With the release of symengine 0.13.0 we discovered a version dependence
on the payload format used for serializing symengine expressions. This
was worked around in Qiskit#13251 but this is not a sustainable solution and
only works for symengine 0.11.0 and 0.13.0 (there was no 0.12.0). While
there was always the option to use sympy to serialize the underlying
symbolic expression (there is a `use_symengine` flag on `qpy.dumps` you
can set to `False` to do this) the sympy serialzation has several
tradeoffs most importantly is much higher runtime overhead. To solve
the issue moving forward a qiskit native representation of the parameter
expression object is necessary for serialization.

This commit bumps the QPY format version to 13 and adds a new
serialization format for ParameterExpression objects. This new format
is a serialization of the API calls made to ParameterExpression that
resulted in the creation of the underlying object. To facilitate this
the ParameterExpression class is expanded to store an internal "replay"
record of the API calls used to construct the ParameterExpression
object. This internal list is what gets serialized by QPY and then on
deserialization the "replay" is replayed to reconstruct the expression
object. This is a different approach to the previous QPY representations
of the ParameterExpression objects which instead represented the internal
state stored in the ParameterExpression object with the symbolic
expression from symengine (or a sympy copy of the expression). Doing
this directly in Qiskit isn't viable though because symengine's internal
expression tree is not exposed to Python directly. There isn't any
method (private or public) to walk the expression tree to construct
a serialization format based off of it. Converting symengine to a sympy
expression and then using sympy's API to walk the expression tree is a
possibility but that would tie us to sympy which would be problematic
for Qiskit#13267 and Qiskit#13131, have significant runtime overhead, and it would
be just easier to rely on sympy's native serialization tools.

The tradeoff with this approach is that it does increase the memory
overhead of the `ParameterExpression` class because for each element
in the expression we have to store a record of it. Depending on the
depth of the expression tree this also could be a lot larger than
symengine's internal representation as we store the raw api calls made
to create the ParameterExpression but symengine is likely simplifying
it's internal representation as it builds it out. But I personally think
this tradeoff is worthwhile as it ties the serialization format to the
Qiskit objects instead of relying on a 3rd party library. This also
gives us the flexibility of changing the internal symbolic expression
library internally in the future if we decide to stop using symengine
at any point.

Fixes Qiskit#13252

This commit changes how the deserialization works to use a postfix
stack based approach. Operands are push on the stack and then popped off
based on the operation being run. The result of the operation is then
pushed on the stack. This handles nested objects much more cleanly than
the recursion based approach because we just keep pushing on the stack
instead of recursing, making the accounting much simpler. After the
expression payload is finished being processed there will be a single
value on the stack and that is returned as the final expression.

Co-authored-by: Elena Peña Tapia <[email protected]>

This commit fixes a bug with handling the operand order of subtraction,
division, and exponentiation. These operations are not commutative but
the qpy deserialization code was treating them as such. So in cases
where the argument order was reversed qpy was trying to flip the
operands around for code simplicity and this would result in incorrect
behavior. This commit fixes this by adding explicit op codes for the
reversed sub, div, and pow and preserving the operand order correctly
in these cases.