Add lazy field to QuantumOpticsRepr (qojulia/QuantumOptics.jl#521)

[mk0dz]

Part 1 of 2 for qojulia/QuantumOptics.jl#521 (lazy operator support).

The ask

Add a lazy::Bool=false keyword to QuantumOpticsRepr so that
express(x, QuantumOpticsRepr(lazy=true)) produces structure-preserving lazy
operators: symbolic sum → LazySum, product → LazyProduct,
tensor → LazyTensor, with dense(lazy) ≈ eager and backward compatibility
for QuantumOpticsRepr() / QuantumOpticsRepr(cutoff).

The key insights

QuantumSymbolics expresses a composite symbolic expression via
operation(s)(express.(arguments(s))...) — it applies the symbolic operation
(+, *, ⊗) to the eagerly-expressed arguments. Making it lazy = swap the
operation for its lazy constructor. operation() is + for SAdd, * for
SMulOperator/SScaled, ⊗ for STensor (verified in source), so a single
dispatch on the operation suffices.

Changes (2 repos → 2 coordinated PRs)

1. QuantumInterface.jl — src/express.jl

Base.@kwdef struct QuantumOpticsRepr <: AbstractRepresentation
    cutoff::Int = 2
    lazy::Bool = false          # NEW
end
QuantumOpticsRepr(cutoff::Int) = QuantumOpticsRepr(cutoff, false)  # keep 1-arg ctor

The explicit 1-arg constructor is required because @kwdef with two fields makes
the positional constructor need both args — without it, QuantumOpticsRepr(2)
(a documented usage) would break.

2. QuantumSymbolics.jl — ext/QuantumOpticsExt/QuantumOpticsExt.jl QuantumSavory/QuantumSymbolics.jl#201

A express_nolookup(s, repr::QuantumOpticsRepr) method that, when repr.lazy,
maps the operation to its lazy constructor (and otherwise reproduces the eager
behaviour exactly). Guards ensure ket/bra cases (which also carry operation===*)
fall through to eager, and that LazyTensor (which needs densifiable factors)
collapses any lazy factor while keeping the tensor product itself lazy.
Plus test/general/express_lazy_tests.jl (auto-discovered) and a paragraph in
docs/src/express.md.

Validation (local, Julia 1.12.6, dev-linked QuantumInterface)

test	result
new express_lazy_tests.jl (constructor, backcompat, sum/product/tensor, dense≈eager, scalar, nesting, eager-unchanged)	12/12 pass
existing express_opt_tests.jl (eager sums/products/tensors/mixed)	15/15 pass — no regression
basis_consistency_tests.jl	pass

Files changed (PR contents)

QuantumInterface.jl:
  src/express.jl                                   (+ lazy field, + 1-arg ctor)
QuantumSymbolics.jl:
  ext/QuantumOpticsExt/QuantumOpticsExt.jl         (+ lazy express method)
  test/general/express_lazy_tests.jl               (new)
  docs/src/express.md                              (+ lazy paragraph)

AI Acknowledgment: i want to thank claude opus 4.6 for making me understand code base of both repos and helpin me running testing and validations