bosonSampler {BosonSampling}

Function for independently sampling from the Boson Sampling distribution

Description

The function implements the Boson Sampling algorithm defined in Clifford and Clifford (2017) https://arxiv.org/abs/1706.01260

Usage

bosonSampler(A, sampleSize, perm = FALSE)

Arguments

A

the first n columns of an (m x m) random unitary matrix,
see randomUnitary

sampleSize

the number of independent sample values required for given A

perm

TRUE if the permanents and pmfs of each sample value are required

Details

Let the matrix A be the first n columns of an (m x m) random unitary matrix, then X <- bosonSampler(A, sampleSize = N, perm = TRUE) provides X$values, X$perms and X$pmfs,

The component X$values is an (n x N) matrix with columns that are independent sample values from the Boson Sampling distribution. Each sample value is a vector of n integer-valued output modes in random order. The elements of the vector can be sorted in increasing order to provide a multiset representation of the sample value.

The outputs X$perms and X$pmfs are vectors of the permanents and probability mass functions (pmfs) associated with the sample values. The permanent associated with a sample value v = (v_1,...,v_n) is the permanent of an (n x n) matrix constructed with rows v_1,...,v_n of A. Note the constructed matrix, M, may have repeated rows since v_1,...,v_n are not necessarily distinct. The pmf is calculated as Mod(pM)^2/prod(factorial(tabulate(c)) where pM is the permanent of M.

Value

X = bosonSampler(A, sampleSize = N, perm = TRUE) provides X$values, X$perms and X$pmfs. See Details.

References

Clifford, P. and Clifford, R. (2017) The Classical Complexity of Boson Sampling, https://arxiv.org/abs/1706.01260

Examples

set.seed(7)
n <- 20  # number of photons
m <- 200 # number of output modes
A <- randomUnitary(m)[,1:n]
# sample of output vectors
valueList <- bosonSampler(A, sampleSize = 10)$values 
valueList
# sample of output multisets 
apply(valueList,2, sort) 
#
set.seed(7)
n <- 12  # number of photons
m <- 30 # number of output modes
A <- randomUnitary(m)[,1:n]
# sample of output vectors
valueList = bosonSampler(A, sampleSize = 1000)$values 
# Compare frequency of output modes at different
# positions in the output vectors 
matplot(1:m,apply(valueList,1,tabulate), pch =20, t = "p", 
xlab = "output modes", ylab = "frequency")