MergeEvolutions¶

class MergeEvolutions(atol=1e-12)¶

Bases: GenericPass[DAGCircuit, DAGCircuit]

A transpilation pass merging consecutive Evolution gates of the same operator.

Two evolutions under the same operator \(H\) satisfy

\[e^{-i t_2 H} e^{-i t_1 H} = e^{-i (t_1 + t_2) H},\]

because \(H\) commutes with itself. This pass finds neighboring Evolution gates of the same operator and replaces them by one gate whose evolution time is the sum of theirs. The rewrite is exact, so it changes neither the simulated state nor the Trotter error of the circuit; it only removes a gate, and with it the synthesized operations that gate would have produced.

Such neighbors arise wherever two sequences of factors meet on the same factor. Examples are the seams between the repetitions of BosonicCircuit.repeat(), or between consecutive samples of BosonicQDrift. BosonicSuzukiTrotter already fuses the seams within its own output (see BosonicSuzukiTrotter.merge_adjacent); this pass is the general mechanism which also acts across gate boundaries.

Two gates merge only when all of the following hold:

they act on the identical wires, in the identical order, with nothing else in between;
their operators are of the same type and equal up to atol as sums of products of ladder operators, which is stricter than BosonOperator.equiv(), see the note below;
they are either both Evolution.atomic or both not, and in the latter case they are decomposed by the same kind of Evolution.synthesis with identical settings.

The merged gate keeps the operator, and thus the groups, of the first gate of the run.

Note

Two operators that are BosonOperator.equiv() are not necessarily the same operator once they are truncated. Normal ordering is an identity of the untruncated Fock space, and a truncation does not preserve it: \(b b^\dagger\) and \(b^\dagger b + 1\) map to different matrices, which differ on the highest level. Gates whose operators are only equiv are therefore not merged, because the merged gate would no longer equal the two it replaces.

Caution

This is an early development prototype. Beware of changes to its interface without warning during the pre-release development of this package.