Gabs.jl
Gabs.jl is a numerical tooling package for simulating Gaussian quantum information.
Gaussian states and operators have the convenient property that they can be characterized by low-dimensional matrices in the phase space representation. Thus, a large class of continuous variable quantum information can be efficiently simulated on a classical computer, lending to applications in quantum cryptography, quantum machine learning, integrated quantum photonics, and more. Gabs.jl provides a high-level Julia interface for straightforward and high performance implementations of Gaussian quantum systems.
See the detailed suggested readings & references page for a background on quantum information with Gaussian states.
Installation
To install Gabs.jl, start Julia and run the following command:
using Pkg
Pkg.add("Gabs")To use the package, run the command
using GabsNow, the entire library is loaded into the current workspace, with access to its high-level interface and predefined objects.
Examples
Gaussian States
A wide variety of predefined methods to create a specific instance of the [`GaussianState`](https://apkille.github.io/Gabs.jl/dev/API/#Gabs.GaussianState) type are available. For a full description of the API for Gaussian states, see the [State Zoo section](https://apkille.github.io/Gabs.jl/dev/zoos/#State-Zoo) of the documentation. Let's examine a few well-known examples with the Julia REPL: ```julia julia> using Gabs julia> s1 = vacuumstate() GaussianState for 1 mode. mean: 2-element Vector{Float64}: 0.0 0.0 covariance: 2×2 Matrix{Float64}: 1.0 0.0 0.0 1.0 julia> s2 = coherentstate(rand(ComplexF64)) GaussianState for 1 mode. mean: 2-element Vector{Float64}: 1.1000447533324929 0.38900397266196973 covariance: 2×2 Matrix{Float64}: 1.0 0.0 0.0 1.0 julia> s3 = squeezedstate(rand(Float64), rand(Float64)) GaussianState for 1 mode. mean: 2-element Vector{Float64}: 0.0 0.0 covariance: 2×2 Matrix{Float64}: 0.414711 0.0537585 0.0537585 0.609798 ``` Tensor products of Gaussian states are called with `⊗` or `tensor`: ```julia julia> tp = s1 ⊗ s2 ⊗ s3 GaussianState for 3 modes. mean: 6-element Vector{Float64}: 0.0 0.0 1.1000447533324929 0.38900397266196973 0.0 0.0 covariance: 6×6 Matrix{Float64}: 1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.414711 0.0537585 0.0 0.0 0.0 0.0 0.0537585 0.609798 ``` Partial traces of Gaussian states are called with `ptrace`: ```julia julia> ptrace(tp, [1, 3]) GaussianState for 2 modes. mean: 4-element Vector{Float64}: 0.0 0.0 0.0 0.0 covariance: 4×4 Matrix{Float64}: 1.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.414711 0.0537585 0.0 0.0 0.0537585 0.609798 ```
Gaussian Operators
Gabs.jl contains many predefined methods to create instances of [`GaussianUnitary`](https://apkille.github.io/Gabs.jl/dev/API/#Gabs.GaussianUnitary) and [`GaussianChannel`](https://apkille.github.io/Gabs.jl/dev/API/#Gabs.GaussianChannel) types. For a full description of the API for Gaussian operators, see the [Operator Zoo section](https://apkille.github.io/Gabs.jl/dev/zoos/#Operator-Zoo) of the documentation. Let's see a few well-known examples: ```julia julia> using Gabs julia> un = displace(rand(ComplexF64)) GaussianUnitary for 1 mode. displacement: 2-element Vector{Float64}: 1.0165172806010776 0.6534135749806397 symplectic: 2×2 Matrix{Float64}: 1.0 0.0 0.0 1.0 julia> ch = amplifier(rand(Float64), rand(Int64)) GaussianChannel for 1 mode. displacement: 2-element Vector{Float64}: 0.0 0.0 transform: 2×2 Matrix{Float64}: 1.49009 0.0 0.0 1.49009 noise: 2×2 Matrix{Float64}: 1.03156e19 0.0 0.0 1.03156e19 ``` Applications of these operators on states can be called in-place with `apply!` and out-of-place with `*`: ```julia julia> s = vacuumstate(); julia> apply!(s, un); s GaussianState for 1 mode. mean: 2-element Vector{Float64}: 1.0165172806010776 0.6534135749806397 covariance: 2×2 Matrix{Float64}: 1.0 0.0 0.0 1.0 julia> tp = (ch ⊗ ch ⊗ ch) * (s ⊗ s ⊗ s) GaussianState for 3 modes. mean: 6-element Vector{Float64}: 1.039294184970358 3.583714987592534 1.039294184970358 3.583714987592534 1.039294184970358 3.583714987592534 covariance: 6×6 Matrix{Float64}: 1.03156e19 0.0 0.0 0.0 0.0 0.0 0.0 1.03156e19 0.0 0.0 0.0 0.0 0.0 0.0 1.03156e19 0.0 0.0 0.0 0.0 0.0 0.0 1.03156e19 0.0 0.0 0.0 0.0 0.0 0.0 1.03156e19 0.0 0.0 0.0 0.0 0.0 0.0 1.03156e19 ```