quara.objects.gate_typical module

calc_1qutrit_single_gellmann_hamiltonian_mat_from_levels_axis_angle(levels, axis, angle)

return a 1-qutrit Hamiltonian matrix for the axis, levels, and angle.

Parameters

• levels (str) –

• axis (str) –

• angle (str) –

Return type

numpy.ndarray

calc_angle_from_str_to_float(angle_str)

return angle value from angle string

Parameters

angle_str (str) –

Return type

float

calc_base_matrix_1qutrit(levels, axis)

Return a base matrix for 1-qutrit Hamiltonian.

Parameters

• axis (str) – specifies “i”, “x”, “y”, or “z”.

• levels (str) – specifies levels for the axis, limited to [“01”, “12”, or “02”] for axis = “x”, “y”, or “z”. levels = None for “i”.

Returns

The base matrix corresponding to the axis and levels, to be complex.

Return type

np.ndarray((3,3), dtype=np.complex128)

calc_base_matrix_1qutrit_identity()

Return the identity matrix on a 1-qutrit system.

Return type

numpy.ndarray

calc_base_matrix_1qutrit_x_01()

Return the base matrix corresponding to the x-axis w.r.t. levels 0 and 1.

Return type

numpy.ndarray

calc_base_matrix_1qutrit_x_02()

Return the base matrix corresponding to the x-axis w.r.t. levels 0 and 2.

Return type

numpy.ndarray

calc_base_matrix_1qutrit_x_12()

Return the base matrix corresponding to the x-axis w.r.t. levels 1 and 2.

Return type

numpy.ndarray

calc_base_matrix_1qutrit_y_01()

Return the base matrix corresponding to the y-axis w.r.t. levels 0 and 1.

Return type

numpy.ndarray

calc_base_matrix_1qutrit_y_02()

Return the base matrix corresponding to the y-axis w.r.t. levels 0 and 2.

Return type

numpy.ndarray

calc_base_matrix_1qutrit_y_12()

Return the base matrix corresponding to the y-axis w.r.t. levels 1 and 2.

Return type

numpy.ndarray

calc_base_matrix_1qutrit_z_01()

Return the base matrix corresponding to the z-axis w.r.t. levels 0 and 1.

Return type

numpy.ndarray

calc_base_matrix_1qutrit_z_02()

Return the base matrix corresponding to the z-axis w.r.t. levels 0 and 2.

Return type

numpy.ndarray

calc_base_matrix_1qutrit_z_12()

Return the base matrix corresponding to the z-axis w.r.t. levels 1 and 2.

Return type

numpy.ndarray

calc_coeff_from_angle_str(angle_str)

return coeff = 0.5 * angle from angle_str.

Parameters

angle_str (str) –

Return type

float

calc_decimal_number_from_pauli_symbol(symbol)

Return the decimal number corresponding to a given pauli symbol.

Parameters

symbol (str) – Ex. i, x, yz, xyz.

Returns

int – Ex. 0, 1, 11, 27

Return type

A decimal number

calc_gate_from_hamiltonian_mat(c_sys, h, is_physicality_required=True)

return a Gate class object for a given Hamiltonian matrix.

Parameters

• c_sys (CompositeSystem, whose basis must be Hermitian.) –

• h (np.ndarray((dim, dim), dtype=np.complex128)) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

Return type

Gate

calc_gate_mat_from_hamiltonian_mat(h, to_basis)

return a HS matrix of a gate for a given Hamiltonian matrix.

Parameters

• h (np.ndarray((dim dim), dtype=np.complex128)) – Hamiltonian matrix

• to_basis (MatrixBasis, to be Hermitian) –

Returns

Return type

np.ndarray((dim^2, dim^2), dtype=np.float64)

calc_gate_mat_from_unitary_mat(from_u, to_basis)

Return the HS matrix for a gate represented by an unitary matrix.

Parameters

• from_u (np.ndarray((dim, dim), dtype=np.complex128)) – The unitary matrix, to be square complex np.ndarray.

• to_basis (MatrixBasis) – The matrix basis for representing the HS matrix, to be orthonormal.

Returns

The HS matrix of the gate corresponding to the unitary matrix.

Return type

np.ndarray((dim^2, dim^2), dtype=np.complex128)

calc_gate_mat_from_unitary_mat_with_hermitian_basis(from_u, to_basis)

Return the HS matrix w.r.t. a Hermitian (orthonormal) matrix basis for a gate represented by an unitary matrix.

Parameters

• from_u (np.ndarray((dim, dim), dtype=np.complex128)) – The unitary matrix, to be square complex np.ndarray.

• to_basis (MatrixBasis) – The matrix basis for representing the HS matrix

Returns

The HS matrix of the gate corresponding to the unitary matrix, to be real.

Return type

np.ndarray((dim^2, dim^2), dtype=np.float64)

calc_hamiltonian_mat_from_gate_name_2qutrit_base_matrices(gate_name)

Return a Hamiltonian matrix that corresponds to a given name of 2-qutirt gate whose Hamiltonian consists of base matrices.

Parameters

gate_name (str) – Ex. 01xi90, 12z01y180

Returns

A Hamiltonian matrix on 2-qutrit system

Return type

np.ndarray((9, 9), dtype=np.complex128)

calc_hamiltonian_mat_from_gate_name_2qutrit_single_base_matrix(gate_name)

Return a Hamiltonian matrix for a given name of gate on 2-qutrit system whose Hamiltonian consists of single base matrix.

Parameters

gate_name (str) –

Returns

Return type

np.ndarray(shape=(9,9), dtype=np.complex128)

calc_levels_axis_angle_from_gate_name_1qutrit_single_gellmann(gate_name)

return dictionary object containing three information for specifying a 1-qutrit Gell-Mann gate.

Parameters

gate_name (str) – A name of gate, e.g., “12x90”.

Returns

Example: {“levels”: “12”, “axis”: “x”, “angle”: “90”}

Return type

Dict[str, str]

calc_pauli_symbol_from_decimal_number(decimal_number, num_qubit)

Return the Pauli symbol corresponding to a given decimal number and number of qubit.

Parameters

• decimal_number (int) –

• num_qubit (int) –

Returns

str

Return type

a Pauli symbol

calc_pauli_symbol_from_quadrant(quadrant)

Return the Pauli symbol from a given quadtant.

Parameters

quadrant (str) – Ex. “0”, “1”, “23”, “123”.

Returns

str

Return type

Ex. i, x, yz, xyz.

calc_quadrant_from_decimal_number(value)

Return a quadrant (4-ary) from a given decimal number.

Parameters

value (int) – a decimal number

Returns

str

Return type

a quadrant

calc_quadrant_from_pauli_symbol(symbol)

Return the quadrant corresponding to a given pauli symbol.

Parameters

symbol (str) – Ex. i, x, yz, xyz.

Returns

str

Return type

Ex. “0”, “1”, “23”, “123”

calc_unitary_mat_from_hamiltonian_mat(h)

return the unitary matrix for a given Hamiltonian matrix.

Parameters

h (np.ndarray((dim, dim), dtype=np.complex128)) – Hamiltonian matrix

Returns

Return type

np.ndarray((dim dim), dtype=np.complex128), U = expm-(1j * h)

convert_1qubit_pauli_index_to_pauli_symbol(index)

Parameters

index (Union[int, str]) –

Return type

str

convert_1qubit_pauli_symbol_to_pauli_index(symbol, mode)

Parameters

• symbol (str) –

• mode (str) –

Return type

Union[int, str]

convert_1qubit_pauli_symbol_to_pauli_index_int(symbol)

Parameters

symbol (str) –

Return type

int

convert_1qubit_pauli_symbol_to_pauli_index_str(symbol)

Parameters

symbol (str) –

Return type

str

convert_pauli_indices_to_pauli_symbol(indices)

Parameters

indices (List[int]) –

Return type

str

convert_pauli_symbol_to_pauli_indices(symbol)

Parameters

symbol (str) –

Return type

List[int]

convert_string_to_strings(s)

Parameters

s (str) –

Return type

List[str]

convert_strings_to_string(s_list)

Parameters

s_list (List[str]) –

Return type

str

generate_gate_1qutrit_single_gellmann(c_sys, gate_name, is_physicality_required=True)

return the Gate for the gate.

Parameters

• c_sys (quara.objects.composite_system.CompositeSystem) –

• gate_name (str) –

• is_physicality_required (bool) –

Return type

quara.objects.gate.Gate

generate_gate_1qutrit_single_gellmann_hamiltonian_mat(gate_name)

return a 1-qutrit Hamiltonian matrix for the gate name.

Parameters

gate_name (str) –

Return type

numpy.ndarray

generate_gate_1qutrit_single_gellmann_mat(gate_name)

return the HS matrix for the gate.

Parameters

gate_name (str) –

Return type

numpy.ndarray

generate_gate_1qutrit_single_gellmann_unitary_mat(gate_name)

return the unitary matrix for the gate.

Parameters

gate_name (str) –

Return type

numpy.ndarray

generate_gate_2qutrit_hamiltonian_mat_from_gate_name(gate_name, ids=None)

Return a Hamiltonian of a 2-qutrit gate for a given gate name.

Parameters

• gate_name (str) –

• ids (List[int] = None, Optional) – a list of elemental system ids, which specifies their roles such as control or target.

Returns

Return type

np.ndarray(shape=(9, 9), dtype=np.complex128)

generate_gate_cx(c_sys, ids, is_physicality_required=True)

Return the Gate class for the Control-X (CX) gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• ids (List[int]) – ids[0] for control system index ids[1] for target system index

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the Control-X (CX) gate on the composite system.

Return type

Gate

generate_gate_cx_mat(ids)

Return the Hilbert-Schmidt representation matrix for a Control-X (CX) gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 16 times 16 real matrix.

Parameters

ids (List[int]) – ids[0] for the control system id, ids[1] for the target system id.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_cx_unitary_mat(ids)

Return the unitary matrix for a Control-X (CX) gate.

The result is the 4 times 4 complex matrix.

Parameters

ids (List[int]) – ids[0] for control system id, and ids[1] for target system id.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_cz(c_sys, is_physicality_required=True)

Return the Gate class for the Control-Z (CZ) gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the Control-Z (CZ) gate on the composite system.

Return type

Gate

generate_gate_cz_mat()

Return the Hilbert-Schmidt representation matrix for a Control-Z (CZ) gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 16 times 16 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_cz_unitary_mat()

Return the unitary matrix for a Control-Z (CZ) gate.

The result is the 4 times 4 complex matrix.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_fredkin_hamiltonian_mat(ids)

Return the Hamiltonian matrix of the Fredkin gate (Controlled-SWAP).

\(H = \frac{\pi}{8} (-III + IXX + IYY + IZZ + ZII - ZXX - ZYY - ZZZ)\)

Parameters

ids (List[int]) – ids[0] is for control, and ids[1] and ids[2] are for target.

Returns

Hamiltonian matrix

Return type

np.ndarray((8 8), dtype=np.complex128)

generate_gate_from_gate_name(gate_name, c_sys, ids=None, is_physicality_required=True)

returns gate class.

Parameters

• gate_name (str) – name of gate

• c_sys (CompositeSystem) –

• ids (List[int] (optional)) – list of ids for elemental systems

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The gate class for the input

Return type

Gate

generate_gate_hadamard(c_sys, is_physicality_required=True)

Return the Gate class for the Hadamard (H) gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the Hadamard (H) gate on the composite system.

Return type

Gate

generate_gate_hadamard_mat()

Return the Hilbert-Schmidt representation matrix for an Hadamard (H) gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_hadamard_unitary_mat()

Return the unitary matrix for an Hadamard (H) gate.

The result is the 2 times 2 complex matrix, H.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_identity(c_sys, is_physicality_required=True)

Return the Gate class for the identity gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the identity gate on the composite system.

Return type

Gate

generate_gate_identity_mat(dim)

Return the Hilbert-Schmidt representation matrix for an Identity gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is the dim^2 times dim^2 real identity matrix.

Parameters

dim (int) – The dimension of the quantum system on which the gate acts.

Returns

The real Hilbert-Schmidt representation matrix for the gate. It is the identity matrix in this case.

Return type

np.ndarray

generate_gate_identity_unitary_mat(dim)

Return the unitary matrix for an identity gate.

The result is the dim times dim complex identity matrix.

Parameters

dim (int) – The dimension of the quantum system on which the gate acts.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_mat_from_gate_name(gate_name, dims=None, ids=None)

returns the Hilbert-Schmidt representation matrix of a gate.

Parameters

• gate_name (str) – name of gate

• dims (List[int]) – list of dimentions of elemental systems that the gate acts on.

• ids (List[int] (optional)) – list of ids for elemental systems

Returns

The HS matrix of the gate, to be real.

Return type

np.ndarray

generate_gate_object_from_gate_name_object_name(gate_name, object_name, dims=None, ids=None, c_sys=None, is_physicality_required=True)

Parameters

• gate_name (str) –

• object_name (str) –

• dims (Optional[List[int]]) –

• ids (Optional[List[int]]) –

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

• is_physicality_required (bool) –

Return type

Union[numpy.ndarray, quara.objects.gate.Gate]

generate_gate_phase(c_sys, is_physicality_required=True)

Return the Gate class for the Phase (S) gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the Phase (S) gate on the composite system.

Return type

Gate

generate_gate_phase_daggered(c_sys, is_physicality_required=True)

Return the Gate class for the Phase daggered (S^dagger) gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the Phase daggered (S^dagger) gate on the composite system.

Return type

Gate

generate_gate_phase_daggered_mat()

Return the Hilbert-Schmidt representation matrix for a Phase daggerd (S^dagger) gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_phase_daggered_unitary_mat()

Return the unitary matrix for a Phase daggerd (S^dagger) gate.

The result is the 2 times 2 complex matrix, S^dagger.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_phase_mat()

Return the Hilbert-Schmidt representation matrix for a Phase (S) gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_phase_unitary_mat()

Return the unitary matrix for a Phase (S) gate.

The result is the 2 times 2 complex matrix, S.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_piover8(c_sys, is_physicality_required=True)

Return the Gate class for the pi/8 (T) gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the pi/8 (T) gate on the composite system.

Return type

Gate

generate_gate_piover8_daggered(c_sys, is_physicality_required=True)

Return the Gate class for the pi/8 daggered (T^dagger) gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the pi/8 daggered (T^dagger) gate on the composite system.

Return type

Gate

generate_gate_piover8_daggered_mat()

Return the Hilbert-Schmidt representation matrix for a pi/8 daggerd (T^dagger) gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_piover8_daggered_unitary_mat()

Return the unitary matrix for a pi/8 daggerd (T^dagger) gate.

The result is the 2 times 2 complex matrix, T^dagger.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_piover8_mat()

Return the Hilbert-Schmidt representation matrix for a pi/8 (T) gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_piover8_unitary_mat()

Return the unitary matrix for a pi/8 (T) gate.

The result is the 2 times 2 complex matrix, T.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_swap(c_sys, is_physicality_required=True)

Return the Gate class for the SWAP gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the SWAP gate on the composite system.

Return type

Gate

generate_gate_swap_mat()

Return the Hilbert-Schmidt representation matrix for a SWAP gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 16 times 16 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_swap_unitary_mat()

Return the unitary matrix for a SWAP gate.

The result is the 4 times 4 complex matrix.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_toffoli_hamiltonian_mat(ids)

Return the Hamiltonian matrix of the Toffoli gate (Controlled-Controlled-NOT).

\(H = \frac{\pi}{8} (-III + IIX + IZI - IZX + ZII - ZIX - ZZI + ZZX)\)

Parameters

ids (List[int]) – ids[0] and ids[1] are for control, and ids[2] is for target.

Returns

Hamiltonian matrix

Return type

np.ndarray((8 8), dtype=np.complex128)

generate_gate_x(c_sys, is_physicality_required=True)

Return the Gate class for the X gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the X gate on the composite system.

Return type

Gate

generate_gate_x180(c_sys, is_physicality_required=True)

Return the Gate class for the X180 gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the identity gate on the composite system.

Return type

Gate

generate_gate_x180_mat()

Return the Hilbert-Schmidt representation matrix for an X180 gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_x180_unitary_mat()

Return the unitary matrix for an X180 gate.

The result is the 2 times 2 complex matrix, -i X.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_x90(c_sys, is_physicality_required=True)

Return the Gate class for the X90 gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the X90 gate on the composite system.

Return type

Gate

generate_gate_x90_mat()

Return the Hilbert-Schmidt representation matrix for an X90 gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_x90_unitary_mat()

Return the unitary matrix for an X90 gate.

The result is the 2 times 2 complex matrix.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_x_mat()

Return the Hilbert-Schmidt representation matrix for an X gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_x_unitary_mat()

Return the unitary matrix for an X gate.

The result is the 2 times 2 complex matrix, X.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_y(c_sys, is_physicality_required=True)

Return the Gate class for the Y gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the Y gate on the composite system.

Return type

Gate

generate_gate_y180(c_sys, is_physicality_required=True)

Return the Gate class for the Y180 gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the Y180 gate on the composite system.

Return type

Gate

generate_gate_y180_mat()

Return the Hilbert-Schmidt representation matrix for a Y180 gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_y180_unitary_mat()

Return the unitary matrix for a Y180 gate.

The result is the 2 times 2 complex matrix, -i Y.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_y90(c_sys, is_physicality_required=True)

Return the Gate class for the Y90 gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the Y90 gate on the composite system.

Return type

Gate

generate_gate_y90_mat()

Return the Hilbert-Schmidt representation matrix for a Y90 gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_y90_unitary_mat()

Return the unitary matrix for an Y90 gate.

The result is a 2 times 2 complex matrix.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_y_mat()

Return the Hilbert-Schmidt representation matrix for a Y gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_y_unitary_mat()

Return the unitary matrix for a Y gate.

The result is the 2 times 2 complex matrix, Y.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_z(c_sys, is_physicality_required=True)

Return the Gate class for the Z gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the Z gate on the composite system.

Return type

Gate

generate_gate_z180(c_sys, is_physicality_required=True)

Return the Gate class for the Z180 gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the Z180 gate on the composite system.

Return type

Gate

generate_gate_z180_mat()

Return the Hilbert-Schmidt representation matrix for a Z180 gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_z180_unitary_mat()

Return the unitary matrix for a Z180 gate.

The result is the 2 times 2 complex matrix, -i Z.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_z90(c_sys, is_physicality_required=True)

Return the Gate class for the Z90 gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the Z90 gate on the composite system.

Return type

Gate

generate_gate_z90_mat()

Return the Hilbert-Schmidt representation matrix for a Z90 gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_z90_unitary_mat()

Return the unitary matrix for a Z90 gate.

The result is a 2 times 2 complex matrix.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_z_mat()

Return the Hilbert-Schmidt representation matrix for a Z gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 4 times 4 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_z_unitary_mat()

Return the unitary matrix for a Z gate.

The result is the 2 times 2 complex matrix, Z.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_zx90(c_sys, ids, is_physicality_required=True)

Return the Gate class for the ZX90 gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• ids (List[int]) – ids[0] for control system index ids[1] for target system index

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the ZX90 gate on the composite system.

Return type

Gate

generate_gate_zx90_mat(ids)

Return the Hilbert-Schmidt representation matrix for a ZX90 gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 16 times 16 real matrix.

Parameters

ids (List[int]) – ids[0] for the control system id, ids[1] for the target system id.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_zx90_unitary_mat(ids)

Return the unitary matrix for a ZX90 gate.

The result is the 4 times 4 complex matrix.

Parameters

ids (List[int]) – ids[0] for control system id, and ids[1] for target system id.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_gate_zz90(c_sys, is_physicality_required=True)

Return the Gate class for the ZZ90 gate on the composite system.

Parameters

• c_sys (CompositeSystem) –

• is_physicality_required (bool = True) – whether the generated object is physicality required, by default True

Returns

The Gate class for the ZZ90 gate on the composite system.

Return type

Gate

generate_gate_zz90_mat()

Return the Hilbert-Schmidt representation matrix for a ZZ90 gate with respect to the orthonormal Hermitian matrix basis with the normalized identity matrix as the 0th element.

The result is a 16 times 16 real matrix.

Returns

The real Hilbert-Schmidt representation matrix for the gate.

Return type

np.ndarray

generate_gate_zz90_unitary_mat()

Return the unitary matrix for a ZZ90 gate.

The result is the 4 times 4 complex matrix.

Returns

The unitary matrix, which is a complex matrix.

Return type

np.ndarray

generate_unitary_mat_from_gate_name(gate_name, dims=None, ids=None)

returns the unitary matrix of a gate.

Parameters

• gate_name (str) – name of gate

• dims (List[int]) – list of dimentions of elemental systems that the gate acts on.

• ids (List[int] (optional)) – list of ids for elemental systems

Returns

The unitary matrix of the gate, to be complex.

Return type

np.ndarray

get_angles_2qutrit()

Return a list of angles for 2-qutrit gates.

Return type

List[str]

get_base_matrices_1qutrit()

Return the dictionary object containing all base matrices for 1-qutrit Hamiltonian.

Returns

The dictionary. The first string of the Tuple is for the levels, “01”, “12”, or “02”. The second string of the Tuple is for the axis, “x”, “y”, or “z”. For example, dict[(“12”, “x”)] is the base matrix for the x-axis w.r.t. the levels 1 and 2.

Return type

Dict[Tuple[str, str], np.ndarray]

get_base_matrix_names_1qutrit()

Return a list of base matrix names for 1-qutrit system.

Return type

List[str]

get_base_matrix_names_2qutrit()

Return a list of base matrix names for 2-qutrit system.

Return type

List[str]

get_gate_names()

Return the list of valid gate names.

Return type

List[str]

get_gate_names_1qubit()

Return the list of valid gate names of 1-qubit gates.

Return type

List[str]

get_gate_names_1qutrit()

return the list of valid (implemented) gate names of 1-qutrit gates.

Return type

List[str]

get_gate_names_1qutrit_single_gellmann()

return the list of valid (implemented) gate names of 1-qutrit single Gell-Mann gates.

Return type

List[str]

get_gate_names_2qubit()

Return the list of valid gate names of 2-qubit gates.

Return type

List[str]

get_gate_names_2qubit_asymmetric()

Return the list of valid gate names of 2-qubit gates that are asymmetric with respect to ids of elemental systems.

Return type

List[str]

get_gate_names_2qutrit()

return the list of valid (implemented) gate names of 2-qutrit gates.

Return type

List[str]

get_gate_names_2qutrit_base_matrices()

return the list of valid (implemented) gate names of 2-qutrit gates.

Return type

List[str]

get_gate_names_2qutrit_single_base_matrix()

Return a list of gate names on 2-qutirt system whose Hamiltonian consists of single base matrix.

Return type

List[str]

get_gate_names_2qutrit_two_base_matrices()

Return a list of gate names on 2-qutrit system whose Hamiltonian consists of two base matrices.

Return type

List[str]

get_gate_names_3qubit()

Return the list of valid gate names of typical 3-qubit gates.

Return type

List[str]

get_gate_names_3qubit_asymmetric()

Return the list of valid gate names of typical 3-qubit gates that are asymmetric with respect to ids of elemental systems.

Return type

List[str]

get_permutation_matrix_from_ascending_order(ids)

Return a permutation matrix that convert soarted(ids) to ids.

Parameters

ids (List[int]) – A list of integers, to have no duplication.

Returns

A permutation matrix that convert the sorted list in the ascending order, sorted(ids), to the original list, ids.

Return type

np.ndarray

is_no_duplication_list(l)

Parameters

l (List) –

Return type

bool

permute_pauli_symbol(symbol, ids)

Parameters

• symbol (str) –

• ids (List[int]) –

Return type

str

split_gate_name_2qutrit_base_matrices(gate_name)

Return a list of gate names that are elements of a given gate name.

Ex. “01x02z90_12yi180” -> [“01x02z90”, “12yi180”]

Parameters

gate_name (str) –

Return type

List[str]

split_gate_name_2qutrit_single_base_matrix_into_base_matrix_names_angle(gate_name)

Return base matrix names and angle for a given 2-qutrit single base matrix name.

Parameters

• gate_names (str) – Ex. “i01x90”, “12yi180”, “02z12y90”

• gate_name (str) –

Returns

key = “base0”, “base1”, “angle”.

Ex.

• {‘base0’: ‘i’, ‘base1’: ‘01x’, ‘angle’:’90’}

• {‘base0’: ‘12y’, ‘base1’: ‘i’, ‘angle’:’180’}

• {‘base0’: ‘02z’, ‘base1’: ‘12y’, ‘angle’:’90’}

Return type

Dict[str, str]