Updates BaseGaussianState to be feature compatible with BaseFockState

[josh146]

Context: More Fock-basis functionality is available for Gaussian state post-processing thanks to The Walrus. This PR integrates the latest Walrus functionality, elevating the Gaussian state to the same level of functionality as the Fock state.

Description of the Change:

• Removes the gaussianbackend.GaussianState class. It is now sufficient to simply use BaseGaussianState, and import needed functions from The Walrus. As a result, several functions in the gaussianbackend.ops package are no longer being used and can be removed:

  • fock_amplitudes_one_mode

  • fock_prob

  • sm_fidelity

  • xmat

  • omega

• BaseGaussianState now supports ket, dm, and all_fock_probs. As a result, these are now abstract methods in BaseState. The tests have been updated so existing tests for these methods are now run on the Gaussian backend.

• BaseGaussianState now uses The Walrus to implement reduced_dm, fidelity, and fock_prob.

• The states.rst quickstart has been updated with the new functionality.

Benefits: The Gaussian state is now feature complete with the Fock state.

Possible Drawbacks: Some of the new functionality is only available in the latest version of The Walrus 0.13.0-dev. Unfortunately, this version of The Walrus breaks Fock gate compatibility. Therefore, this PR branches off #381, as the corresponding Walrus fix has already been implemented there.

Related GitHub Issues: n/a

[codecov[bot]]

Codecov Report

Merging #407 into update_fock_ops will increase coverage by 0.00%. The diff coverage is 100.00%.

@@               Coverage Diff                @@
##           update_fock_ops     #407   +/-   ##
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  Coverage            97.84%   97.84%           
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  Files                   58       57    -1     
  Lines                 6784     6740   -44     
================================================
- Hits                  6638     6595   -43     
+ Misses                 146      145    -1     

Impacted Files	Coverage Δ
...awberryfields/backends/gaussianbackend/__init__.py	100.00% <ø> (ø)
strawberryfields/backends/gaussianbackend/ops.py	100.00% <ø> (+2.70%)	:arrow_up:
...rawberryfields/backends/gaussianbackend/backend.py	98.56% <100.00%> (-0.11%)	:arrow_down:
...fields/backends/gaussianbackend/gaussiancircuit.py	98.09% <100.00%> (-0.38%)	:arrow_down:
strawberryfields/backends/states.py	97.41% <100.00%> (+0.31%)	:arrow_up:

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