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qwalkr

Overview

qwalkr is a numerical suite for investigating quantum walks, providing estimates of matrices of interests that help you obtain insight into the evolution of such systems:

Quantum Walks

• ctqwalk() creates a continuous-time quantum walk.

Investigate the Hamiltonian

• get_eigspace() obtains the eigenvectors associated with an eigenspace.
• get_eigproj() obtains the orthogonal projector associated with an eigenspace.
• get_eigschur()obtains the Schur product of orthogonal projectors.
• act_eigfun() applies a function to the Hamiltonian.

Time Evolution

• unitary_matrix() returns the unitary time evolution operator at a given time.
• mixing_matrix() returns the mixing matrix at a given time.

Average Evolution

• avg_matrix() returns the average mixing matrix.
• gavg_matrix() returns the generalized average mixing matrix under a probability distribution.

Installation

You can install the stable version of qwalkr from CRAN:

install.packages("qwalkr")

For the development version, you can install from Github like so:

# install.packages("devtools")
devtools::install_github("vitormarquesr/qwalkr")

Usage

library(qwalkr)

K3 <- rbind(c(0, 1, 1),
            c(1, 0, 1),
            c(1, 1, 0))

w <- ctqwalk(hamiltonian = K3)

w
#> Continuous-Time Quantum Walk
#> 
#> [+]Order: 3 
#> 
#> [+]Spectrum of the Hamiltonian:
#>                   
#> Eigenvalue:   2 -1
#> Multiplicity: 1  2


get_eigproj(w, id=2)
#>            [,1]       [,2]       [,3]
#> [1,]  0.6666667 -0.3333333 -0.3333333
#> [2,] -0.3333333  0.6666667 -0.3333333
#> [3,] -0.3333333 -0.3333333  0.6666667

unitary_matrix(w, t=pi/3)
#>                       [,1]                  [,2]                  [,3]
#> [1,]  0.1666667-0.2886751i -0.3333333+0.5773503i -0.3333333+0.5773503i
#> [2,] -0.3333333+0.5773503i  0.1666667-0.2886751i -0.3333333+0.5773503i
#> [3,] -0.3333333+0.5773503i -0.3333333+0.5773503i  0.1666667-0.2886751i

mixing_matrix(w, t=pi/3)
#>           [,1]      [,2]      [,3]
#> [1,] 0.1111111 0.4444444 0.4444444
#> [2,] 0.4444444 0.1111111 0.4444444
#> [3,] 0.4444444 0.4444444 0.1111111

avg_matrix(w)
#>           [,1]      [,2]      [,3]
#> [1,] 0.5555556 0.2222222 0.2222222
#> [2,] 0.2222222 0.5555556 0.2222222
#> [3,] 0.2222222 0.2222222 0.5555556

Getting Help

For further reference on the usability, check the vignette or the website of the package.

If you happen to encounter a bug, please file an issue on GitHub.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.