quara.objects.effective_lindbladian module

class EffectiveLindbladian(c_sys, hs, 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.gate.Gate

Constructor

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
hs (np.ndarray) – HS representation of this EffectiveLindbladian.
is_physicality_required (bool, optional) –
checks whether the EffectiveLindbladian is physically wrong, by default True. if at least one of the following conditions is False, the EffectiveLindbladian is physically wrong:
- EffectiveLindbladian is TP(trace-preserving map).
- EffectiveLindbladian is CP(Complete-Positivity-Preserving).
If you want to ignore the above requirements and create a EffectiveLindbladian 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 – HS representation is not square matrix.
ValueError – dim of HS representation is not square number.
ValueError – HS representation is not real matrix.
ValueError – dim of HS representation does not equal dim of CompositeSystem.
ValueError – is_physicality_required is True and the gate is not physically correct.

calc_d_part(mode_basis='hermitian_basis')[source]

calculates d part of this EffectiveLindbladian.

mode_basis allows the following values: - hermitian_basis - comp_basis

Parameters: mode_basis (str, optional) – basis for calculating d part, by default “hermitian_basis”
Returns: d part of this EffectiveLindbladian.
Return type: np.ndarray

calc_gradient(var_index)[source]

calculates gradient of QOperation.

this function must be implemented in the subclass.

Parameters: var_index (int) – index of variables to calculate gradient.
Returns: gradient of QOperation.
Return type: QOperation
Raises: NotImplementedError – this function does not be implemented in the subclass.

calc_h_mat()[source]

calculates h matrix of this EffectiveLindbladian.

Returns: h matrix of this EffectiveLindbladian.
Return type: np.ndarray

calc_h_part(mode_basis='hermitian_basis')[source]

calculates h part of this EffectiveLindbladian.

mode_basis allows the following values: - hermitian_basis - comp_basis

Parameters: mode_basis (str, optional) – basis for calculating h part, by default “hermitian_basis”
Returns: h part of this EffectiveLindbladian.
Return type: np.ndarray

calc_j_mat()[source]

calculates j matrix of this EffectiveLindbladian.

Returns: j matrix of this EffectiveLindbladian.
Return type: np.ndarray

calc_j_part(mode_basis='hermitian_basis')[source]

calculates j part of this EffectiveLindbladian.

mode_basis allows the following values: - hermitian_basis - comp_basis

Parameters: mode_basis (str, optional) – basis for calculating j part, by default “hermitian_basis”
Returns: j part of this EffectiveLindbladian.
Return type: np.ndarray

calc_k_mat()[source]

calculates k matrix of this EffectiveLindbladian.

Returns: k matrix of this EffectiveLindbladian.
Return type: np.ndarray

calc_k_part(mode_basis='hermitian_basis')[source]

calculates k part of this EffectiveLindbladian.

mode_basis allows the following values: - hermitian_basis - comp_basis

Parameters: mode_basis (str, optional) – basis for calculating k part, by default “hermitian_basis”
Returns: k part of this EffectiveLindbladian.
Return type: np.ndarray

calc_proj_eq_constraint()[source]

calculates the projection of QOperation on equal constraint.

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

calc_proj_ineq_constraint()[source]

calculates the projection of QOperation on inequal constraint.

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

is_cp(atol=None)[source]

returns whether effective Lindbladian is CP(Complete-Positivity-Preserving).

Parameters: atol (float, optional) – the absolute tolerance parameter, uses get_atol() by default. this function ignores eigenvalues close zero.
Returns: True where the effective Lindbladian is CP, False otherwise.
Return type: bool

is_tp(atol=None)[source]

returns whether the effective Lindbladian is TP(trace-preserving map).

Parameters: atol (float, optional) – the absolute tolerance parameter, uses get_atol() by default. this function checks absolute(trace after mapped - trace before mapped) <= atol.
Returns: True where the effective Lindbladian is TP, False otherwise.
Return type: bool

to_gate()[source]

returns the Gate corresponding to this EffectiveLindbladian.

Returns: the Gate corresponding to this EffectiveLindbladian.
Return type: Gate

to_kraus_matrices()[source]

returns Kraus matrices of EffectiveLindbladian.

if \(A\) is Hermitian preserve matrix, then \(A(X) = \sum_i a_i A_i X A_i^{\dagger}\), where \(a_i\) are real numbers and \(A_i\) are complex square matrices. this function returns the list of \((a_i, A_i)\) sorted in descending order by \(a_i\).

Returns: Kraus matrices of EffectiveLindbladian.
Return type: List[Tuple[np.float64, np.ndarray]]

calc_gradient_from_effective_lindbladian(c_sys, hs, var_index, is_estimation_object=True, on_para_eq_constraint=True, on_algo_eq_constraint=True, on_algo_ineq_constraint=True, eps_proj_physical=None, eps_truncate_imaginary_part=None)[source]

calculates gradient from EffectiveLindbladian.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
hs (np.ndarray) – HS representation of this gate.
var_index (int) – variable index.
on_para_eq_constraint (bool, optional) – uses equal constraints, by default True.
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()
is_estimation_object (bool) –
on_algo_eq_constraint (bool) –
on_algo_ineq_constraint (bool) –
eps_proj_physical (Optional[float]) –

Returns

EffectiveLindbladian with gradient as hs.

Return type

EffectiveLindbladian

convert_effective_lindbladian_index_to_var_index(c_sys, effective_lindbladian_index, on_para_eq_constraint=True)[source]

converts effective_lindbladian_index index to variable index.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
effective_lindbladian_index (Tuple[int, int]) – index of EffectiveLindbladian. first value of tuple is row number of HS representation of this EffectiveLindbladian. second value of tuple is column number of HS representation of this EffectiveLindbladian.
on_para_eq_constraint (bool, optional) – uses equal constraints, by default True.

Returns

variable index.

Return type

int

convert_effective_lindbladian_to_var(c_sys, hs, on_para_eq_constraint=True)[source]

converts hs of EffectiveLindbladian to vec of variables.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
hs (np.ndarray) – HS representation of this EffectiveLindbladian.
on_para_eq_constraint (bool, optional) – uses equal constraints, by default True.

Returns

vec of variables.

Return type

np.ndarray

convert_var_index_to_effective_lindbladian_index(c_sys, var_index, on_para_eq_constraint=True)[source]

converts variable index to EffectiveLindbladian index.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
var_index (int) – variable index.
on_para_eq_constraint (bool, optional) – uses equal constraints, by default True.

Returns

index of EffectiveLindbladian. first value of tuple is row number of HS representation of this EffectiveLindbladian. second value of tuple is column number of HS representation of this EffectiveLindbladian.

Return type

Tuple[int, int]

convert_var_to_effective_lindbladian(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, eps_proj_physical=None, eps_truncate_imaginary_part=None)[source]

converts vec of variables to EffectiveLindbladian.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
var (np.ndarray) – vec of variables.
on_para_eq_constraint (bool, optional) – uses equal constraints, by default True.
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()
is_physicality_required (bool) –
is_estimation_object (bool) –
on_algo_eq_constraint (bool) –
on_algo_ineq_constraint (bool) –
eps_proj_physical (Optional[float]) –

Returns

converted EffectiveLindbladian.

Return type

EffectiveLindbladian

generate_d_part_cb_from_jump_operators(jump_operators)[source]

generates d part of EffectiveLindbladian from jump operators.

this d part is represented by computational basis.

Parameters: jump_operators (List[np.ndarray]) – jump_operators to generate d part.
Returns: d part of EffectiveLindbladian.
Return type: np.ndarray

generate_d_part_gb_from_jump_operators(jump_operators, basis, eps_truncate_imaginary_part=None)[source]

generates d part of EffectiveLindbladian from jump operators.

this d part is represented by general basis.

Parameters

jump_operators (List[np.ndarray]) – jump operators to generate d part.
basis (MatrixBasis) – MatrixBasis to present d part.
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()

Returns

d part of EffectiveLindbladian.

Return type

np.ndarray

generate_effective_lindbladian_from_h(c_sys, h_mat, 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]

generates EffectiveLindbladian from h matrix.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
h_mat (np.ndarray) – h matrix.
is_physicality_required (bool, optional) – whether this QOperation is physicality required, by default True
is_estimation_object (bool, optional) – whether this QOperation is estimation object, by default True
on_para_eq_constraint (bool, optional) – whether this QOperation is on parameter equality constraint, by default True
on_algo_eq_constraint (bool, optional) – whether this QOperation is on algorithm equality constraint, by default True
on_algo_ineq_constraint (bool, optional) – whether this QOperation is on algorithm inequality constraint, by default True
mode_proj_order (str, optional) – the order in which the projections are performed, by default “eq_ineq”
eps_proj_physical (float, optional) – epsilon that is projection algorithm error threshold for being physical, by default get_atol() / 10.0
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()

Returns

EffectiveLindbladian.

Return type

np.ndarray

generate_effective_lindbladian_from_hjk(c_sys, h_mat, j_mat, k_mat, 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]

generates EffectiveLindbladian from h matrix, j matrix and k matrix.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
h_mat (np.ndarray) – h matrix.
j_mat (np.ndarray) – j matrix.
k_mat (np.ndarray) – k matrix.
is_physicality_required (bool, optional) – whether this QOperation is physicality required, by default True
is_estimation_object (bool, optional) – whether this QOperation is estimation object, by default True
on_para_eq_constraint (bool, optional) – whether this QOperation is on parameter equality constraint, by default True
on_algo_eq_constraint (bool, optional) – whether this QOperation is on algorithm equality constraint, by default True
on_algo_ineq_constraint (bool, optional) – whether this QOperation is on algorithm inequality constraint, by default True
mode_proj_order (str, optional) – the order in which the projections are performed, by default “eq_ineq”
eps_proj_physical (float, optional) – epsilon that is projection algorithm error threshold for being physical, by default get_atol() / 10.0
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()

Returns

EffectiveLindbladian.

Return type

np.ndarray

generate_effective_lindbladian_from_hk(c_sys, h_mat, k_mat, 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]

generates EffectiveLindbladian from h matrix and k matrix.

j matrix is calculated from k matrix.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
h_mat (np.ndarray) – h matrix.
k_mat (np.ndarray) – k matrix.
is_physicality_required (bool, optional) – whether this QOperation is physicality required, by default True
is_estimation_object (bool, optional) – whether this QOperation is estimation object, by default True
on_para_eq_constraint (bool, optional) – whether this QOperation is on parameter equality constraint, by default True
on_algo_eq_constraint (bool, optional) – whether this QOperation is on algorithm equality constraint, by default True
on_algo_ineq_constraint (bool, optional) – whether this QOperation is on algorithm inequality constraint, by default True
mode_proj_order (str, optional) – the order in which the projections are performed, by default “eq_ineq”
eps_proj_physical (float, optional) – epsilon that is projection algorithm error threshold for being physical, by default get_atol() / 10.0
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()

Returns

EffectiveLindbladian.

Return type

np.ndarray

generate_effective_lindbladian_from_jump_operators(c_sys, jump_operators, 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]

generates EffectiveLindbladian from jump operators.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
jump_operators (List[np.ndarray]) – jump operators to generate EffectiveLindbladian.
is_physicality_required (bool, optional) – whether this QOperation is physicality required, by default True
is_estimation_object (bool, optional) – whether this QOperation is estimation object, by default True
on_para_eq_constraint (bool, optional) – whether this QOperation is on parameter equality constraint, by default True
on_algo_eq_constraint (bool, optional) – whether this QOperation is on algorithm equality constraint, by default True
on_algo_ineq_constraint (bool, optional) – whether this QOperation is on algorithm inequality constraint, by default True
mode_proj_order (str, optional) – the order in which the projections are performed, by default “eq_ineq”
eps_proj_physical (float, optional) – epsilon that is projection algorithm error threshold for being physical, by default get_atol() / 10.0
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()

Returns

EffectiveLindbladian.

Return type

np.ndarray

generate_effective_lindbladian_from_k(c_sys, k_mat, 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]

generates EffectiveLindbladian from k matrix.

j matrix is calculated from k matrix.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
k_mat (np.ndarray) – k matrix.
is_physicality_required (bool, optional) – whether this QOperation is physicality required, by default True
is_estimation_object (bool, optional) – whether this QOperation is estimation object, by default True
on_para_eq_constraint (bool, optional) – whether this QOperation is on parameter equality constraint, by default True
on_algo_eq_constraint (bool, optional) – whether this QOperation is on algorithm equality constraint, by default True
on_algo_ineq_constraint (bool, optional) – whether this QOperation is on algorithm inequality constraint, by default True
mode_proj_order (str, optional) – the order in which the projections are performed, by default “eq_ineq”
eps_proj_physical (float, optional) – epsilon that is projection algorithm error threshold for being physical, by default get_atol() / 10.0
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()

Returns

EffectiveLindbladian.

Return type

np.ndarray

generate_hs_from_h(c_sys, h_mat, eps_truncate_imaginary_part=None)[source]

generates HS matrix of EffectiveLindbladian from h matrix.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
h_mat (np.ndarray) – h matrix.
eps_truncate_imaginary_part (Optional[float]) –

Returns

HS matrix of EffectiveLindbladian.

Return type

np.ndarray

generate_hs_from_hjk(c_sys, h_mat, j_mat, k_mat, eps_truncate_imaginary_part=None)[source]

generates HS matrix of EffectiveLindbladian from h matrix, j matrix and k matrix.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
h_mat (np.ndarray) – h matrix.
j_mat (np.ndarray) – j matrix.
k_mat (np.ndarray) – k matrix.
eps_truncate_imaginary_part (Optional[float]) –

Returns

HS matrix of EffectiveLindbladian.

Return type

np.ndarray

generate_hs_from_hk(c_sys, h_mat, k_mat, eps_truncate_imaginary_part=None)[source]

generates HS matrix of EffectiveLindbladian from h matrix and k matrix.

j matrix is calculated from k matrix.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
h_mat (np.ndarray) – h matrix.
k_mat (np.ndarray) – k matrix.
eps_truncate_imaginary_part (Optional[float]) –

Returns

HS matrix of EffectiveLindbladian.

Return type

np.ndarray

generate_hs_from_k(c_sys, k_mat, eps_truncate_imaginary_part=None)[source]

generates HS matrix of EffectiveLindbladian from k matrix.

j matrix is calculated from k matrix.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this EffectiveLindbladian.
k_mat (np.ndarray) – k matrix.
eps_truncate_imaginary_part (Optional[float]) –

Returns

HS matrix of EffectiveLindbladian.

Return type

np.ndarray

generate_j_part_cb_from_jump_operators(jump_operators)[source]

generates j part of EffectiveLindbladian from jump operators.

this j part is represented by computational basis.

Parameters: jump_operators (List[np.ndarray]) – jump operators to generate j part.
Returns: j part of EffectiveLindbladian.
Return type: np.ndarray

generate_j_part_gb_from_jump_operators(jump_operators, basis, eps_truncate_imaginary_part=None)[source]

generates j part of EffectiveLindbladian from jump operators.

this j part is represented by general basis.

Parameters

jump_operators (List[np.ndarray]) – jump operators to generate j part.
basis (MatrixBasis) – MatrixBasis to present j part.
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()

Returns

j part of EffectiveLindbladian.

Return type

np.ndarray

generate_k_part_cb_from_jump_operators(jump_operators)[source]

generates k part of EffectiveLindbladian from jump operators.

this k part is represented by computational basis.

Parameters: jump_operators (List[np.ndarray]) – jump operators to generate k part.
Returns: k part of EffectiveLindbladian.
Return type: np.ndarray

generate_k_part_gb_from_jump_operators(jump_operators, basis, eps_truncate_imaginary_part=None)[source]

generates k part of EffectiveLindbladian from jump operators.

this k part is represented by general basis.

Parameters

jump_operators (List[np.ndarray]) – jump operators to generate k part.
basis (MatrixBasis) – MatrixBasis to present k part.
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()

Returns

k part of EffectiveLindbladian.

Return type

np.ndarray