feat: add QuantumOpticsRepr(lazy=true) support for LazyOperator output

[ibishal]

adds express_nolookup methods for SAdd, SMulOperator, and STensor that return LazySum, LazyProduct, and LazyTensor when r.lazy is true. when its false, falls back to the existing eager path. includes tests and a short docs example. depends on qojulia/QuantumInterface.jl#80

before this, express(op, QuantumOpticsRepr()) would produce an eager Operator. now it produces lazy types:

using Test
using QuantumSymbolics
using QuantumOptics

r_lazy = QuantumOpticsRepr(lazy=true)

op = tensor(X, I) + tensor(I, Z)

eager_op = express(op, QuantumOpticsRepr())
lazy_op  = express(op, r_lazy)

println("lazy_op type:  ", typeof(lazy_op))
@test lazy_op isa LazySum
@test isapprox(dense(lazy_op), eager_op)
println("sum tests passed")

prod_op  = tensor(X, I) * tensor(I, Z)
lazy_prod = express(prod_op, r_lazy)

println("lazy_prod type: ", typeof(lazy_prod))
@test lazy_prod isa LazyProduct
@test isapprox(dense(lazy_prod), express(prod_op, QuantumOpticsRepr()))
println("product tests passed")

it produces

lazy_op type:  LazySum{CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, Vector{Any}, Tuple{LazyTensor{CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, ComplexF64, Vector{Int64}, Tuple{Operator{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}, LinearAlgebra.Diagonal{ComplexF64, FillArrays.Ones{ComplexF64, 1, Tuple{Base.OneTo{Int64}}}}}, Operator{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}}, LazyTensor{CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, ComplexF64, Vector{Int64}, Tuple{Operator{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, Operator{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}, LinearAlgebra.Diagonal{ComplexF64, FillArrays.Ones{ComplexF64, 1, Tuple{Base.OneTo{Int64}}}}}}}}}
sum tests passed
lazy_prod type: LazyProduct{CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, Int64, Tuple{LazyTensor{CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, ComplexF64, Vector{Int64}, Tuple{Operator{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, Operator{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}, LinearAlgebra.Diagonal{ComplexF64, FillArrays.Ones{ComplexF64, 1, Tuple{Base.OneTo{Int64}}}}}}}, LazyTensor{CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, ComplexF64, Vector{Int64}, Tuple{Operator{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}, LinearAlgebra.Diagonal{ComplexF64, FillArrays.Ones{ComplexF64, 1, Tuple{Base.OneTo{Int64}}}}}, Operator{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}}}, Tuple{Ket{CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, Vector{ComplexF64}}}, Tuple{Bra{CompositeBasis{Vector{Int64}, Tuple{SpinBasis{1//2, Int64}, SpinBasis{1//2, Int64}}}, Vector{ComplexF64}}}}
product tests passed

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Part of qojulia/QuantumOptics.jl#521

[ibishal]

the changelog i have pasted here to avoid merge conflicts

• Add lazy=true option to QuantumOpticsRepr. When set, express returns LazySum, LazyProduct, or LazyTensor for symbolic operator sums, products, and tensor products instead of materializing full matrices.

[ibishal]

@Krastanov can i get a review on this ?