−q))) (Bhattacharyya, Bull. Calcutta Math. Soc. 35, 1943). Zero when p = q, and the coefficient inside the logarithm is the overlap of the two distributions.
born_probability: Causal wrapper for mechanics::born_probability_kernel.
born_probability_kernel: Calculates the Born probability: $P = |\langle \text{basis} | \text{state} \rangle|^2$.
born_projective_prob: The Born-rule probability as the Prob MV-algebra verdict — the boundary where a quantum measurement becomes a classical (fuzzy) verdict.
born_projective_probability: The Born-rule probability of the measurement outcome projection on state rho: Tr(P ρ), clamped to [0, 1]. Real for a Hermitian P and ρ; a non-negligible imaginary part signals a malformed input and errors.
channel_compose: Causal wrapper for Channel::compose.
channel_from_kraus: Causal wrapper for Channel::from_kraus.
channel_unitary: Causal wrapper for Channel::unitary.
check_alignment_structure: Definition 49’s predicates on a partition. partition[X] lists the low-level vertices of the high-level vertex X; high_inputs are the high-level input vertices, whose blocks fullness does not ask about.
check_completely_positive: Complete positivity check: E is CP iff its Choi operator is PSD (spectrum ≥ −tol via the Hermitian eigendecomposition).
check_completely_positive_report: The report-returning form of check_completely_positive.
check_ldpc_weights: Both weights of both check matrices against one declared bound.
check_trace_preserving: Trace-preservation check: E is TP iff Tr_out(J) = I_in, computed with the named-subset partial trace over the out leg.
check_trace_preserving_report: The report-returning form of check_trace_preserving.
choi_compose: Composes two channels through their Choi operators.
choi_from_kraus: Builds the Choi operator J(E) from a Kraus family {K_κ} of d_out×d_in matrices: J[(i,j),(k,l)] = Σ_κ K_κ[j,i]·conj(K_κ[l,k]).
choi_identity: The Choi operator of the identity channel on a d-dimensional space.
clifford_conjugate: The image U P U† of a Pauli under a Clifford program, up to phase.
clifford_conjugation: The Clifford conjugation with coefficient conjugation: the grade-k blade picks up the sign (−1)^(k(k+1)/2) (grade involution ∘ reversion) and every coefficient is complex-conjugated. On a negative-signature metric this is the adjoint whose minimal-left-ideal restriction matches the matrix-column Hermitian adjoint.
commutator: Causal wrapper for mechanics::commutator_kernel.
commutator_kernel: Calculates commutator $[A, B] = AB - BA$.
derive_code: The CSS code of a chain complex at grade 1, composed from the shipped counts and columns.
design: The exact minimum-cost cover of the C(n, 2) hypothesis pairs by the offered experiments.
dirac_bracket_kernel: The metric-correct Dirac inner product ⟨φ|ψ⟩ on kets: the scalar part of adj(φ)·ψ, where adj is QuantumOps::dag (reversion + conjugation) for a positive-signature metric and clifford_conjugation for a negative-signature metric. On the minimal left ideal this equals the raw column inner product of to_ket(φ) and to_ket(ψ).
embed_on_legs: Embeds an operator acting on the legs op_legs into the full space (leg → dimension, ascending leg order = factor order), acting as the identity on every other leg — the Kronecker-with-identity alignment the freeze commutator uses to compare factors on their support union.
expectation_value: Causal wrapper for mechanics::expectation_value_kernel.
expectation_value_kernel: Calculates the expectation value: $\langle A \rangle = \langle \psi | A | \psi \rangle$.
fidelity: Causal wrapper for mechanics::fidelity_kernel.
fidelity_kernel: Calculates Quantum Fidelity: $F = |\langle \psi_{\text{ideal}} | \psi_{\text{actual}} \rangle|^2$.
freeze_quantum: Freezes graph with the built-in Stage-4 checks and the quantum Markov commutativity check as the level-specific hook, returning the instrumented report on success. On a quantum-check failure the graph is rolled back to the dynamic state (the hook’s unfreeze) and the structured QuantumError is recovered via an internal stash — not merely its Display message. A failure in the built-in checks (acyclicity / single-writer) surfaces as a QuantumError::CalculationError carrying the graph error’s message.
frobenius_norm: The Frobenius norm ‖M‖_F = √(Σ |m_ij|²).
gate_unitary: The unitary matrix of one gate over its qubits in ascending order, the first qubit most significant, which is the row-major leg order embed_on_legs and the numeric semantics use.
haruna_cz_gate: Causal wrapper for gates_haruna::logical_cz.
haruna_hadamard_gate: Causal wrapper for gates_haruna::logical_hadamard.
haruna_s_gate: Causal wrapper for gates_haruna::logical_s.
haruna_t_gate: Causal wrapper for gates_haruna::logical_t.
haruna_x_gate: Causal wrapper for gates_haruna::logical_x.
haruna_z_gate: Causal wrapper for gates_haruna::logical_z.
hermiticity_defect: The Hermiticity defect max_ij |M_ij − conj(M_ji)| (zero iff M = Mᴴ).
identity_channel: An identity channel on d dimensions, the box a noiseless wire carries.
identity_matrix: The d×d complex identity matrix.
is_clifford_gate: Whether a gate is Clifford.
is_diagonal_gate: Whether a gate is diagonal in the computational basis.
kraus_from_choi: Recovers a Kraus family from a (PSD) Choi operator via the Hermitian eigendecomposition: K_κ = √λ_κ · unvec(v_κ) for λ_κ > tol.
logical_cz: The logical CZ gate, Table 1 row 5 and Eq. (3.42):
logical_hadamard: The logical Hadamard, Table 1 row 4 and Eq. (3.27):
logical_multi_cz: The logical multi-controlled Z, Table 1 row 6:
logical_multi_cz_with_cap: logical_multi_cz under an explicit cap on the tuple enumeration.
logical_s: The logical S gate, Table 1 row 3 and Eq. (3.17):
logical_t: The logical T gate, Table 1 row 7 and Eq. (3.59):
logical_t_with_cap: logical_t under an explicit cap on the tuple enumeration.
logical_x: The logical X gate, Table 1 row 2: X̄(γ̃) = ∏_k X_{ĩ_k} over supp(γ̃).
logical_z: The logical Z gate, Table 1 row 1: Z̄(γ) = ∏_k Z_{i_k} over supp(γ).
markov_certificate: The certificate a Markov report grants, or the error its first rejection means.
matrix_commutator: The operator commutator [A, B] = A·B − B·A on complex matrices.
matrix_trace: The matrix trace Tr(M).
max_modulus: The largest modulus over a sequence of complex numbers, or zero over an empty one.
multi_cz_tuple_count: The number of tuples logical_multi_cz emits over: the product of the supports’ weights. Saturates rather than overflowing. An empty support makes the product empty, so the count is zero wherever that chain sits, saturated prefix or not.
observable_from_ket: Causal wrapper for Observable::from_ket.
observable_read_out: Causal wrapper for Observable::read_out.
partial_trace: The partial trace over a named subset of tensor legs.
partial_trace_preservation_boundary: The sound path past partial_trace’s non-preservation: given Z on the kept factor and M on the whole space, measure how nearly Z ⊗ 1_B commutes with M, and return the bound that buys on [Z, Tr_B(M)].
plant_evolve: Causal wrapper for QuantumPlant::evolve.
plant_from_ket: Causal wrapper for QuantumPlant::from_ket.
qpu_effect: Lifts a physical-QPU call into a causaloid f at the Kleisli boundary: on success the shot histogram rides the VALUE channel, the requested parameters the STATE channel, the device calibration the CONTEXT channel, and the provenance the LOG channel; a job failure rides the ERROR channel with the value absent. Generic over S: QpuSampler (no dyn).
quantum_markov_check: Runs the quantum Markov commutativity check over the external factor store, pair by pair, on intersecting Hilbert supports only. Returns the instrumented report on success, or a QuantumError::CommutatorNonZero naming the first offending pair. Sound: it never accepts a pair whose commutator exceeds the Q-TOL threshold.
quantum_markov_check_report: The report-returning form of quantum_markov_check, on the model’s own factors.
quantum_markov_check_report_as: quantum_markov_check_report with the provenance of the factors stated.
qubit_phase: Causal wrapper for QubitOperator::phase.
qubit_rotation: Causal wrapper for QubitOperator::rotation.
reduce_turns: t reduced to [0, 1) turns.
sample_projector: shots Bernoulli draws at Tr(Pρ), seeded, as a one-bit histogram: outcome 1 is the projector accepting, 0 rejecting.
sample_within_budget: request shots of a projector read-out, drawn against budget.
separation_bits: The separation of two Bernoulli read-outs at shots independent draws, in bits. The Bhattacharyya distance is additive over a product of independent samples, so this is shots times bhattacharyya_bits_per_shot; it is what a floor in bits is compared against.
shots_to_observable: An observable Uncertain<f64> from the histogram: each outcome is mapped to a real value by value_of, and the empirical mean and unbiased (n−1) sample variance are summarized as a normal Uncertain. O(distinct outcomes) — the statistics are accumulated directly from the (outcome, count) entries, never by materializing one sample per shot.
shots_to_qubit_bernoulli: A per-qubit UncertainBool<f64> from the histogram: the Bernoulli distribution whose success probability is the measured frequency of 1 on the bit_index-th measured qubit (LSB-first in measurement order).
supports_intersect: Whether two Hilbert supports (sets of leg indices) intersect — the freeze check computes a commutator only for intersecting supports.
swap_channel: The swap of two d-dimensional systems as a channel.
symplectic_dual_basis: A symplectic dual basis: one cocycle γ̃_j per homology generator, with ⟨γ_i, γ̃_j⟩ = δ_ij.
t_tuple_count: C(w, 2) + C(w, 3): the pair and triple tuples logical_t emits over for a chain of weight w. Saturates rather than overflowing, so a count that does not fit reads as “above any cap”.

Type Aliases§

AlignmentSpec: One alignment entry as given to TypeAlignment::new: (high wires, low wires, τ, E).
BoxId: A box’s index in a CircuitModel.
CjFactor: A single Choi–Jamiołkowski factor ρ_{Aᵢ|Pa(Aᵢ)} — a complex matrix on the composite Hilbert space of node Aᵢ and its parents.
ClassicalValues: Classical values on a list of classical wires, in wire order.
Gate
NodeId: A node’s index in a CircuitModel’s grouping.
Operator
Turns: The phase a diagonal logical gate applies, as an exact rational multiple of 2π.
WireId: A wire’s index in a CircuitModel.
Word: The word width of the 𝔽₂ chains the code stages carry.