V0.16.0 bump (#1414)

* changelog new features sections

* version bump, organize changelog

* qchem version

* contributors list

* changelog and remove assign bugs for Unitary HACK

* qchem changelog

* updated contributors; qchem intro PR item

* Update .github/CHANGELOG.md

Co-authored-by: Nathan Killoran <[email protected]>

* depth=1 for ControlledCX

* Update module headers based on Josh's suggestion

* shorten kernels example, indentation care

* qaoa and pauli group headers

* link qaoa cycle

* no mixer

* reorder qmc

* specs rephrase

* reorganize new ops as suggested

* rephrase custom observable support

* move around items as suggested

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* Update code example as suggested

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* separate python and pycon as suggested

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* pycon

* perf improvement comment adjoint

* group Projector improvement with main addition

* groupped decomposition entries

* no CSWAP separately

* further decomposition entries

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* add ongoing deprecations to Breaking changes

* Add QMC transform example

* Update QMC in changelog (#1422)

* Update changelog

* Edit

* Projector example

* add example for diff observable change

* bracket

* wires, num_wires and dev for kernels example

* pauli group typo fix

* add prefix qml.utils when calling sparse_hamiltonian

* custom obs diff example adjust

* update QMC docs to use qml.specs

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* Update .github/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* Update qchem/CHANGELOG.md

Co-authored-by: Josh Izaac <[email protected]>

* shorten def of SpecialObject; add disclaimer

Co-authored-by: Nathan Killoran <[email protected]>
Co-authored-by: Josh Izaac <[email protected]>
Co-authored-by: Tom Bromley <[email protected]>