LogarithmicMapper#

class LogarithmicMapper(*, padding=1, embed_upper=True)[source]#

Bases: SpinMapper

A mapper for Logarithmic spin-to-qubit mapping. In this local encoding transformation, each individual spin S system is represented via the lowest lying \(2S+1\) states in a qubit system with the minimal number of qubits needed to represent \(>= 2S+1\) distinct states [1].

References

[1] S. V. Mathis, G. Mazzola and I. Tavernelli. Toward scalable simulations of lattice gauge theories on quantum computers. Phys. Rev. D, 102 (9), 094501 (2020). https://doi.org/10.1103/PhysRevD.102.094501

Parameters:

  • padding (float) – When embedding a matrix into the upper/lower diagonal block of a \(2^n\) by \(2^n\) matrix ,where \(n\) is the number of qubits, pads the diagonal of the block matrix with the value of padding.

  • embed_upper (bool) –

    This parameter sets whether the given matrix is embedded in the upper left hand corner or the lower right hand corner of the larger matrix. I.e. using embed_upper = True returns the matrix:

    \[\begin{split}\begin{pmatrix} \text{matrix} & 0 \\ 0 & \text{padding} * I \end{pmatrix}\end{split}\]

    Using embed_upper = False returns the matrix:

    \[\begin{split}\begin{pmatrix} \text{padding} * I & 0 \\ 0 & \text{matrix} \end{pmatrix}\end{split}\]

Methods

map(second_q_ops, *, register_length=None)#

Maps a second quantized operator or a list, dict of second quantized operators based on the current mapper.

Parameters:

  • second_q_ops (SpinOp | ListOrDictType[SpinOp]) – A second quantized operator, or list thereof.

  • register_length (int | None) – when provided, this will be used to overwrite the register_length attribute of the SparseLabelOp being mapped. This is possible because the register_length is considered a lower bound in a SparseLabelOp.

Returns:

A qubit operator in the form of a SparsePauliOp, or list (resp. dict) thereof if a list (resp. dict) of second quantized operators was supplied.

Return type:

SparsePauliOp | ListOrDictType[SparsePauliOp]

classmethod mode_based_mapping(second_q_op, register_length=None)#

Utility method to map a SparseLabelOp to a qubit operator using a pauli table.

Parameters:

  • second_q_op (SparseLabelOp) – the SparseLabelOp to be mapped.

  • register_length (int | None) – when provided, this will be used to overwrite the register_length attribute of the operator being mapped. This is possible because the register_length is considered a lower bound.

Returns:

The qubit operator corresponding to the problem-Hamiltonian in the qubit space.

Raises:

QiskitNatureError – If number length of pauli table does not match the number of operator modes, or if the operator has unexpected label content

Return type:

SparsePauliOp

classmethod pauli_table(register_length)#

Generates a Pauli-lookup table mapping from modes to pauli pairs.

The generated table is processed by QubitMapper.sparse_pauli_operators().

Parameters:

register_length (int) – the register length for which to generate the table.

Returns:

A list of tuples in which the first and second Pauli operator the real and imaginary Pauli strings, respectively.

Return type:

list[tuple[Pauli, Pauli]]

classmethod sparse_pauli_operators(register_length)#

Generates the cached SparsePauliOp terms.

This uses QubitMapper.pauli_table() to construct a list of operators used to translate the second-quantization symbols into qubit operators.

Parameters:

register_length (int) – the register length for which to generate the operators.

Returns:

Two lists stored in a tuple, consisting of the creation and annihilation operators, applied on the individual modes.

Return type:

tuple[list[SparsePauliOp], list[SparsePauliOp]]