quara.objects.state module

class State(c_sys, vec, is_physicality_required=True, is_estimation_object=True, on_para_eq_constraint=True, on_algo_eq_constraint=True, on_algo_ineq_constraint=True, mode_proj_order='eq_ineq', eps_proj_physical=None, eps_truncate_imaginary_part=None)[source]

Bases: quara.objects.qoperation.QOperation

Constructor

Parameters

c_sys (CompositeSystem) – CompositeSystem of this state.
vec (np.ndarray) – vec of this state.
is_physicality_required (bool, optional) –
checks whether the state is physically correct, by default True. all of the following conditions are True, the state is physically correct:
- trace of density matrix equals 1.
- density matrix is Hermitian.
- density matrix is positive semidefinite.
If you want to ignore the above requirements and create a State object, set is_physicality_required to False.
is_estimation_object (bool) –
on_para_eq_constraint (bool) –
on_algo_eq_constraint (bool) –
on_algo_ineq_constraint (bool) –
mode_proj_order (str) –
eps_proj_physical (float) –
eps_truncate_imaginary_part (float) –

Raises

ValueError – vec is not one-dimensional array.
ValueError – size of vec is not square number.
ValueError – entries of vec are not real numbers.
ValueError – dim of CompositeSystem does not equal dim of vec.
ValueError – is_physicality_required is True and the state is not physically correct.

calc_eigenvalues()[source]

calculates eigen values of density matrix.

this function uses numpy API. see this URL for details: https://numpy.org/doc/1.18/reference/generated/numpy.linalg.eigvalsh.html

Returns: eigen values of density matrix.
Return type: List

calc_gradient(var_index)[source]

calculates gradient of State.

Parameters: var_index (int) – index of variables to calculate gradient.
Returns: gradient of State.
Return type: State

calc_proj_eq_constraint()[source]

calculates the projection of State on equal constraint.

Returns: the projection of State on equal constraint.
Return type: State

static calc_proj_eq_constraint_with_var(c_sys, var, on_para_eq_constraint=True)[source]

calculates the projection of State on equal constraint.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this variables.
var (np.ndarray) – variables.
on_para_eq_constraint (bool, optional) – whether this variables is on parameter equality constraint, by default True.

Returns

the projection of State on equal constraint.

Return type

np.ndarray

calc_proj_ineq_constraint()[source]

calculates the projection of State on inequal constraint.

Returns: the projection of State on inequal constraint.
Return type: State

static calc_proj_ineq_constraint_with_var(c_sys, var, on_para_eq_constraint=True, eps_truncate_imaginary_part=None)[source]

calculates the projection of State on inequal constraint.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this variables.
var (np.ndarray) – variables.
on_para_eq_constraint (bool, optional) – whether this variables is on parameter equality constraint, by default True.
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()

Returns

the projection of State on inequal constraint.

Return type

np.ndarray

convert_basis(other_basis)[source]

returns vector representation for other_basis.

Parameters: other_basis (MatrixBasis) – basis.
Returns: vector representation for other_basis.
Return type: np.ndarray

static convert_stacked_vector_to_var(c_sys, stacked_vector, on_para_eq_constraint=True)[source]

converts stacked vector of state to variables of state.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this state.
stacked_vector (np.ndarray) – stacked vector of state.
on_para_eq_constraint (bool, optional) – uses equal constraints, by default True.

Returns

variables of state.

Return type

np.ndarray

static convert_var_to_stacked_vector(c_sys, var, on_para_eq_constraint=True)[source]

converts variables of state to stacked vector of state.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this state.
var (np.ndarray) – variables of state.
on_para_eq_constraint (bool, optional) – uses equal constraints, by default True.

Returns

stacked vector of state.

Return type

np.ndarray

property dim

returns dim of this state.

Returns: dim of this state.
Return type: int

is_eq_constraint_satisfied(atol=None)[source]

Parameters: atol (Optional[float]) –

is_hermitian(atol=None)[source]

returns whether density matrix is Hermitian.

Parameters

atol (float, optional) – the absolute tolerance parameter, uses get_atol() by default.

Returns

bool
True where density matrix, False otherwise.

Return type

bool

is_ineq_constraint_satisfied(atol=None)[source]

Parameters: atol (Optional[float]) –

is_positive_semidefinite(atol=None)[source]

returns whether density matrix is positive semidifinite.

Parameters: atol (float, optional) – the absolute tolerance parameter, uses get_atol() by default.
Returns: True where density matrix is positive semidifinite, False otherwise.
Return type: bool

is_trace_one(atol=None)[source]

returns whether trace of density matrix is one.

Parameters: atol (float, optional) – the absolute tolerance parameter, uses get_atol() by default.
Returns: True where trace of density matrix is one, False otherwise.
Return type: bool

set_zero()[source]: sets parameters to zero.

to_density_matrix()[source]

returns density matrix.

Returns: density matrix.
Return type: int

to_density_matrix_with_sparsity()[source]

returns density matrix.

this function uses the scipy.sparse module.

Returns: density matrix.
Return type: int

to_stacked_vector()[source]

converts State to stacked vector.

Returns: stacked vector representation of State.
Return type: np.ndarray

to_var()[source]

converts State to variables.

Returns: variable representation of State.
Return type: np.ndarray

property vec

returns vec of this state.

Returns: vec of this state.
Return type: np.ndarray

calc_gradient_from_state(c_sys, vec, var_index, is_estimation_object=True, on_para_eq_constraint=True, on_algo_eq_constraint=True, on_algo_ineq_constraint=True, mode_proj_order='eq_ineq', eps_proj_physical=0.0001, eps_truncate_imaginary_part=None)[source]

calculates gradient from State.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this state.
vec (np.ndarray) – vec of state.
var_index (int) – variable index.
on_para_eq_constraint (bool, optional) – uses equal constraints, by default True.
is_estimation_object (bool) –
on_algo_eq_constraint (bool) –
on_algo_ineq_constraint (bool) –
mode_proj_order (str) –
eps_proj_physical (float) –
eps_truncate_imaginary_part (Optional[float]) –

Returns

State with gradient as vec.

Return type

State

convert_state_index_to_var_index(state_index, on_para_eq_constraint=True)[source]

converts state index to variable index.

Parameters

state_index (int) – state index.
on_para_eq_constraint (bool, optional) – uses equal constraints, by default True.

Returns

variable index.

Return type

int

convert_var_index_to_state_index(var_index, on_para_eq_constraint=True)[source]

converts variable index to state index.

Parameters

var_index (int) – variable index.
on_para_eq_constraint (bool, optional) – uses equal constraints, by default True.

Returns

state index.

Return type

int

convert_var_to_state(c_sys, var, is_physicality_required=True, is_estimation_object=True, on_para_eq_constraint=True, on_algo_eq_constraint=True, on_algo_ineq_constraint=True, mode_proj_order='eq_ineq', eps_proj_physical=0.0001)[source]

converts vec of variables to state.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this state.
var (np.ndarray) – vec of variables.
on_para_eq_constraint (bool, optional) – uses equal constraints, by default True.
is_physicality_required (bool) –
is_estimation_object (bool) –
on_algo_eq_constraint (bool) –
on_algo_ineq_constraint (bool) –
mode_proj_order (str) –
eps_proj_physical (float) –

Returns

converted state.

Return type

State

convert_var_to_vec(c_sys, var, on_para_eq_constraint=True)[source]

converts variables of state to vec of state.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this state.
var (np.ndarray) – variables of state.
on_para_eq_constraint (bool, optional) – uses equal constraints, by default True.

Returns

vec of state.

Return type

np.ndarray

convert_vec_to_var(c_sys, vec, on_para_eq_constraint=True)[source]

converts vec of state to variables of state.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this state.
vec (np.ndarray) – vec of state.
on_para_eq_constraint (bool, optional) – uses equal constraints, by default True.

Returns

variables of state.

Return type

np.ndarray

get_bell_2q(c_sys)[source]

returns vec of Bell state, \(\frac{1}{2} (|00\rangle + |11\rangle)(\langle00| + \langle11|)\), with the basis of c_sys.

Parameters: c_sys (CompositeSystem) – CompositeSystem containing state.
Returns: vec of state.
Return type: State

get_x0_1q(c_sys)[source]

returns vec of state X_0 with the basis of c_sys.

Parameters: c_sys (CompositeSystem) – CompositeSystem containing state.
Returns: vec of state.
Return type: np.ndarray

get_x1_1q(c_sys)[source]

returns vec of state X_1 with the basis of c_sys.

Parameters: c_sys (CompositeSystem) – CompositeSystem containing state.
Returns: vec of state.
Return type: np.ndarray

get_y0_1q(c_sys)[source]

returns vec of state Y_0 with the basis of c_sys.

Parameters: c_sys (CompositeSystem) – CompositeSystem containing state.
Returns: vec of state.
Return type: np.ndarray

get_y1_1q(c_sys)[source]

returns vec of state Y_1 with the basis of c_sys.

Parameters: c_sys (CompositeSystem) – CompositeSystem containing state.
Returns: vec of state.
Return type: np.ndarray

get_z0_1q(c_sys)[source]

returns vec of state Z_0 with the basis of c_sys.

Parameters: c_sys (CompositeSystem) – CompositeSystem containing state.
Returns: vec of state.
Return type: np.ndarray

get_z1_1q(c_sys)[source]

returns vec of state Z_1 with the basis of c_sys.

Parameters: c_sys (CompositeSystem) – CompositeSystem containing state.
Returns: vec of state.
Return type: np.ndarray

to_density_matrix_from_var(c_sys, var, on_para_eq_constraint=True)[source]

converts var to density matrix.

this function uses the scipy.sparse module.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this state.
var (np.ndarray) – variables.
on_para_eq_constraint (bool, optional) – whether this state is on parameter equality constraint, by default True

Returns

density matrix of this state.

Return type

np.ndarray

to_density_matrix_from_vec(c_sys, vec)[source]

converts vec to density matrix.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this state.
vec (np.ndarray) – vec of state of this state.

Returns

density matrix of this state.

Return type

np.ndarray

to_var_from_density_matrix(c_sys, density_matrix, on_para_eq_constraint=True)[source]

converts density matrix to variables.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this state.
density_matrix (np.ndarray) – density matrix of this state.
on_para_eq_constraint (bool, optional) – whether this state is on parameter equality constraint, by default True

Returns

variables.

Return type

np.ndarray

to_vec_from_density_matrix_with_sparsity(c_sys, density_matrix, eps_truncate_imaginary_part=None)[source]

converts density matrix to vec.

this function uses the scipy.sparse module.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this state.
density_matrix (np.ndarray) – density matrix of this state.
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()

Returns

vec of variables.

Return type

np.ndarray