Add information about converting to and from non-Mitiq supported circuits

[purva-thakre]

Previously discussed here.

The Frontends section of the documentation only discusses circuits that have mitiq supported converters. Digging through the functions in mitiq/interface, there exists a function to let a user define a converter for an unsupported circuit as long as it follows the format defined in mitiq/typing.

mitiq/mitiq/interface/conversions.py

Lines 37 to 49 in bf82e84

	def register_mitiq_converters(
	package_name: str,
	*,
	convert_to_function: Callable[[cirq.Circuit], Any],
	convert_from_function: Callable[[Any], cirq.Circuit],
	) -> None:
	"""Registers converters for unsupported circuit types.
	Args:
	package_name: A quantum circuit module name that is not currently
	supported by Mitiq. Note: this name should be the same as the
	return from "circuit".__module__.
	See mitiq.SUPPORTED_PROGRAM_TYPES.

We want to describe this process in detail in a subsection of the Frontends portion of the documentation.

[purva-thakre]

Use this issue to also add functions to the API-doc. #2408 (reply in thread)

Not all functions in mitiq/interface/conversions will be used by a Mitiq user. Only add functions that will be required to register an interface not already in Mitiq.

For example, atomic_converter is more useful than accept_qprogram_and_validate

https://mitiq.readthedocs.io/en/stable/guide/zne-4-low-level.html#custom-noise-scaling-methods

[purva-thakre]

I do not think the register_mitiq_converters function is compatible with how we define SUPPORTED_PROGRAM_TYPES currently. So, this issue might also require a refactor of register_mitiq_converters.

The non-mitiq compatible frontend is utilized as a dictionary by register_mitiq_converters.

mitiq/mitiq/interface/conversions.py

Line 24 in 20732a0

FROM_MITIQ_DICT: Dict[str, Callable[[cirq.Circuit], Any]]

mitiq/mitiq/interface/conversions.py

Line 30 in 20732a0

TO_MITIQ_DICT: Dict[str, Callable[[Any], cirq.Circuit]]

SUPPORTED_PROGRAM_TYPES is a class now and the older definition used a dictionary. I think register_mitiq_converters is based off of this previous version of SUPPORTED_PROGRAM_TYPES.

mitiq/mitiq/typing.py

Lines 44 to 45 in 20732a0

	# This is for backwards compatibility with the old representation
	# of SUPPORTED_PROGRAM_TYPES, which was a dictionary