Support for symbolic expressions in FreeParameters

[kshyatt-aws]

Describe the feature you'd like
Currently only numerical values are allowed for FreeParameter. We should replicate the Python SDK support for FreeParameterExpression, allowing gates like Rx( 2 * alpha /3), for example.

Is this feature already present in the Python SDK?
Yes. https://github.com/amazon-braket/amazon-braket-sdk-python/blob/main/src/braket/parametric/free_parameter_expression.py

How would this feature be used? Please describe.
This would allow more complex expressions for parametrized gates.

Describe alternatives you've considered
Currently users have to create new parameters to capture cases like 2 * alpha.

Additional context
An appropriate Julia package should be chosen for the symbolic expressions. SymbolicExpressions.jl is one example.

[Fe-r-oz]

Hi @kshyatt-aws , Sounds Interesting! I would like to work on this issue.

Should I include theFreeParameterExpression details after FreeExpression ?

Braket.jl/src/Braket.jl

Line 129 in 1d05da0

struct FreeParameter

[kshyatt-aws]

Yes, I think that would make sense, because FreeParameterExpression might contain one or multiple FreeParameters (e.g. Rx(alpha + 2*beta)).

[Fe-r-oz]

Hi, @kshyatt-aws,

Please let me know that the output looks something like this:

I have used α + 2θ as FreeParameterExpression

julia> new_circ = circ(theta=2.0, alpha=1.0)
T  : |    0     |   1   |   2   |Result Types|
                                              
q0 : -H----------Ry(2.0)-Ry(2.0)-Probability--
                                 |            
q1 : -Rx(α + 2θ)-----------------Probability--
                                              
T  : |    0     |   1   |   2   |Result Types|

I was spending time with reading the guidelines. Shall I open a PR now?

[kshyatt-aws]

Yes, something like this would be great. You might want to consider using showcompact if the expression is really long/complex.

[Fe-r-oz]

Hi, @kshyatt-aws, Please assign the issue to me after closing it! 😬 All suggestions have been incorporated 🙏🏼 !

[Fe-r-oz]

Hi, Please assign the closed issue. Thanks.

[Fe-r-oz]

The closed by:"hacker name" that appears under closed Bounties is empty because the issue is unassigned. Please fix the issue, @kshyatt-aws, Thanks!

Please see that theclosed_byis not appearing which means that issue is not assigned to me.