Function recognize_variational_pattern 

pub fn recognize_variational_pattern(
    expr: &Expression,
) -> Option<VariationalPattern>

Try to recognize a single-gate variational-circuit pattern.

Structurally recognizes exp(-i θ G / 2) (via is_rotation_gate) where G is a single-qubit Pauli generator:

• if θ contains an is_qaoa_parameter-recognized beta* factor and G is the X generator, this is a VariationalPattern::QaoaMixer;
• if θ contains an is_qaoa_parameter-recognized gamma* factor and G is the Z generator, this is a VariationalPattern::QaoaCost;
• otherwise it is a generic VariationalPattern::SingleRotation around the recognized axis.

Returns None when expr is not a structurally recognizable single-axis rotation. This function never produces VariationalPattern::EntanglingLayer/VariationalPattern::VqeAnsatz; see the enum-level doc comment on VariationalPattern for why those require multi-gate context that this function does not have.