Initialisation and updates

The top-level classes are MajoranaPropagator and PauliPropagator (Python) / MonomialPropagator<NumModes> (C++). Every significant aspect of the simulation can be tuned at construction time and updated at runtime without rebuilding. The structural and coefficient cutoffs are covered separately in Truncation and cutoffs.

Heisenberg and Schrödinger pictures

Pass schrodinger_cutoff to switch from the default Heisenberg picture (operator evolution) to the Schrödinger picture (density matrix evolution). In the Schrödinger picture gates are applied to the state, whereas in the Heisenberg picture they are applied to the observable.

schrodinger_cutoff is the truncation applied to the initial state. It must be set higher than the regular cutoff for the Schrödinger-picture result to match the Heisenberg-picture one: under length truncation the two pictures agree on fermionic circuits when schrodinger_cutoff = cutoff + 2 (see Appendix of (Chakraborty et al., 2026)).

Operator updates

The coefficients of the initial operator can be patched after construction without rebuilding the simulator or the graph. The keys are Majorana monomials (tuples of indices); the values are the new coefficients, which must keep each monomial Hermitian (real for length-4 terms, imaginary for length-2 — see the Notation page):

from monoprop import MajoranaPropagator, MajoranaOperator

observable = MajoranaOperator({(0, 1, 2, 3): 1.0}, 4)
sim = MajoranaPropagator(observable, initial_state=[0, 1], cutoff=4)
sim.update_initial_operator({(0, 1, 2, 3): 0.5})

This lets you estimate several observables without re-propagating: in the Schrödinger picture the state is evolved independently, so you can re-weight the observable and read it off against the same evolved state; in the Heisenberg picture the same graph can be reused with different initial operators.

import pytest
from monoprop import MajoranaPropagator, MajoranaOperator

observable = MajoranaOperator({(0, 1, 2, 3): 1.0}, 4)
sim = MajoranaPropagator(observable, initial_state=[0, 1], cutoff=4)
with pytest.raises(RuntimeError):
    sim.update_initial_operator({(1, 2, 3, 4): 0.5})  # This monomial doesn't exist