QPY: Correctly load ParameterExpression with empty replay

[gadial]

Summary

Fixes a bug where ParameterExpression did not load correctly when the expression was "empty" (e.g. 0*x).

Fixes #15355

Details and comments

ParameterExpressions are stored using a "replay" which enables to reconstruct them step by step. An expression like 0*x reduces to an empty expression (considered as the value 0) with an empty replay - this crashes when trying to reconstruct the expression with the ParameterExpression::from_qpy method.

To solve this, explicit handling of the empty replay case was added. The subtle point is that the symbol table should be preserved, so the parameter list of the circuit will be as before even if those parameters were not used in practice. This was also simple to implement as the QPY file already has this data.

[qiskit-bot]

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

• @Qiskit/terra-core
• @mtreinish

[jakelishman]

I tried this locally, and while it fixes all the instances listed in the test, I'm not convinced it's solving the true underlying issue, because you can have an expression with cancelled-out parameters that isn't 0 too:

import io
from qiskit import qpy, QuantumCircuit
from qiskit.circuit import Parameter

x = Parameter("x")
# Using either of these triggers the same bug.
bad = [0 * x + 2]

qc = QuantumCircuit(1)
qc.rz(bad[0], 0)

with io.BytesIO() as fptr:
    qpy.dump(qc, fptr)
    fptr.seek(0)
    x = qpy.load(fptr)[0]

This should satisfy x[0].params[0] == 2, but it's still coming out as 0 after this PR. Without this PR it fails with the same "empty replay" bug.

This feels like it might be a problem with the dump rather than the load?

Also: I'm getting a panic in qiskit_circuit::parameter::parameter_expression::ParameterExpression::from_qpy with these (without this PR) which we could do with turning into a safer exception too (but can be a follow-up).

[gadial]

This should satisfy x[0].params[0] == 2, but it's still coming out as 0 after this PR. Without this PR it fails with the same "empty replay" bug.

This feels like it might be a problem with the dump rather than the load?

Also: I'm getting a panic in qiskit_circuit::parameter::parameter_expression::ParameterExpression::from_qpy with these (without this PR) which we could do with turning into a safer exception too (but can be a follow-up).

This actually makes a lot of sense. The replay doesn't have x while the instruction still lists it as a parameter. So even in the case where we use the replay, we need to verify the symbol table is correct - I'll fix this.

EDIT: after playing with this a little, the problem is more serious than I thought, and it's present even in the Python implementation. 0*x+2 reduces to the value 2, which in our current rust implementation for parameter expressions has an empty replay. Obviously, loading as the value 0 is incorrect here, so we need a better mechanism altogether to store a parameter expression with an empty replay. We can't simply store it as value since we need to store the symbol table as well, to account for the unused parameters. And in QPY17, we don't have an op for constants.

The workaround I suggest is saving the constant value a as the parameter expression a+0, i.e. use an ADD operand. This will simplify out when reconstructing the expression, and will enable us to store parameter information. This should be added to the QPY18 TODO pile, since this is obviously not a perfect solution.

[gadial]

Done in #15900