README.md

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. 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 Gabs

Now, the entire library is loaded into the current workspace, with access to its high-level interface and predefined objects.

Example Usage

julia> basis = QuadPairBasis(1)
QuadPairBasis(1)

julia> state = vacuumstate(basis) ⊗ coherentstate(basis, 1.0-im)
GaussianState for 2 modes.
  symplectic basis: QuadPairBasis
mean: 4-element Vector{Float64}:
  0.0
  0.0
  1.4142135623730951
 -1.4142135623730951
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  1.0  0.0
 0.0  0.0  0.0  1.0

julia> op = beamsplitter(basis ⊕ basis, 0.75)
GaussianUnitary for 2 modes.
  symplectic basis: QuadPairBasis
displacement: 4-element Vector{Float64}:
 0.0
 0.0
 0.0
 0.0
symplectic: 4×4 Matrix{Float64}:
  0.5        0.0       0.866025  0.0
  0.0        0.5       0.0       0.866025
 -0.866025   0.0       0.5       0.0
  0.0       -0.866025  0.0       0.5

julia> apply!(state, op)
GaussianState for 2 modes.
  symplectic basis: QuadPairBasis
mean: 4-element Vector{Float64}:
  1.2247448713915892
 -1.2247448713915892
  0.7071067811865476
 -0.7071067811865476
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  1.0  0.0
 0.0  0.0  0.0  1.0

julia> ptrace(state, 1)
GaussianState for 1 mode.
  symplectic basis: QuadPairBasis
mean: 2-element Vector{Float64}:
  1.2247448713915892
 -1.2247448713915892
covariance: 2×2 Matrix{Float64}:
 1.0  0.0
 0.0  1.0