quairkit.core.hamiltonian¶

The module of the hamiltonian class.

class quairkit.core.hamiltonian.Hamiltonian(pauli_str, compress=True)¶

Hamiltonian class in QuAIRKit.

User can instantiate the class with a Pauli string.

Parameters:¶

pauli_str : list¶

A list of Hamiltonian information, e.g. [(1, 'Z0, Z1'), (2, 'I')]

compress : bool | None¶

Determines whether the input list will be automatically merged (e.g. (1, 'Z0, Z1') and (2, 'Z1, Z0'), these two items will be automatically merged). Defaults to True.

Returns:¶

Create a Hamiltonian class

Note

If compress=False, the legitimacy of the input will not be checked.

property n_terms : int¶

Number of terms of the hamiltonian.

property pauli_str : list¶

The Pauli string corresponding to the hamiltonian.

property terms : Iterable[float]¶

All items in hamiltonian, i.e. [['Z0, Z1'], ['I']].

property coefficients : list[float]¶

The coefficient of each term in the Hamiltonian, i.e. [1.0, 2.0].

property pauli_words : list[str]¶

The Pauli word of each term, i.e. ['ZIZ', 'IIX'].

property pauli_words_r : list[str]¶

A list of Pauli word (exclude I), i.e. ['ZXZZ', 'Z', 'X'].

property pauli_words_matrix : list[Tensor]¶

The list of matrices with respect to simplied Pauli words.

property matrix : Tensor¶

The matrix form of the Hamiltonian.

property sites : list¶

A list of qubits index corresponding to the hamiltonian.

property n_qubits : int¶

Number of qubits.

decompose_with_sites()¶

Decompose pauli_str into coefficients, a simplified form of Pauli strings, and the indices of qubits on which the Pauli operators act on.

Returns:¶

• coefficients: the coefficient for each term.

• pauli_words_r: the simplified form of the Pauli string for each item, e.g. the Pauli word of ‘Z0, Z1, X3’ is ‘ZZX’.

• sites: a list of qubits index, e.g. the site of ‘Z0, Z1, X3’ is [0, 1, 3].

Return type:¶

A tuple containing the following elements

decompose_pauli_words()¶

Decompose pauli_str into coefficients and Pauli strings.

Returns:¶

• coefficients: the coefficient for each term.

• the Pauli string for each item, e.g. the Pauli word of ‘Z0, Z1, X3’ is ‘ZZIX’.

Return type:¶

A tuple containing the following elements

construct_h_matrix(qubit_num=None)¶

Construct a matrix form of the Hamiltonian in Z-basis.

Parameters:¶

qubit_num : int | None¶

The number of qubits. Defaults to None.

Returns:¶

The matrix form of the Hamiltonian in Z-basis.

Return type:¶

ndarray

class quairkit.core.hamiltonian.SpinOps(size, use_sparse=False)¶

The spin operators in matrix forms, could be used to construct Hamiltonian matrix or spin observables.

Parameters:¶

size : int¶

Size of the system (number of qubits).

use_sparse : bool | None¶

Decide whether to use the sparse matrix to calculate. Default is False.

property sigz_p : list¶

A list of \(S^z_i\) operators, different elements correspond to different indices \(i\).

property sigy_p : list¶

A list of \(S^y_i\) operators, different elements correspond to different indices \(i\).

property sigx_p : list¶

A list of \(S^x_i\) operators, different elements correspond to different indices \(i\).