Add QuantumProgram to providers crate

[Ian Hincks (ihincks)]

This PR adds the QuantumProgram struct with owns a vector of QuantumFunction.

The QuantumProgram has some well-typedness/type safety requirements. These requirements
ultimately stem from the expense of quantum compute resources: we never want to end
up in a situation where a program fails and quantum resources are effectively wasted
because the program was somehow malformed and a runtime error occurs during the classical
parts of a program. We want every instruction to have a well-defined result type, and the that
the validitiy of and result type of every operation is determined statically from the IR
itself.

To this end, the QuantumProgram enforces several structural invariants intended to prevent malformed programs from reaching execution time. In particular, the IR maintains:

• SSA discipline: every value has a single definition.
• Static type discipline: every instruction has a well-defined result type, and instruction validity can be checked during construction.
• Monomorphism: every instruction instance has a concrete output type.

Notably, some operations permit implicit type promotion (e.g. combining i32 and f64). However, the resulting type is still determined statically and recorded in the IR.

On construction, each function is traversed looking for function call instructions.
All function calls must point at a function that exists at a (strictly) previous
location in the list, and the type signature must be correct. If it is not, then
program construction fails. Functions are already checked for self-consistency during their construction.

As a result of the function call rule, we use the convention that the last function in
a program is its entry point; code after this is by construction dead code.
We also assign DataTree<TensorType> structures to both the input and output of the
entry function. These are zipped against the positional slots of the function's inputs
and ouputs in the DFS order defined by the data tree API. These data trees are for
the convenience of users who want to format the stucture of their data, or assign names
to them.

AI/LLM disclosure

• No part of this submission is LLM generated.
• Some written text was generated by:
• Some submitted code was generated by: claude opus 5

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[Coveralls (coveralls)]

Coverage Report for CI Build 34398812926

Coverage increased (+0.02%) to 88.045%

Details

• Coverage increased (+0.02%) from the base build.
• Patch coverage: 10 uncovered changes across 1 file (303 of 313 lines covered, 96.81%).
• 10 coverage regressions across 2 files.

Uncovered Changes

File	Changed	Covered	%
crates/providers/src/program/quantum_program.rs	293	283	96.59%
Total (2 files)	313	303	96.81%

Coverage Regressions

10 previously-covered lines in 2 files lost coverage.

File	Lines Losing Coverage	Coverage
crates/qasm2/src/lex.rs	8	91.52%
crates/circuit/src/parameter/symbol_expr.rs	2	81.74%

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Coverage Stats

Relevant Lines:	135090
Covered Lines:	118940
Line Coverage:	88.05%
Coverage Strength:	967488.84 hits per line

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💛 - Coveralls

[qiskit-bot]

One or more of the following people are relevant to this code:

• @Qiskit/terra-core