Implementing Exact Tensor Network method for default.tensor

[PietropaoloFrisoni]

Context: Currently, the new default.tensor device can only simulate quantum circuits using the Matrix Product State (MPS) method, based on quimb's CircuitMPS class.

Description of the Change: With this PR, the device also supports the Exact Tensor Network method based on quimb's Circuit class. This completes the implementation of the method keyword argument, which can be set to either mps or tn. For this quarter, this is expected to be the last feature for the default.tensor device (except for refinements, bug fixes, and performance improvements).

Benefits: A new simulation method is implemented for this device, enabling new functionalities for users.

Possible Drawbacks: This PR just implements an additional method, but it does not modify the existing functionalities (except for some minor improvements and clarifications in the documentation).

Related GitHub Issues: None.

Related Shortcut Stories:
[sc-60805]
[sc-64011]
[sc-64284]

[PietropaoloFrisoni]

Thanks @vincentmr, I am in total favor of adding rehearsals for the TN method in another PR. This argument can be passed indeed to the local_expectation function

[PietropaoloFrisoni]

Thank you @Qottmann.

How would you feel about making two separate toggle sections "MPS method" and "TN method"? I think it would make sense to separate the two.

I agree. I tried to separate the two in the Usage details section (for example with subtitles), but actually, Sphyinx is giving me some problems (probably because everything is in an expandable section, but I am not sure).

I am also thinking if some simple pictorial illustrations could significantly ease communicating the difference between the two methods. Not sure this has to be in this PR, a general idea to put out there. I would be happy to help with this.

Good point, I think that would be very helpful, but probably in a separate tutorial or a slightly different context. Here I think we already provided a lot of information compared to the docs of other devices

[vincentmr]

Nice work landing all TN features @PietropaoloFrisoni . I think this is ready to merge. I'm leaving suggestions but nothing blocking on my side.

[PietropaoloFrisoni]

@vincentmr Thanks, excellent suggestions!

[Qottmann]

Looks good to me, great work @PietropaoloFrisoni !

The docs could still be a bit more beginner friendly for a lay person but that should not block this PR 👍