index permutation symmetry

[janbrandejs]

I would like to extend TAPP for index permutation symmetry (with a draft on a branch first).
I think it's enough to declare which groups of indices are mutually symmetric or antisymmetric using the proposed key-value pair storage (hashtable) parameter of TAPP_create_tensor_info.

(example for T3 amplitude tensor in coupled cluster)

Approach 1:
This information could be passed by adding these keys to the hashtable:

key: AS_ngroups, val: 2 // two groups
key: AS_groups_nmodes, val: {3, 3} (pointer to int64_t array) // first and second AS groups all have 3 indices
key: AS_indices, value: {0,1,2,3,4,5} (pointer to int64_t array) // list of all indices involved in groups
key: S_ngroups, val: 0

Approach 2:
key: perm_symm_size, value: 25 (int64_t) // number of characters
key: perm_symm, value "AS:{{0,1,2},{3,4,5}},S:{}" (pointer to int64_t array) // ASCII char numbers

This is just 'a' solution (in fact 2), but I'd be happy to see more elegant ways!
I prefer approach 2!

[evaleev]

I don't know how general we want to go. Antisymmetric and symmetric groups are only a particular example of more general symmetries (but in QC the former is what everyone wants :). In general

• symmetries will refer to groups of indices, e.g. (μ ν|ρ σ) <-> (ρ σ|μ ν)
• byproducts of permutations may not be simple scalings like in the antisymmetric case (e.g. (μ ν|ρ σ) <-> (σ ρ|ν μ)^* )
• general permutation symmetry refer to a general irrep of a symmetric group, corresponding to a Young tableaux; antisymmetric and symmetric are only the simplest 1-d irreps (alternating and trivial) of S^n. Other irreps will occur for nonabelian symmetries (i.e. n>2).

[pauldj]

let's bring this up at the workshop in Toulouse (Sept'25)

[janbrandejs]

for completeness, during discussion at ReLibQC in Finland, @devinamatthews suggested to follow the way of enconding index permutation symmetry from Cyclops CTF, e.g.
enum 0: NS, 1: S, 2: AS // (non-symm, symm, anti-symm)
for T3 amplitude tensor with 2 groups of 3 indices mutually antisymmetric within the group
T3[ijk abc]

                i   j   k   a   b   c
T3_perm_symm = {AS, AS, NS, AS, AS, NS}

where each element expresses the relation of the present index to the next index

with the assumption of having the indices with permutation symmetry next to one another (continuos groups)
Then during last Friday's call @evaleev commented on this that this is too restrictive/ too specific. (in light of his above comment)