Fix TypeError in pqk data_map_func with unbound ParameterExpression (Qiskit 2.2.0)

[cgaylord-gwu]

Problem

Running pqk() in qbiocode/embeddings/embed.py raises:

TypeError: Parameter expression with unbound parameters {Symbol { name: "_", ... }} is not numeric.

This fires during quantum circuit construction — specifically in circuit.compose(feature_map, inplace=True),
which triggers PauliFeatureMap's lazy _build(), which in turn calls the user-supplied data_map_func
with symbolic (unbound) ParameterExpression objects rather than concrete numeric values.

Root cause

Qiskit's documented signature for data_map_func is Callable[[Parameter], ParameterExpression]
(see zz_feature_map docs) —
i.e. it's expected to handle symbolic parameters, not only bound numeric data. In current Qiskit
(tested on 2.2.0), this function is invoked during circuit construction, before any real data is bound,
so x contains ParameterExpression objects. The existing float(coeff) call assumes coeff is always
a plain number, which breaks under this calling convention.

Fix

Wrap the numeric cast in a try/except TypeError. When coeff is a concrete number, behavior is unchanged
(float(coeff) succeeds as before). When coeff is a symbolic, unbound ParameterExpression, return it
unevaluated so Qiskit can bind real values later during circuit execution.

To reproduce (pre-fix)

Run the PQK cell in the QSage tutorial notebook (tutorial/QSage/qsage.ipynb) with qiskit==2.2.0 —
fails at circuit.compose(feature_map, inplace=True) inside pqk().

Testing done

Ran the PQK workflow end-to-end post-fix, including live execution against real IBM Quantum hardware
(ibm_fez), with no regressions observed in the numeric-input path.

Found while working through the ISMB 2026 tutorial materials.