quara.objects.gate module

class Gate(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.qoperation.QOperation

Constructor

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
hs (np.ndarray) – HS representation of this gate.
is_physicality_required (bool, optional) –
checks whether the gate is physically wrong, by default True. if at least one of the following conditions is False, the gate is physically wrong:
- gate is TP(trace-preserving map).
- gate is CP(Complete-Positivity-Preserving).
If you want to ignore the above requirements and create a Gate 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_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_proj_eq_constraint()[source]

calculates the projection of QOperation on equal constraint.

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

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

calculates the projection of Gate 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 Gate on equal constraint.

Return type

np.ndarray

calc_proj_ineq_constraint()[source]

calculates the projection of QOperation on inequal constraint.

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

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 Gate 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 Gate on equal constraint.

Return type

np.ndarray

convert_basis(other_basis)[source]

returns HS representation for other_basis.

Parameters: other_basis (MatrixBasis) – basis.
Returns: HS 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 gate to variables of gate.

Parameters

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

Returns

variables of gate.

Return type

np.ndarray

convert_to_comp_basis(mode='row_major')[source]

returns HS representation for computational basis.

Parameters: mode (str, optional) – specify whether the order of basis is “row_major” or “column_major”, by default “row_major”.
Returns: HS representation for computational basis.
Return type: np.ndarray

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

converts variables of gate to stacked vector of gate.

Parameters

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

Returns

stacked vector of gate.

Return type

np.ndarray

property dim

returns dim of gate.

Returns: dim of gate.
Return type: int

get_basis()[source]

returns MatrixBasis of gate.

Returns: MatrixBasis of gate.
Return type: MatrixBasis

property hs

returns HS representation of gate.

Returns: HS representation of gate.
Return type: np.ndarray

is_cp(atol=None)[source]

returns whether gate 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 gate is CP, False otherwise.
Return type: bool

is_eq_constraint_satisfied(atol=None)[source]

Parameters: atol (Optional[float]) –

is_ineq_constraint_satisfied(atol=None)[source]

Parameters: atol (Optional[float]) –

is_tp(atol=None)[source]

returns whether the gate 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 gate is TP, False otherwise.
Return type: bool

set_zero()[source]

sets parameters to zero.

this function must be implemented in the subclass.

Raises: NotImplementedError – this function does not be implemented in the subclass.

to_choi_matrix()[source]

returns Choi matrix of gate.

Returns: Choi matrix of gate.
Return type: np.ndarray

to_choi_matrix_with_dict()[source]

returns Choi matrix of gate.

this function uses the scipy.sparse module.

Returns: Choi matrix of gate.
Return type: np.ndarray

to_choi_matrix_with_sparsity()[source]

returns Choi matrix of gate.

this function uses the scipy.sparse module.

Returns: Choi matrix of gate.
Return type: np.ndarray

to_kraus_matrices()[source]

returns Kraus matrices of gate.

this function returns Kraus matrices as list of np.ndarray with dtype=np.complex128. the list is sorted large eigenvalue order. if HS of gate is not CP, then returns empty list because Kraus matrices does not exist.

Returns: Kraus matrices of gate.
Return type: List[np.ndarray]

to_process_matrix()[source]

returns process matrix of gate.

Returns: process matrix of gate.
Return type: np.ndarray

to_stacked_vector()[source]

converts QOperation to stacked vector.

this function must be implemented in the subclass.

Returns: stacked vector representation of QOperation.
Return type: np.ndarray
Raises: NotImplementedError – this function does not be implemented in the subclass.

to_var()[source]

converts QOperation to variables.

this function must be implemented in the subclass.

Returns: variable representation of QOperation.
Return type: np.ndarray
Raises: NotImplementedError – this function does not be implemented in the subclass.

calc_agf(g, u)[source]

returns AGF(Average Gate Fidelity) and g and u.

Parameters

g (Gate) – L-TP-CP map.
u (Gate) – unitary gate.

Returns

AGF.

Return type

np.float64

Raises

ValueError – HS representation of u is not Hermitian.

calc_gradient_from_gate(c_sys, hs, 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=None, eps_truncate_imaginary_part=None)[source]

calculates gradient from gate.

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.
is_estimation_object (bool) –
on_algo_eq_constraint (bool) –
on_algo_ineq_constraint (bool) –
mode_proj_order (str) –
eps_proj_physical (Optional[float]) –
eps_truncate_imaginary_part (Optional[float]) –

Returns

Gate with gradient as hs.

Return type

Gate

convert_gate_index_to_var_index(c_sys, gate_index, on_para_eq_constraint=True)[source]

converts gate index to variable index.

Parameters

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

Returns

variable index.

Return type

int

convert_hs(from_hs, from_basis, to_basis)[source]

returns HS representation for to_basis

Parameters

from_hs (np.ndarray) – HS representation before convert.
from_basis (MatrixBasis) – basis before convert.
to_basis (MatrixBasis) – basis after convert.

Returns

HS representation for to_basis.

Return type

np.ndarray

Raises

ValueError – from_hs is not square matrix.
ValueError – dim of from_hs is not square number.
ValueError – dim of from_basis does not equal dim of to_basis.
ValueError – length of from_basis does not equal length of to_basis.

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

converts hs of gate to vec of variables.

Parameters

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

Returns

vec of variables.

Return type

np.ndarray

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

converts variable index to gate index.

Parameters

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

Returns

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

Return type

Tuple[int, int]

convert_var_to_gate(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=None, eps_truncate_imaginary_part=None)[source]

converts vec of variables to gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
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 (Optional[float]) –
eps_truncate_imaginary_part (Optional[float]) –

Returns

converted gate.

Return type

Gate

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

converts variables of gate to HS representation.

Parameters

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

Returns

HS representation of this gate.

Return type

np.ndarray

get_amplitutde_damping_channel(gamma, c_sys=None)[source]

Parameters

gamma (float) –
c_sys (Optional[quara.objects.composite_system.CompositeSystem]) –

Return type

quara.objects.gate.Gate

get_cnot(c_sys, control)[source]

returns CNOT gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem containing gate.
control (ElementalSystem) – ElementalSystem of control qubit.

Returns

CNOT gate.

Return type

Gate

Raises

ValueError – CompositeSystem is not 2quits.
ValueError – dim of CompositeSystem does not equal 4.

get_cz(c_sys)[source]

returns CZ gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem containing gate.

Returns

CZ gate.

Return type

Gate

Raises

ValueError – CompositeSystem is not 2quits.
ValueError – dim of CompositeSystem does not equal 4.

get_depolarizing_channel(p, c_sys=None)[source]

Parameters

p (float) –
c_sys (Optional[quara.objects.composite_system.CompositeSystem]) –

Return type

quara.objects.gate.Gate

get_h(c_sys)[source]

returns H gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem containing gate.

Returns

H gate.

Return type

Gate

Raises

ValueError – CompositeSystem is not 1quit.
ValueError – dim of CompositeSystem does not equal 2

get_i(c_sys)[source]

returns identity gate.

Parameters: c_sys (CompositeSystem) – CompositeSystem containing gate.
Returns: identity gate.
Return type: Gate

get_root_x(c_sys)[source]

returns root of X gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem containing gate.

Returns

root of X gate.

Return type

Gate

Raises

ValueError – CompositeSystem is not 1quit.
ValueError – dim of CompositeSystem does not equal 2

get_root_y(c_sys)[source]

returns root of Y gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem containing gate.

Returns

root of Y gate.

Return type

Gate

Raises

ValueError – CompositeSystem is not 1quit.
ValueError – dim of CompositeSystem does not equal 2

get_s(c_sys)[source]

returns S gate(root of Z).

Parameters

c_sys (CompositeSystem) – CompositeSystem containing gate.

Returns

S gate(root of Z).

Return type

Gate

Raises

ValueError – CompositeSystem is not 1quit.
ValueError – dim of CompositeSystem does not equal 2

get_sdg(c_sys)[source]

returns dagger of S gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem containing gate.

Returns

dagger of S gate.

Return type

Gate

Raises

ValueError – CompositeSystem is not 1quit.
ValueError – dim of CompositeSystem does not equal 2

get_swap(c_sys)[source]

returns SWAP gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem containing gate.

Returns

SWAP gate.

Return type

Gate

Raises

ValueError – CompositeSystem is not 2quits.
ValueError – dim of CompositeSystem does not equal 4

get_t(c_sys)[source]

returns T gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem containing gate.

Returns

T gate.

Return type

Gate

Raises

ValueError – CompositeSystem is not 1quit.
ValueError – dim of CompositeSystem does not equal 2

get_x(c_sys)[source]

returns Pauli X gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem containing gate.

Returns

Pauli X gate.

Return type

Gate

Raises

ValueError – CompositeSystem is not 1quit.
ValueError – dim of CompositeSystem does not equal 2

get_x_rotation(theta, c_sys=None)[source]

Parameters

theta (float) –
c_sys (Optional[quara.objects.composite_system.CompositeSystem]) –

Return type

quara.objects.gate.Gate

get_y(c_sys)[source]

returns Pauli Y gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem containing gate.

Returns

Pauli Y gate.

Return type

Gate

Raises

ValueError – CompositeSystem is not 1quit.
ValueError – dim of CompositeSystem does not equal 2

get_z(c_sys)[source]

returns Pauli Z gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem containing gate.

Returns

Pauli Z gate.

Return type

Gate

Raises

ValueError – CompositeSystem is not 1quit.
ValueError – dim of CompositeSystem does not equal 2

is_cp(c_sys, hs, atol=None)[source]

returns whether gate is CP(Complete-Positivity-Preserving).

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
hs (np.ndarray) – HS representation of this gate.
atol (float, optional) – the absolute tolerance parameter, uses get_atol() by default. this function ignores eigenvalues close zero.

Returns

True where gate is CP, False otherwise.

Return type

bool

is_hp(hs, basis, atol=None)[source]

returns whether gate is HP(Hermiticity-Preserving).

HP <=> HS on Hermitian basis is real matrix. therefore converts input basis to Pauli basis, and checks whetever converted HS is real matrix.

Parameters

hs (np.ndarray) – HS representation of gate.
basis (MatrixBasis) – basis of HS representation.
atol (float, optional) – the absolute tolerance parameter, uses get_atol() by default. this function checks absolute(imaginary part of matrix - zero matrix) <= atol.

Returns

True where gate is EP, False otherwise.

Return type

bool

is_tp(c_sys, hs, atol=None)[source]

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

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
hs (np.ndarray) – HS representation of this gate.
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 gate is TP, False otherwise.

Return type

bool

to_choi_from_hs(c_sys, hs)[source]

converts HS representation to Choi matrix of this gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
hs (np.ndarray) – HS representation of this gate.

Returns

Choi matrix of this gate.

Return type

np.ndarray

to_choi_from_hs_with_dict(c_sys, hs)[source]

converts HS representation to Choi matrix of this gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
hs (np.ndarray) – HS representation of this gate.

Returns

Choi matrix of this gate.

Return type

np.ndarray

to_choi_from_hs_with_sparsity(c_sys, hs)[source]

converts HS representation to Choi matrix of this gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
hs (np.ndarray) – HS representation of this gate.

Returns

Choi matrix of this gate.

Return type

np.ndarray

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

converts variables to Choi matrix.

Parameters

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

Returns

Choi matrix of this gate.

Return type

np.ndarray

to_hs_from_choi(c_sys, choi)[source]

converts Choi matrix to HS representation of this gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
choi (np.ndarray) – Choi matrix of this gate.

Returns

HS representation of this gate.

Return type

np.ndarray

to_hs_from_choi_with_dict(c_sys, choi, eps_truncate_imaginary_part=None)[source]

converts Choi matrix to HS representation of this gate.

this function uses dict to calculate fast.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
choi (np.ndarray) – Choi matrix of this gate.
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()

Returns

HS representation of this gate.

Return type

np.ndarray

to_hs_from_choi_with_sparsity(c_sys, choi, eps_truncate_imaginary_part=None)[source]

converts Choi matrix to HS representation of this gate.

this function uses the scipy.sparse module.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
choi (np.ndarray) – Choi matrix of this gate.
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()

Returns

HS representation of this gate.

Return type

np.ndarray

to_hs_from_kraus_matrices(c_sys, kraus, eps_truncate_imaginary_part=None)[source]

returns HS representation of this gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
kraus (List[np.ndarray]) – Kraus matrices of gate.
eps_truncate_imaginary_part (float, optional) – threshold to truncate imaginary part, by default get_atol()

Returns

HS representation of this gate.

Return type

np.ndarray

to_kraus_matrices_from_hs(c_sys, hs, atol=None)[source]

returns Kraus matrices of gate.

this function returns Kraus matrices as list of np.ndarray with dtype=np.complex128. the list is sorted large eigenvalue order. if HS of gate is not CP, then returns empty list because Kraus matrices does not exist.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
hs (np.ndarray) – HS representation of this gate.
atol (float, optional) – the absolute tolerance parameter, uses get_atol() by default. this function ignores eigenvalues close zero.

Returns

Kraus matrices of gate.

Return type

List[np.ndarray]

to_process_matrix_from_hs(c_sys, hs)[source]

returns process matrix of gate.

Parameters

c_sys (CompositeSystem) – CompositeSystem of this gate.
hs (np.ndarray) – HS representation of this gate.

Returns

process matrix of gate.

Return type

np.ndarray

to_var_from_choi(c_sys, choi, on_para_eq_constraint=True)[source]

converts Choi matrix to variables.

Parameters

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

Returns

variables.

Return type

np.ndarray