在Julia中使用狄拉克符号执行量子力学的库_Julia_.zip

Latest Stable Release (v0.1): [](https://travis-ci.org/JuliaQuantum/QuDirac.jl) Upcoming Release (v0.2): [](https://travis-ci.org/JuliaQuantum/QuDirac.jl) # QuDirac.jl QuDirac.jl is a [Julia](http://julialang.org/) library for using Dirac notation to perform quantum mechanics computations. Documentation for the current release version (v0.1) can be found [**here**](http://qudiracjl.readthedocs.org/en/release-0.1/). ## Installation To install QuDirac.jl, you should have [a working build of Julia v0.3](https://github.com/JuliaLang/julia#source-download-and-compilation). Then, you can grab QuDirac.jl via the package manager: ```julia julia> Pkg.add("QuDirac") ``` ## Features These are toy examples for demoing features. See [below for more involved examples](https://github.com/JuliaQuantum/QuDirac.jl#examples). #### Ket, Bra, and Operator types ```julia julia> bell = d" 1/√2 * (| 0,0 > + | 1,1 >) " Ket{KroneckerDelta,2,Float64} with 2 state(s): 0.7071067811865475 | 0,0 ⟩ 0.7071067811865475 | 1,1 ⟩ julia> bell' Bra{KroneckerDelta,2,Float64} with 2 state(s): 0.7071067811865475 ⟨ 0,0 | 0.7071067811865475 ⟨ 1,1 | julia> ptrace(bell * bell', 1) OpSum{KroneckerDelta,1,Float64} with 2 operator(s): 0.4999999999999999 | 0 ⟩⟨ 0 | 0.4999999999999999 | 1 ⟩⟨ 1 | ``` #### Support for undefined inner products ```julia # tells QuDirac to use the rule for undefined inner products julia> default_inner(UndefinedInner()) INFO: QuDirac's default inner product type is currently UndefinedInner() julia> d" < 0,0 | * (| 0,0 > + | 1,1 >)/√2 " ((⟨ 0,0 | 0,0 ⟩ + ⟨ 0,0 | 1,1 ⟩) / 1.4142135623730951) julia> s = d" (e^( < 1,2 | 3,4 > ) + < 5,6 | 7,8 > * im)^4 " (((exp(⟨ 1,2 | 3,4 ⟩)) + (⟨ 5,6 | 7,8 ⟩ * im))^4) julia> inner_eval((b, k) -> sum(k) - sum(b), s) 8.600194553751864e6 + 2.5900995362955774e6im ``` #### Custom inner product rules ```julia julia> immutable MyInner <: AbstractInner end julia> QuDirac.inner_rule(::MyInner, ktlabel, brlabel) = sqrt(ktlabel[1]+brlabel[1]) inner_rule (generic function with 3 methods) julia> default_inner(MyInner()) INFO: QuDirac's default inner product type is currently MyInner() # eval ⟨ π | e ⟩ with MyInner rule -> sqrt(π + e) julia> d" < π | e > " 2.420717761749361 ``` #### Functional operator construction ```julia # define a₂ on Ket julia> @def_op " a₂ | x, y, z > = √y * | x, y - 1, z > " a₂ (generic function with 1 method) # define a₂ on Bra julia> @def_op " < x, y, z | a₂ = √(y + 1) * < x, y + 1, z | " a₂ (generic function with 2 methods) julia> d" a₂ * | 3,5,5 > " Ket{KroneckerDelta,3,Float64} with 1 state(s): 2.23606797749979 | 3,4,5 ⟩ julia> d" a₂' * | 3,4,5 > " Ket{KroneckerDelta,3,Float64} with 1 state(s): 2.23606797749979 | 3,5,5 ⟩ julia> d" < 3,4,5 | * a₂ * | 3,5,5 > " 2.23606797749979 # Hadamard operator julia> @rep_op " H | n > = 1/√2 * ( | 0 > + (-1)^n *| 1 > ) " 0:1; julia> H OpSum{KroneckerDelta,1,Float64} with 4 operator(s): 0.7071067811865475 | 1 ⟩⟨ 0 | 0.7071067811865475 | 0 ⟩⟨ 0 | 0.7071067811865475 | 0 ⟩⟨ 1 | -0.7071067811865475 | 1 ⟩⟨ 1 | ``` #### ...and other stuff - Implementation of common operations like partial trace (`ptrace`) and partial transpose (`ptranspose`) - Treat states and operators as map-like data structures, enabling label-based analysis for spectroscopy purposes - `xsubspace` allows easy selection of excitation subspaces of states and operators - `permute` and `switch` allows generic permutation of factor labels for states - `filter`/`filter!` for the filtering out component states/operators via predicate functions - Arbitrary mapping functions (`map`/`maplabels`/`mapcoeffs`) for applying functions to labels and coefficients ## Examples There are currently two example files, `qho.jl` and `randwalk.jl`. The former implements methods for plotting quantum harmonic oscillator wave functions using Plotly. The latter is a simple implementation of a quantum random walk. To run the examples, one can do the following (using `qho.jl` as an example): ```julia julia> cd(Pkg.dir("QuDirac")) julia> include("examples/qho.jl") ```