avg_matrix.ctqwalk {qwalkr}

The Average Mixing Matrix of a Continuous-Time Quantum Walk

Description

The Average Mixing Matrix of a Continuous-Time Quantum Walk

Usage

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

Arguments

object

a representation of the quantum walk.

...

further arguments passed to or from other methods.

Details

Let M(t) be the mixing matrix of the quantum walk, then the average mixing matrix is defined as

\widehat{M} := \lim_{T \to \infty} \frac{1}{T}\int_{0}^T M(t)\textrm{d}t

and encodes the long-term average behavior of the walk. Given the Hamiltonian H = \sum_r \lambda_r E_r, it is possible to prove that

\widehat{M} = \sum_r E_r \circ E_r

Value

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

See Also

ctqwalk(), avg_matrix()

Examples

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

# Return the average mixing matrix
avg_matrix(walk)