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Changelog

All notable changes to SecondQuantizedAlgebra.jl will be documented in this file.

The format is based on Keep a Changelog, and this project adheres to Semantic Versioning.

[v0.14.0]

Adds symbolic dissipative dynamics and exact GKSL extraction, with breaking API changes for type stability.

Added

  • Symbolic Lindbladian, SuperOperator and SuperExpr maps, including collective dissipators, composition, Heisenberg generators, indexed sums and frame transformations. Use to_numeric for backend superoperators and to_numeric_master for Hamiltonian/collapse operators.
  • Exact GKSL extraction through Lindbladian(S[, basis]) and kossakowski(S, basis), with JumpBasis, support_basis, independent_basis and GKSLFormError. No Hilbert-space cutoff is needed; accepting floating-point roundoff requires an explicit rtol.
  • coefficient reads an operator-product or superoperator-sandwich coefficient; ambiguous constraints and summed expressions throw. map_coefficients transforms coefficients, while coefficient_terms, CoefficientTerm and has_coefficient_terms expose their scalar factors and atom powers.
  • harmonics, harmonic and secular extract exact Fourier components from coefficients, operators and dissipative maps. Noninteger harmonics throw.
  • displacement(U, a) reads a frame's displacement amplitude; UnitaryTransform(G, θ) supports symmetric hopping and squeezing generators.
  • Introspection through get_sum_indices(::QAdd), n_levels, ground_state, transition_levels and operator_axis. Indexed to_numeric accepts parameter and operators keywords.

Changed (breaking)

  • index_slot returns 0 instead of nothing for an abstract index; use iszero(index_slot(x)).
  • to_numeric, numeric_average and expect default to op_type = EagerOperator(). Custom backends must dispatch numeric_materialize on ::EagerOperator instead of ::Nothing.
  • fundamental_operators and find_operators use names = Symbol[] instead of nothing for automatic names. find_operators returns Vector{Union{Op, QAdd}} instead of Vector{QField}.
  • channels(L) returns a sorted vector of Channel => rate pairs in channel_order_key order, replacing unordered dictionary pairs.
  • For custom numeric backends, the numeric_operator(be, ::Val{kind}, op, subbasis) fallback is removed; unsupported roles throw. numeric_assemble_td receives plain (p, t) closures instead of PControlCoeff wrappers.
  • numeric_basis returns a tuple of dimensions for composite QuantumToolbox states.

Changed

  • Faster symbolic coefficient arithmetic, sparse QuantumOptics conversion on composite bases, LazyKet expectation values and QuantumToolbox time-dependent coefficient evaluation. Runtime-dispatch checks now cover both backend extensions.
  • substitute rejects parameter values that are neither numeric nor symbolic scalars with ArgumentError.

Fixed

  • Indexed sums preserve site counts after substitution or coefficient simplification, respect excluded sites and count overlapping diagonal cases once, including products of sums and dependent binders.
  • Coefficient arithmetic cancels positive numeric factors in roots without changing symbolic root branches, recognizes zero sums across different denominators and accepts bare symbolic scalars alongside phases. More large-prime radicals are canonical ([#291]).
  • Time-dependent squeezing requires Squeeze(a, r, ϕ, t); ambiguous Squeeze(a, r * t, t) calls now throw.
  • Indexed numeric conversion applies parameters even without sums; numeric_average handles constant imaginary terms. qadjoint and inner_adjoint accept averages and phase coefficients.
  • Single-operator expressions compare correctly (2a - a == a), find_operators removes duplicates, and LaTeX renders zero expressions and brackets complex prefactors correctly.

[v0.13.0]

Changed (breaking)

  • Exactness follows the numeric type: 2.0 stays floating point, including when combined with rationals. ComplexF64 coefficients arise only from floating-point input or division by an exact zero.
  • Internal coefficient storage replaces Coeff.z with Coeff.slot, accessed through native_scalar, and makes Monomial parametric in its exact tier.

Added

  • Scalar broadcasting, generic reductions and linear algebra for coefficient arrays, including det, adjoints, transposes, inner products and norms. LinearAlgebra is now a hard dependency.

Fixed

  • Exact arithmetic promotes beyond Int without overflow or conversion to floats. Raw symbolic rational coefficients and moving-frame conjugation preserve exact complex values.
  • Exact numeric radicals canonicalize when every prime factor is below 2^32; larger factors remain symbolic ([#291]).
  • Coefficient and operator arrays render correctly through latexify and text/latex.

[v0.12.0]

Added

  • Exact unitary transformations for bosonic and phase-space displacements, Bogoliubov maps, mode mixing, squeezing, spin/Pauli rotations and N-level basis changes, with composition, inversion, rotating/displacement frames and moving-frame gauges.
  • Formal operator functions sin(A), cos(A) and Hermitian-only expim(A), with exact structural rewrites and unitary conjugation. Use taylor(expr, 0:n) to lower them to polynomials before numeric conversion.
  • get_variables discovers scalar parameters, including filtered and buffer forms of the Symbolics interface.

Changed (breaking)

  • Rename prefactor to get_prefactor, and unique_ops / unique_ops! to unique_up_to_adjoint / unique_up_to_adjoint!.
  • Replace single-term operators(::QAdd) with expression-wide get_operators, which returns unique operators in canonical order. For repeated factors and their order, iterate the expression and read each QTerm.ops.

Fixed

  • Type-stable QuantumToolbox conversion and standalone coefficient LaTeX rendering.
  • Import tensor and ⊗ from TensorCore for QuantumInterface 0.4.4 compatibility; zero-argument Hilbert-space tensor products throw instead of recursing indefinitely.

[v0.11.0]

Fixed

  • Preserve compact expim phases through simplification, substitution, differentiation, unitary transformations, printing and averaging.

[v0.10.1]

Added

  • Exact named unitary transformations for Fock, phase-space, spin/Pauli and N-level operators, including composition, inversion and time-dependent gauges.
  • Canonical expim phase arithmetic, with substitution, differentiation and exponential/trigonometric conversion; simplification of exact trigonometric and hyperbolic identities.
  • A unitary-transformation guide and moving-frame resonator example.

Fixed

  • dagger(::QField) extends QuantumInterface.dagger and forwards to qadjoint. Use qadjoint or qconj for scalar and symbolic adjoints.

[v0.10.0]

Numeric conversion gains extensible QuantumOpticsBase and QuantumToolbox backends.

Added

  • QuantumOpticsBackend() and QuantumToolboxBackend(), selected through to_numeric(op, h::HilbertSpace, dims; backend, parameter, time_parameter, operators, adjoint_ops, op_type).
  • Public numeric_* hooks for basis construction, operator assembly, materialization and expectation values, allowing downstream numeric backends.
  • QuantumToolbox coefficients of the form (p, t) -> value for differentiable solver controls; QuantumOptics rejects this form.
  • Expanded precompilation workloads to reduce first-call latency.

Changed (breaking)

  • Numeric APIs require explicitly loading QuantumOpticsBase or QuantumToolbox; QuantumOpticsBase is now a weak dependency and QuantumInterface a hard dependency.
  • Time-dependent conversion returns native TimeDependentSum or QobjEvo objects instead of t -> op(t) closures. It accepts only op_type = nothing or identity.
  • Product-space dims requires one entry per symbolic subspace. Indexed layouts reject duplicate or out-of-range physical slots.

Changed

  • Averages of provably Hermitian operators carry real symbolic type, allowing their conjugates to simplify directly.

Fixed

  • Coefficients fold elementary functions at literal zero to exact values.
  • Leaf commutators distinguish different operator names on the same space, agreeing with a*b - b*a.

[v0.9.4]

Added

  • CollectiveNLevelSpace and CollectiveTransition describe identical multilevel systems exactly in the permutation-symmetric subspace, including QuantumOpticsBase ManyBodyBasis conversion. Collective transitions cannot be site-indexed; their diagonal sum is N I, not I.
  • OP_COLLECTIVE_TRANSITION = 7, preserving existing OpKind values.
  • Public indexed-average construction and access through indexed_sum(body, indices; non_equal) and get_sum_body.
  • Operator/index accessors and rebuilders: operator_index, acts_on(::Index), set_acts_on and rename.

Changed

  • Commutation supports both residual terms of collective-transition algebra.
  • Constructors reject string names with a clear ArgumentError; names must be Symbols.

Fixed

  • Index suffixes such as i_2_1 render as i_{2,1}, avoiding invalid LaTeX double subscripts.

Documentation

  • Indexed versus collective descriptions and a finite-N Tavis-Cummings example.

[v0.9.3]

Fixed

  • Products crossing indexed sums preserve diagonal exclusions when the summed index occurs only in the coefficient, preventing spurious diagonal contributions.

[v0.9.2]

Changed (breaking)

  • to_numeric defaults to concrete sparse operators consistently across expression forms. Use op_type = dense for dense output or op_type = identity to retain the previous lazy representation.

[v0.9.1]

Fixed

  • Sums of averages containing different operator types print without comparison errors.

[v0.9.0]

Added

  • Simultaneous operator and scalar substitution. Replacements are applied once; adjoint rules are inferred unless replace_adjoint = false.
  • to_numeric(op, basis; parameter, time_parameter, operators, adjoint_ops, op_type) and vector conversion. Time-dependent parameters may be constants or functions, producing t -> op(t) closures.
  • Public to_num(::Coeff), Coeff and CNum, with API declarations through SciMLPublic.

Changed

  • Expressions display in Hilbert-space order, then operator-kind order.

[v0.8.3]

Changed

  • average of a many-term operator is now O(n) instead of O(n²): a 500-term sum drops from about 31 ms to 9.6 ms.
  • Wide symbolic prefactors build in O(n log n) instead of O(n²), with measured speedups of about 12.5× for sums and 17× for products at 800 terms.

[v0.8.2]

Changed

  • Non-indexed commutators allocate less and run about twice as fast on measured many-mode workloads, using about five times less memory.

Fixed

  • Double conjugation returns the original coefficient, and conjugated expressions that become constants fold numerically.

[v0.8.1]

Added

  • In-place sum and reduce(+, …) for Vector{QAdd}, integrated with MutableArithmetics. Use sum([terms...]); bare generators retain the generic fold. Measured many-mode construction is about 4–12× faster with 5–11× less memory.

Changed

  • Faster hashing of non-indexed operators reduces product, power, commutator and substitution costs without changing canonical results.

[v0.8.0]

Changed (breaking)

  • Operator roles share one concrete Op type. Destroy, Create, Transition, Pauli, Spin, Position and Momentum remain constructors, but type dispatch such as isa Destroy must use role predicates (is_destroy, is_transition, etc.) or optype(op)::OpKind.
  • Transition fields i, j, ground_state, n_levels become l1, l2, g, nlev; the Pauli/Spin axis field becomes l1.
  • Op and Index use interned IDs. Replace direct .name, .range and .sym reads with operator_name, index_name, index_range and index_sym. Subspace indices are Int32; interned IDs must not be serialized across sessions.

Changed

  • Concrete operator storage and faster coefficient arithmetic reduce dispatch and allocations in products, powers and normal ordering.

[v0.7.2]

Changed

  • Complex parameters and scalar functions stay on the native polynomial coefficient path, including conjugation. A measured three-cavity SLH construction is about 18× faster.
  • Single-parameter radicals canonicalize, so sqrt(p)^2 folds to p. Roots of composite expressions remain undistributed to preserve branches.

[v0.7.1]

Changed

  • Cached term hashes and faster operator-reduction checks improve measured product and power workloads by about 1.5–1.8×, with roughly half the allocations.

[v0.7.0]

Changed

  • make_time_dependent preserves per-site moments inside indexed sums instead of creating one collective unknown.
  • Concrete coefficients keep numeric and parameter-polynomial arithmetic native, expanding polynomials canonically. Measured algebra workloads improve by about 2–3.5×.

Fixed

  • Averaged indexed sums retain their full body and summation scope through symbolic arithmetic; differently scoped sums no longer cancel incorrectly. Added is_indexed_sum; existing sum metadata accessors remain supported.

[v0.6.5]

Added

  • @variables η::Number keeps a complex parameter atomic, with symbolic conj(η) and correct adjoint/numeric conversion, avoiding the real/imaginary expansion of ::Complex parameters.

[v0.6.4]

Fixed

  • change_index zeros DoubleIndexedVariable terms marked identical = false when their indices coincide, including occurrences nested in sums and products.

[v0.6.3]

Changed

  • Time-dependent averages display as ⟨op⟩(t) in text and LaTeX instead of internal variable names.

[v0.6.2]

Added

  • index_slot recovers the position of a per-slot index created with (i::Index)(k) without parsing its name.

[v0.6.1]

Added

  • Public order_key, term_order_key and qadd_order_key provide reproducible structural ordering, with equal keys exactly when expressions are isequal.

[v0.6.0]

Changed

  • Averages use symbolic type Number; make_time_dependent lifts them to time-dependent unknowns while preserving average metadata.

[v0.5.2]

Fixed

  • Commuting expressions with symbolic rational coefficients cancel exactly instead of leaving spurious terms in derived equations. Disjoint-subspace commutators avoid forming cancelling products.

[v0.5.1]

Changed

  • Averaged expressions use angle brackets in LaTeX; averaged indexed sums retain their summation prefix.

Fixed

  • Diagonal splitting preserves index-inequality constraints, preventing double-counting in nested and collective sums.

Documentation

  • Explain explicit bound-index naming and why alpha-equivalent sums are not automatically collected ([#156]).

[v0.5.0]

Breaking redesign of the algebraic core. The following changes apply when migrating from SecondQuantizedAlgebra v0.4 or the corresponding QuantumCumulants API.

Renamed

Previous APIReplacement
reorder(expr, pairs)assume_distinct_index(expr, pairs)
simplify(expr, h)expand_completeness(simplify(expr))
normal_order(expr, h)expand_completeness(normal_order(expr))
@cnumbers a b@variables a b
@rnumbers a b@variables a::Real b::Real
Parameter(:x)@variables x

Removed

Removed constructMigration
ClusterSpaceUse Index and Σ; pass truncation order to downstream moment expansion, e.g. meanfield(...; order = k).
SingleSum, DoubleSum, SpecialIndexedTermUse Σ, returning a QAdd; inspect bound indices and each term's ne constraints.
NumberedOperator, insert_indexKeep indices symbolic; instantiate sites in the numeric layer.
IndexedAverageSum, IndexedAverageDoubleSumAveraging handles indexed sums through symbolic metadata.
QMulArithmetic returns QAdd; iteration yields QTerm => CNum pairs with operator strings in term.ops and constraints in term.ne.
order_by_indexDeclare unresolved index inequalities with assume_distinct_index.

Changed

  • Ground-state projectors remain atomic through arithmetic, normal_order and simplify. Use expand_completeness to expand them explicitly.
  • simplify also simplifies scalar coefficients and removes unused sum indices.
  • Transition stores its ground state and level count, inferred from its NLevelSpace.
  • Free indices with unknown relationships retain physical order; use assume_distinct_index(expr, pairs) to enable sorting.

Migration example

Use @variables instead of @cnumbers, and specify the atom's subsystem when constructing transitions on a product space:

hc = FockSpace(:cavity)ha = NLevelSpace(:atom, 2)h = hc ⊗ ha@variables N Δ@qnumbers a::Destroy(h, 1)i = Index(h, :i, N, ha)g(i) = IndexedVariable(:g, i)σ(α, β, k) = IndexedOperator(Transition(h, :σ, α, β, 2), k)H = -Δ * a' * a + Σ(g(i) * (a' * σ(1, 2, i) + a * σ(2, 1, i)), i)

The final 2 in Transition selects the atom's subsystem in h, not its level count. Other constructor names and the commutator, averaging and numeric-conversion entry points remain available.

<!– Links generated by Changelog.jl –>

[v0.5.0]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.5.0 [v0.5.1]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.5.1 [v0.5.2]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.5.2 [v0.6.0]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.6.0 [v0.6.1]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.6.1 [v0.6.2]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.6.2 [v0.6.3]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.6.3 [v0.6.4]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.6.4 [v0.6.5]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.6.5 [v0.7.0]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.7.0 [v0.7.1]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.7.1 [v0.7.2]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.7.2 [v0.8.0]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.8.0 [v0.8.1]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.8.1 [v0.8.2]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.8.2 [v0.8.3]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.8.3 [v0.9.0]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.9.0 [v0.9.1]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.9.1 [v0.9.2]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.9.2 [v0.9.3]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.9.3 [v0.9.4]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.9.4 [v0.10.0]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.10.0 [v0.10.1]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.10.1 [v0.11.0]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.11.0 [v0.12.0]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.12.0 [v0.13.0]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.13.0 [v0.14.0]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/releases/tag/v0.14.0 [#156]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/issues/156 [#291]: https://github.com/qojulia/SecondQuantizedAlgebra.jl/issues/291