RandomQuantum

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This Julia package provides functions to sample from various random matrix ensebles associated with quantum information applications.

Here is a table of currently support ensembles:

Type	Ensemble
GinibreEnsemble	Ginibre unitarily invariant matrix ensemble
FubiniStudyPureState	Fubini-Study pure ensemble
FubiniStudyMixedState	Mixed-state ensemble induced by tracing out elements of Fubini-Study ensenble on a larger space
HilbertSchmidtMixedState	Mixed-state ensemble given by the "flat" Hilbert-Schmidt
BuresMixedState	Mixed-state ensemble given by the Bures metric.
ClosedHaarEnsemble	Circular Unitary Ensemble (CUE), unitaries distributed according to the Haar measure.
OpenHaarEnsemble	Quantum channel ensemble induced by Haar-distributed unitaries (CUE) on a larger space.
RandomClosedEvolution	Unitary matrix ensemble obtained by evolving under a Hamiltonian sampled from a Gaussian unitary ensemble
RandomOpenEvolution	Quantum channel ensemble induced by integrated GUE evolution on a larger space.

The interface is emulates the interface of Distributions.jl, although there is a lot missing at the moment.

Installation

Install it with the following command:

  julia> Pkg.add("RandomQuantum")

For Julia v1.0 use the master branch:

  (v1.0) pkg> add RandomQuantum

Examples

julia> using RandomQuantum

julia> rand(BuresMixedState(2))
2x2 Array{Complex{Float64},2}:
   0.771511+0.0im       -0.0632581+0.116198im
 -0.0632581-0.116198im    0.228489+0.0im    

References

Francesco Mezzadri, How to Generate Random Matrices from the Classical Compact Groups Notices Amer Math Soc 54 4 592 (2007) arXiv:math-ph/0609050

Wojciech Bruzda, Valerio Cappellini, Hans-Jürgen Sommers, Karol Życzkowski, Random quantum operations, Physics Letters A, Volume 373, Issue 3, 12 January 2009, Pages 320-324 arXiv:0804.2361

Karol Życzkowski, Karol A. Penson, Ion Nechita, and Benoît Collins, Generating random density matrices, Journal of Mathematical Physics, 52, 062201 (2011) arXiv:1010.3570

License

MIT License

Acknowledgements

This research was funded by the Intelligence Advanced Research Projects Activity (IARPA) Multi Qubit Coherent Operations (MQCO) program under Contract No. W911NF-10-1-0324. All statements of fact, opinion, or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of IARPA, ODNI, or the US Government.

Copyright

(c) Raytheon BBN Technologies, 2015

Contributors

Marcus P S (@marcusps)