Quantum.jl is a toolset for Julia designed around the efficient and idiomatic manipulation of abstract quantum objects, so that one can easily transfer reasoning about quantum systems from the chalkboard to the computer without getting too bogged down in implementation details. Almost all quantum mechanics libraries work solely with vector/matrix representations of states, without storing the bases in which states and operators are represented. Quantum.jl is designed to enable transformations of those representations to extend naturally to the abstract quantum objects that underlie them (bases of bras, kets, outer products, etc.), and conversely use abstract quantum objects to aid in the manipulation and analysis of representations.
Many other libraries that offer a similarly abstract feature set (e.g. Quantum Mathematica) are either:
a) poorly optimized for heavy numeric work performed on matrix representations or
b) don't preserve abstract structure when representation optimization is present.
The goal of Quantum.jl is to be as optimized for numeric work as a library like QuTiP, while still having the abstract feature set that other libraries have shown to be useful. Luckily, Julia is a language that quite naturally supports high levels of abstraction with little sacrifice in performance.
Quantum.jl currently only supports work in discrete spaces, but provides a foundation that could be extended to support work in continuous spaces in the future.
Additionally, it has been suggested that Quantum.jl implement an interface for other popular quantum libraries like QuTiP in order to more quickly offer up a host of advanced optimized features, such as continuous space support, visualization systems, and common algorithms used in quantum mechanics.
For more information, check out Quantum.jl's documentation or the Quantum.jl API (W.I.P.).
###Current: - Basis, State, ScalarExpr, DiracVector, and DiracMatrix type implementations - Tensor product structure for Dirac objects - Application of arbitrary selection rules to extract subspaces from most types of Quantum.jl collection objects. Related methods: - filter - map - filtercoeffs - filterstates - find/findstates - The ability to index into Dirac objects using States, e.g. to find the coefficient of a state in a DiracVector, one can simply call get(d::DiracVector, s::State) - Arithmetic/Linear algebra operations that are logically consistent w.r.t. to user defined bases. Examples: - matrix/vector arithmetic for Dirac objects - inner/outer products implementations - idiomatic computation of expectation values/transition matrices - commutator of DiracMatrices - trace/partial trace, normalization, kron, and more - arithmetic operations between Dirac types and generic arrays - ScalarExpr objects for delayed calculation of mixed-basis inner products. ScalarExpr objects support all basic arithmetic operations. - The ability to perform mixed basis calculation via the use of ScalarExprs and InnerProducts
###In The Works: - Code clean-up/organization - Write up the API - registration of Quantum.jl as Julia package
###Post-Release Goals/Ideas:
- More mixed-basis functionality for addition of Dirac objects
- A functional Operator type
- Interface with other similar libraries (eg. QuTiP)
- Continuous space support
- HDF5 support using HDF5.jl (https://github.com/timholy/HDF5.jl)
- Visualization system (probably via interfacing to more mature libraries)
- incorporate units using SIUnits.jl (https://github.com/Keno/SIUnits.jl)