gavg_matrix.ctqwalk {qwalkr}

The Generalized Average Mixing Matrix of a Continuous-Time Quantum Walk

Description

The Generalized Average Mixing Matrix of a Continuous-Time Quantum Walk

Usage

## S3 method for class 'ctqwalk'
gavg_matrix(object, R, ...)

Arguments

object

a representation of the quantum walk.

R

samples from the random variable R (For performance, it is recommended at most 10000 samples).

...

further arguments passed to or from other methods.

Details

Let M(t) be the mixing matrix of the quantum walk and R a random variable with associated probability density function f_R(t). Then the generalized average mixing matrix under R is defined as

\widehat{M}_R := \mathbb{E}[M(R)] = \int_{-\infty}^{\infty} M(t)f_R(t)\textrm{d}t

Value

gavg_matrix() returns the generalized average mixing matrix as a square matrix of the same order as the walk.

See Also

ctqwalk(), gavg_matrix()

Examples

walk <- ctqwalk(matrix(c(0,1,0,1,0,1,0,1,0), nrow=3))

# Return the average mixing matrix under a Standard Gaussian distribution
gavg_matrix(walk, rnorm(1000))