Make GlobalPhase not differentiable

[Tarun-Kumar07]

Context:
When using the following state preparation methods (AmplitudeEmbedding, StatePrep, MottonenStatePreparation) with jit and grad, the error ValueError: need at least one array to stack was encountered.

Description of the Change:
All state preparation strategies used GlobalPhase under the hood, which caused the above error. After this PR, GlobalPhase may not be differentiable anymore, as its grad_method is set to None.

Benefits:

Possible Drawbacks:

Related GitHub Issues:
It fixes #5541

[albi3ro]

Thanks for this @Tarun-Kumar07

For the failures due to errors:

ValueError: Computing the gradient of circuits that return the state with the parameter-shift rule gradient transform is not supported, as it is a hardware-compatible method.

That would be expected, and we should shift the measurement to expectation values.

For the failures due to:

FAILED tests/templates/test_state_preparations/test_mottonen_state_prep.py::test_jacobian_with_and_without_jit_has_same_output_with_high_shots[StatePrep] - AssertionError: assert Array(False, dtype=bool)
 +  where Array(False, dtype=bool) = <function allclose at 0x7fdb77481940>(Array([-0.0003,  0.0153, -0.0153,  0.0003], dtype=float64), Array([ 1.0187, -0.9953, -1.0047,  0.9813], dtype=float64), atol=0.02)

Those are legitimately different results, so we can safely safe we are getting wrong results in that case 😢 I'll investigate.

[dwierichs]

I left a couple of small comments and one major suggestion: Could we set GlobalPhase.grad_method = "F"? This will produce unnecessary shifted tapes for expectation values and probabilities, but it will avoid wrong results when differentiating qml.state with finite_diff and param_shift.

[dwierichs]

Those are legitimately different results, so we can safely safe we are getting wrong results in that case 😢 I'll investigate.

@Tarun-Kumar07 @albi3ro Not sure you got to this yet, but it seems that the decomposition of those state preparation methods handle special parameter values differently than others. This makes the derivative wrong at those special values, because param_shift is handed a tape that does not contain the general decomposition, so it will not shift all operations that need shifting. As JITting does not allow such special cases, we only make this mistake without JITting, hence the difference in the results within those tests.

Basically, the decomposition does something like the following decomposition for RZ:

def compute_decomposition(theta, wires):
    if not qml.math.is_abstract(theta) and qml.math.isclose(theta, 0):
        return []
    return [qml.RZ(theta, wires)]

It's correct but it does not have the correct parameter-shift derivative at 0.

This looks like an independent bug to me, and like one that could be hiding across the codebase for other ops as well, theoretically.

[dwierichs]

@Tarun-Kumar07 Sorry for taking so long with this! We decided to move ahead with this PR as you originally drafted it (with grad_method=None). Before this PR can be merged, the fix in #5774 will need to be merged in, though.
I took the liberty of using a test you wrote here for that PR, your work is much appreciated! 🙏

[Tarun-Kumar07]

Hey @dwierichs , once the PR #5774 is merged I will revert changes to grad_method=None. Thanks for updating :)

[dwierichs]

@Tarun-Kumar07 It is merged :)
I took the liberty to merge the master branch into your branch, updating the tests you wrote (and that made it into #5774) accordingly.

[dwierichs]

Hi @Tarun-Kumar07 ,
Do you know when you might have time to get back to this? :) Or would you prefer us to finalize it?

[Tarun-Kumar07]

Hi @dwierichs,

I am currently tied up until August 17th. After that, I will be able to work on this.
If this is a priority, I suggest assigning someone else to take over in the meantime.

Thank you for understanding.

[dwierichs]

Thanks @Tarun-Kumar07.
That is very understandable of course! I'll try and push your PR through, as it is closed to finish anyways, I think.
Thank you for your contribution, looking forward to the next one 🤩

[dwierichs]

Approving the first part of this PR. I modified it slightly, which will need approval by someone else.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.65%. Comparing base (20eed81) to head (a7d2aeb).
Report is 297 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff            @@
##           master    #5620    +/-   ##
========================================
  Coverage   99.65%   99.65%            
========================================
  Files         430      430            
  Lines       41505    41210   -295     
========================================
- Hits        41362    41069   -293     
+ Misses        143      141     -2     

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[Alex-Preciado]

Thank you so much for this contribution @Tarun-Kumar07!! 🚀