CHA model

Convex Hull Approximation (CHA)

Accessible in both numqi.entangle (recommended) and numqi.entangle.cha

numqi.entangle.CHABoundaryBagging

Convex Hull Approximation with Bagging

Separability-entanglement classifier via machine learning doi-link

__init__(dim, num_state=None, solver=None)

initialize the model

Parameters:

Name	Type	Description	Default
dim	tuple[int]	dimension of the bipartite system, len(dim) must be 2	required
num_state	int	number of states in the convex hull, default to 2(dim[0]dim[1])**2	None

solve(dm, maxiter=150, norm2_init=1, decay_rate=0.97, threshold=1e-07, num_init_retry=10, use_tqdm=False, return_info=False, seed=None)

solve the convex hull approximation

Parameters:

Name	Type	Description	Default
dm	ndarray	target density matrix	required
maxiter	int	maximum number of iterations, default to 150	150
norm2_init	float	initial norm2 bound, default to 1	1
decay_rate	float	decay rate of the norm2 bound, default to 0.97	0.97
threshold	float	threshold for the probability, default to 1e-7. if solver=MOSEK, then a more precise threshold is required, otherwise the solver will fail sometimes	1e-07
num_init_retry	int	number of retries for the initial state, default to 10	10
use_tqdm	bool	use tqdm, default to False	False
return_info	bool	return the information of the optimization, default to False	False
seed	int	random seed, default to None	None

Returns:

Name	Type	Description
beta	float	the optimal beta, boundary length
info	tuple[ndarray, ndarray, ndarray, ndarray]	the information of the optimization

numqi.entangle.AutodiffCHAREE

Bases: Module

Gradient descent model for convex hull approximation to separable states

__init__(dim, num_state=None, distance_kind='ree')

initialize the model

Parameters:

Name	Type	Description	Default
dim	tuple[int]	dimension of the bipartite system, len(dim) must be 2	required
num_state	int	number of states in the convex hull, default to 2dim0dim1 (seems to work well)	None
distance_kind	str	'gellmann' or 'ree', default to 'ree'	'ree'

get_boundary(dm0, xtol=0.0001, converge_tol=1e-10, threshold=1e-07, num_repeat=1, use_tqdm=True, return_info=False, seed=None)

get the boundary of the convex hull approximation

Parameters:

Name	Type	Description	Default
dm0	ndarray	initial density matrix	required
xtol	float	tolerance for the bisection, default to 1e-4	0.0001
converge_tol	float	tolerance for the optimization, default to 1e-10	1e-10
threshold	float	threshold for the probability, default to 1e-7	1e-07
num_repeat	int	number of repeats for the optimization, default to 1	1
use_tqdm	bool	use tqdm, default to True	True
return_info	bool	return the information of the optimization, default to False	False
seed	int	random seed, default to None	None

Returns:

Name	Type	Description
beta	float	the optimal beta, boundary length
info	ndarray	the information of the optimization

get_numerical_range(op0, op1, num_theta=400, converge_tol=1e-05, num_repeat=1, use_tqdm=True, seed=None)

get the numerical range of the two Hermitian operators

Parameters:

Name	Type	Description	Default
op0	ndarray	the first Hermitian operator	required
op1	ndarray	the second Hermitian operator	required
num_theta	int	number of theta, default to 400	400
converge_tol	float	tolerance for the optimization, default to 1e-5	1e-05
num_repeat	int	number of repeats for the optimization, default to 1	1
use_tqdm	bool	use tqdm, default to True	True
seed	int	random seed, default to None	None

Returns:

Name	Type	Description
ret	ndarray	the numerical range of the two Hermitian operators, shape=(num_theta,2)

set_dm_target(rho)

set the target density matrix

Parameters:

Name	Type	Description	Default
rho	ndarray	target density matrix	required

set_expectation_op(op)

set the expectation operator

Parameters:

Name	Type	Description	Default
op	ndarray	the expectation operator	required