Support for arbitrary element types and sparse matrices (#108)

* support for arvitrary element types

* add sparse matrix support

* reformat

* more tests

* reformat

* Prepare v0.7.0 release

* Only patch version change

* update docs

Author: lpawela

Project.toml

@@ -1,44 +1,48 @@
 name = "QuantumInformation"
 uuid = "3c0b384b-479c-5684-b2ef-9d7a46dd931e"
+version = "0.5.1"
 authors = ["Dariusz Kurzyk <dkurzyk@iitis.pl>", "Łukasz Pawela <lpawela@iitis.pl>", "Piotr Gawron <gawron@iitis.pl>", "Marcin Przewięźlikowski <m.przewie@gmail.com>"]
-version = "0.5.0"
 
 [deps]
+Arpack = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
 Convex = "f65535da-76fb-5f13-bab9-19810c17039a"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MatrixEnsembles = "c7015dd7-3fb7-4a4c-827e-526313618491"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SCS = "c946c3f1-0d1f-5ce8-9dea-7daa1f7e2d13"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 TensorCast = "02d47bb6-7ce6-556a-be16-bb1710789e2b"
 TensorOperations = "6aa20fa7-93e2-5fca-9bc0-fbd0db3c71a2"
 
 [compat]
+Aqua = "0.8"
+Arpack = "0.5.4"
 Convex = "0.13.7, 0.14, 0.15, 0.16"
 DocStringExtensions = "0.8.3, 0.9"
-MatrixEnsembles = "0.1"
+DoubleFloats = "1.5.0"
+JET = "0.9, 0.10, 0.11"
+LinearAlgebra = "1"
+MatrixEnsembles = "0.2"
+Pkg = "1"
+PrecompileTools = "1"
+Random = "1"
 SCS = "1.1.0, 2, 3"
+SparseArrays = "1"
 StatsBase = "0.33.2, 0.34"
-PrecompileTools = "1"
 TensorCast = "0.4"
 TensorOperations = "4"
-julia = "1.7"
-Aqua = "0.8"
-JET = "0.9, 0.10, 0.11"
-SparseArrays = "1"
 Test = "1"
-LinearAlgebra = "1"
-Pkg = "1"
-Random = "1"
+julia = "1.7"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+DoubleFloats = "497a8b3b-efae-58df-a0af-a86822472b78"
 JET = "c3a54625-cd67-489e-a8e7-0a5a0ff4e31b"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
-SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 
 [targets]
-test = ["Aqua", "JET", "Pkg", "SparseArrays", "StatsBase", "Test", "PrecompileTools"]
+test = ["Aqua", "JET", "Pkg", "StatsBase", "Test", "PrecompileTools", "DoubleFloats"]

bench.jl

@@ -14,4 +14,4 @@ end
 bench_device()
 bench_device()
 bench_cpu()
-bench_cpu()
+bench_cpu()

docs/build.jl

@@ -18,24 +18,27 @@ cd(dirname(@__FILE__)) do
     include("../examples/ex1.jl")
 
     # Generate and save the contents of docstrings as markdown files.
-    index  = Index()
+    index = Index()
     for mod in modules
         update!(index, save(joinpath(api_directory, "$(mod).md"), mod))
     end
-    save(joinpath(api_directory, "index.md"), index; md_subheader = :category)
+    save(joinpath(api_directory, "index.md"), index; md_subheader=:category)
 
     # Add a reminder not to edit the generated files.
     open(joinpath(api_directory, "README.md"), "w") do f
-        print(f, """
-        Files in this directory are generated using the `build.jl` script. Make
-        all changes to the originating docstrings/files rather than these ones.
-        Documentation should *only* be built directly on the `master` branch.
-        Source links would otherwise become unavailable should a branch be
-        deleted from the `origin`. This means potential pull request authors
-        *should not* run the build script when filing a PR.
-        """)
+        return print(
+            f,
+            """
+   Files in this directory are generated using the `build.jl` script. Make
+   all changes to the originating docstrings/files rather than these ones.
+   Documentation should *only* be built directly on the `master` branch.
+   Source links would otherwise become unavailable should a branch be
+   deleted from the `origin`. This means potential pull request authors
+   *should not* run the build script when filing a PR.
+   """,
+        )
     end
 
     info("Adding all documentation changes in $(api_directory) to this commit.")
-    success(`git add $(api_directory)`) || exit(1)
+    return success(`git add $(api_directory)`) || exit(1)
 end

docs/make.jl

@@ -1,17 +1,17 @@
 using Documenter, QuantumInformation
 
-format = Documenter.HTML(edit_link = "master",
-                         prettyurls = get(ENV, "CI", nothing) == "true",
-                         assets = ["assets/favicon.ico"],
+format = Documenter.HTML(
+    edit_link="master",
+    prettyurls=get(ENV, "CI", nothing) == "true",
+    assets=["assets/favicon.ico"],
 )
 
 makedocs(
-    clean = true,
-    format = format,
-    sitename = "QuantumInformation.jl",
-    authors = "Piotr Gawron, Dariusz Kurzyk, Łukasz Pawela",
-
-    pages = [
+    clean=true,
+    format=format,
+    sitename="QuantumInformation.jl",
+    authors="Piotr Gawron, Dariusz Kurzyk, Łukasz Pawela",
+    pages=[
         "Home" => "index.md",
         "Manual" => Any[
             "man/quickstart.md",
@@ -20,9 +20,9 @@ makedocs(
             "man/functionals.md",
             "man/measurement.md",
             "man/channels.md",
-            "man/random.md"
+            "man/random.md",
         ],
-        "Library" => "lib/QuantumInformation.md"
+        "Library" => "lib/QuantumInformation.md",
         # Any[
         #     "lib/QuantumInformation.md",
         #     "lib/content/base.md",
@@ -31,11 +31,7 @@ makedocs(
         #     "lib/content/randomstate.md",
         #     "lib/content/utils.md"
         # ]
-    ]
+    ],
 )
 
-deploydocs(
-
-    target = "build",
-    repo = "github.com/iitis/QuantumInformation.jl.git"
-)
+deploydocs(target="build", repo="github.com/iitis/QuantumInformation.jl.git")

docs/src/man/channels.md

@@ -25,6 +25,13 @@ Also, channels object are callable
 Φ(ρ)
 ```
 
+Additionally, `SuperOperator` can be constructed directly from a Julia function:
+```@repl QuantumInformation
+ρ = [0.25 0.25im; -0.25im 0.75]
+Ψ = SuperOperator(x -> ρ*x*ρ, 2, 2)
+```
+
+
 ## Channel Representations
 
 Channels can be represented in various bases. The `channelbasis` function generates a basis for quantum channels, which can then be used with `represent` to find the coefficients of a channel in that basis, or `combine` to reconstruct the channel from coefficients.

docs/src/man/examples.md

@@ -32,13 +32,14 @@ $100$ random pure initial states. We also check how the parameter $\gamma$
 influences this fidelity.
 
 ```@repl QuantumInformation
+using Statistics
 steps = 100
 haar = HaarKet(2)
-ψ = (ket(0, 4) + ket(3, 4))/sqrt(2)
+ψ = (ket(1, 4) + ket(4, 4))/sqrt(2)
 γs = 0.0:0.01:1.0
 Φ = KrausOperators([[1 0; 0 sqrt(1-γ)], [0 sqrt(γ); 0 0]])
-post = [PostSelectionMeasurement(proj(ket(i, 4)) ⊗ eye(2)) for i=0:3]
-rots = [UnitaryChannel(eye(2)), UnitaryChannel(sx), UnitaryChannel(sz),
+post = [PostSelectionMeasurement(proj(ket(i, 4)) ⊗ 𝕀(2)) for i=1:4]
+rots = [UnitaryChannel(𝕀(2)), UnitaryChannel(sx), UnitaryChannel(sz),
 UnitaryChannel(sx*sz)]
 had = UnitaryChannel{Matrix{ComplexF64}}(hadamard(2))
 cnot = UnitaryChannel{Matrix{ComplexF64}}([1 0 0 0; 0 1 0 0; 0 0 0 1; 0 0 1 0])
@@ -55,5 +56,5 @@ IdentityChannel(2))∘(IdentityChannel(4) ⊗ Φ))(ξ)
         end
     end
 end
-mean(r, 1)
+mean(r, dims=1)
 ```

docs/src/man/functionals.md

@@ -184,3 +184,29 @@ $C(\rho)=0$, then $\rho$ is separable.
 concurrence(ρ ⊗ σ)
 concurrence(proj(max_entangled(4)))
 ```
+
+## Sparse Matrix Support
+
+Many functionals in **QuantumInformation.jl** provide native support for sparse matrices. For large systems (typically larger than 32x32), we utilize iterative solvers from [Arpack.jl](https://github.com/JuliaLinearAlgebra/Arpack.jl) to efficiently compute a subset of eigenvalues or singular values.
+
+The following functionals have optimized sparse implementations:
+- `norm_trace`
+- `fidelity_sqrt`
+- `vonneumann_entropy`
+- `renyi_entropy`
+- `relative_entropy`
+- `negativity`
+- `ppt`
+
+```@example QuantumInformation
+using SparseArrays
+n = 6
+d = n^2
+ψ = max_entangled(SparseVector{ComplexF64, Int}, d)
+ρ = proj(ψ)
+negativity(ρ, [n, n], 1)
+```
+
+> [!NOTE]
+> For very large or high-rank sparse matrices, iterative solvers may have convergence issues or miss small eigenvalues. We cap the number of computed values at 32 for performance and stability.
+

docs/src/man/states.md

@@ -61,6 +61,12 @@ max_mixed(4)
 werner_state(4, 0.4)
 ```
 
+For identity transformations, the library provides the `𝕀` (or `identity_gate`) function:
+```@repl QuantumInformation
+𝕀(2)
+```
+
+
 ## Non-standard matrix transformations
 We will now introduce
 reshaping operators, which map matrices to vectors and vice versa. We start with
@@ -134,6 +140,11 @@ The `permutesystems` function allows permuting subsystems of a composite quantum
 permutesystems(ρ, [2, 2], [2, 1])
 ```
 
+## Sparse matrix support
+
+Many of these transformations natively support sparse matrices from the `SparseArrays` library. Functions such as `ptrace`, `ptranspose`, `reshuffle`, and `permutesystems` have been optimized to return sparse results when given sparse inputs, preserving memory for large quantum systems.
+
+
 
 ## Channels