Random permutation of strings in Trotterisation

[vaferreiQMT]

Implements

• random permutations of Pauli strings in a PauliStrSum
• option to use random permutations during Trotterisation

See also #596

[otbrown]

Hi Vasco,

Thanks for this -- just wanted to confirm that I've seen it and will try to review once I'm back from SC (which is next week!).

Cheers,
Oliver

[TysonRayJones]

Hi Vasco and Oliver,

Here are some thoughts before merging:

• Making a new randomiseString parameter constitutes an API break - but I personally think that's fine and doesn't warrant a new major version.
• The new randomiseString parameter needs to be added to the docstrings.
• Is randomiseString the most illustrative name? I worry the String suffix doesn't clarify much - the code is shuffling the order of the prescribed Pauli rotations within each Trotter repetition - so I would personally advocate for simplifying it to randomise.
• The current implementation mutates the passed PauliStrSum, so a user printing their PauliStrSum will see it changed pre- and post-call of any of the Trotter functions. If that's a desired/acceptable postcondition, we need to doc that. If that's undesirable, it'd be straightforward to additionally maintain a list of the original indices with respect to the current mutation and restore the original order before function return. That requires O(#terms) temporary memory which may be justifiable (e.g. the Lindblad functions use greater temp mem).