build_excitation_span_minimization_model

build_excitation_span_minimization_model(excitations, num_modes, *, objective='multi', mix_delta=0.1)

Build a Pyomo model for ordering fermionic modes to minimize excitation spans.

The model constructs a permutation where each original mode index is assigned to exactly one position in a linear ordering. For every 2-mode and 4-mode excitation tuple, the span of occupied positions is minimized according to the chosen objective.

Note

The excitations list is pre-processed as follows:

• indices that occur twice within the same tuple get cancelled

• resulting tuples of length 0 or 1 are ignored, therefore not imposing a distance constraint in the resulting minimization model

• consequently, only post-processed tuples of length 2 or 4 are expected

See also

For a more detailed discussion and explanation of the reasoning behind this pre-processing, refer to section III.B of this paper.

Parameters:

• excitations (Sequence[tuple[int, int] | tuple[int, int, int, int]]) – a sequence of excitation index tuples over fermionic mode indices.

• num_modes (int) – the total number of fermionic modes to be ordered.

• objective (Literal['minmax', 'multi', 'avg']) –

  the chosen objective mode. This may be one of the following literals:

  • minmax: minimizes the maximum excitation span.

  • avg: minimizes the average excitation span.

  • multi: minimizes max_span + mix_delta * average_span.

• mix_delta (float) – the mixing weight used in the case of objective="multi".

Returns:

A Pyomo optimization model encoding the permutation variables, span variables, constraints, and objective. Solve this model with a Pyomo solver to obtain an optimized ordering.

Raises:

• ValueError – if a post-processed excitation tuple has length unequal to 2 or 4.

• ValueError – if an unknown objective is chosen.

Return type:

pyomo.core.base.PyomoModel.ConcreteModel