Qiskit / qiskit
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Add `SparseObservable.compose` (#13766)

* Add `SparseObservable.compose`

This adds matrix multiplication between `SparseObservable`s (or one
`SparseObservable` and anything that can be coerced to an observable),
using the same signature as similar methods in `quantum_info`.

The current implementation attempts to be relatively memory efficient,
though there are specialisations that may be implemented if we wanted to
be faster:

- if all the contained terms are Paulis, so each pairwise multiplication
  produces either zero or one alphabet letters, we currently have a
  redundant copy-in and copy-out of the Cartesian-product generator that
  effectively doubles the overhead.  We could check whether each term
  contains only Paulis once, and then avoid that overhead in those
  cases.

- alternatively, the Cartesian-product iterator could be taught to use
  the buffers of the output `SparseObservable` directly as its output
  space, rather than requiring copy-out of its buffers, which would
  remove the overhead from all calls, not just the single-Pauli ones,
  but requires a bit more bookkeeping, since the references would keep
  need to be updated.

- the case of `qargs` being not `None` and `front=True` currently
  involves an extra copy step to simplify the logic.  If this is an
  important case, we could add a right-matmul specialisation of
  `compose_map`.

This commit currently does not contain tests, because we currently don't
have suitable methods to test the validity of the output without
coupling to the particular choice of factorisation of the matrix
multiplication.  We need either a way to convert to a Pauli-only
representation (with the exponential explosion that entails) or to a
matrix; either of these can be uniquely canonicalised.

* Make `lookup::matmul` non-`const`

Before Rust 1.83, `const` functions can't borrow `static`s, even
immutably and without interior mutability.o

There's no need for `matmul` to be `const`; it's always inlin... (continued)

285 of 446 new or added lines in 2 files covered. (63.9%)

7 existing lines in 3 files now uncovered.

75845 of 87068 relevant lines covered (87.11%)

332806.8 hits per line

Relevant lines Covered
87068 RELEVANT LINES 75845 COVERED LINES
332806.8 HITS PER LINE
Source Files on gh-readonly-queue/main/pr-13766-3ae0d14e434113943b7b893b4e69161a5b78c6ef

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13634863236 gh-readonly-queue/main/pr-13766-3ae0d14e434113943b7b893b4e69161a5b78c6ef Add `SparseObservable.compose` (#13766) * Add `SparseObservable.compose` This adds matrix multiplication between `SparseObservable`s (or one `SparseObservable` and anything that can be coerced to an observable), using the same signature as simil... push web-flow github
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