Handle Continuous-Time Quantum Walks with R.

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.