Fix reference formatting in KAK demo (#1395)

I used nested formatting in reference links in #1372.
ReST does not support this.
Here we remove the nested formatting (and adjust two small wordings that
struck me as suboptimal upon re-reading)

---------

Co-authored-by: Korbinian Kottmann <43949391+Qottmann@users.noreply.github.com>

Author: dwierichs

demonstrations/tutorial_unitary_synthesis_kak.metadata.json

@@ -6,7 +6,7 @@
         }
     ],
     "dateOfPublication": "2025-05-30T09:00:00+00:00",
-    "dateOfLastModification": "2025-05-30T09:00:00+00:00",
+    "dateOfLastModification": "2025-06-03T09:00:00+00:00",
     "categories": [
         "Quantum Computing"
     ],

demonstrations/tutorial_unitary_synthesis_kak.py

@@ -21,7 +21,7 @@
 Crucially, we will not just go through these three techniques separately, but we will explain
 how they are variants of the same underlying mathematical factorization, which is called
 a recursive KAK, or Cartan, decomposition [#Wierichs_CartanSynthesis]_.
-One of the recursion steps will be implemented by a Cosine-Sine Decomposition (CSD), maybe the
+One of the recursion steps will be implemented by a Cosine-Sine Decomposition (CSD), which may be the
 most well-known KAK decomposition.
 
 In the appendix, we will derive the CNOT and rotation gate counts for all three decompositions,
@@ -31,7 +31,7 @@
 for example using :doc:`our introductory demo </demos/tutorial_kak_decomposition>` or our
 :doc:`demo on compiling Hamiltonian simulation variationally
 </demos/tutorial_fixed_depth_hamiltonian_simulation_via_cartan_decomposition>`,
-which follows [#Kökcü_FDHS]_.
+which follows reference [#Kökcü_FDHS]_.
 
 
 KAK decompositions
@@ -649,58 +649,61 @@ def demultiplex(U, V):
 # .. [#Khaneja_Glaser]
 #
 #     Navin Khaneja, Steffen Glaser (2000) *Cartan Decomposition of SU(2^n), Constructive
-#     Controllability of Spin systems and Universal Quantum Computing.* arXiv preprint
-#     `quant-ph/0010100 <https://doi.org/10.48550/arXiv.quant-ph/0010100>`__.
+#     Controllability of Spin systems and Universal Quantum Computing.*
+#     `arXiv:quant-ph/0010100 <https://doi.org/10.48550/arXiv.quant-ph/0010100>`__.
 #
 # .. [#Shende_QSD]
 #
 #     Vivek V Shende, Stephen S Bullock, Igor L Markov (2006)
-#     *Synthesis of Quantum Logic Circuits.* IEEE Trans. on Computer-Aided Design,
-#     `Vol. 25, No. 6 <https://doi.org/10.1109/TCAD.2005.855930>`__.
+#     *Synthesis of Quantum Logic Circuits.*
+#     `arXiv:quant-ph/0406176 <https://doi.org/10.48550/arXiv.quant-ph/0406176>`__,
+#     `IEEE Trans. on Computer-Aided Design, Vol. 25, No. 6 <https://doi.org/10.1109/TCAD.2005.855930>`__.
 #
 # .. [#Krol_BlockZXZ]
 #
 #     Anna M Krol, Zaid Al-Ars (2024) *Beyond Quantum Shannon: Circuit Construction for General
-#     n-Qubit Gates Based on Block ZXZ-Decomposition.* arXiv preprint
-#     `2403.13692 <https://doi.org/10.48550/arXiv.2403.13692>`__.
+#     n-Qubit Gates Based on Block ZXZ-Decomposition.*
+#     `arXiv:2403.13692 <https://doi.org/10.48550/arXiv.2403.13692>`__.
 #
 # .. [#Mansky_Linnhoff-Popien]
 #
 #     Maximilian Balthasar Mansky, Santiago Londoño Castillo, Victor Ramos Puigvert, Claudia Linnhoff-Popien (2023).
 #     *Near-optimal quantum circuit construction via Cartan decomposition.*
-#     arXiv preprint `2212.12934 <https://arxiv.org/abs/2212.12934>`__.
-#     `Phys. Rev. A **108**, 052607 <https://doi.org/10.1103/PhysRevA.108.052607>`__.
+#     `arXiv:2212.12934 <https://arxiv.org/abs/2212.12934>`__,
+#     `Phys. Rev. A 108, 052607 <https://doi.org/10.1103/PhysRevA.108.052607>`__.
 #
 # .. [#Wierichs_CartanSynthesis]
 #
 #     David Wierichs, Maxwell West, Roy T. Forestano, M. Cerezo, Nathan Killoran (2025)
-#     *Recursive Cartan decompositions for unitary synthesis.* arXiv preprint
-#     `2503.19014 <https://doi.org/10.48550/arXiv.2503.19014>`__.
+#     *Recursive Cartan decompositions for unitary synthesis.*
+#     `arXiv:2503.19014 <https://doi.org/10.48550/arXiv.2503.19014>`__.
 #
 # .. [#Kökcü_FDHS]
 #
 #     Efekan Kökcü, Thomas Steckmann, Yan Wang, J K Freericks, Eugene F Dumitrescu,
 #     Alexander F. Kemper (2021) *Fixed Depth Hamiltonian Simulation via Cartan Decomposition.*
-#     arXiv preprint `2104.00728 <https://doi.org/10.48550/arXiv.2104.00728>`__. Phys. Rev. Lett. **129**, 070501
+#     `arXiv:2104.00728 <https://doi.org/10.48550/arXiv.2104.00728>`__,
+#     `Phys. Rev. Lett. 129, 070501 <https://doi.org/10.1103/PhysRevLett.129.070501>`__
 #
 # .. [#Bullock_Note]
 #
 #     Stephen S Bullock (2004) *Note on the Khaneja Glaser Decomposition.*
-#     arXiv preprint `quant-ph/0403141 <https://doi.org/10.48550/arXiv.quant-ph/0403141>`__.
+#     `arXiv:quant-ph/0403141 <https://doi.org/10.48550/arXiv.quant-ph/0403141>`__,
+#     `Quantum Inf. Comput., Vol. 4, No. 5, 396-400 <https://doi.org/10.26421/QIC4.5-5>`__.
 #
 # .. [#Dagli_Framework]
 #
 #     Mehmet Dagli, Domenico D'Alessandro, Jonathan D H Smith (2007) *A General Framework
 #     for Recursive Decompositions of Unitary Quantum Evolutions.*
-#     arXiv preprint `quant-ph/0701193 <https://doi.org/10.48550/arXiv.quant-ph/0701193>`__.
-#     `J. Phys. A: Math. Theor. **41** 155302 <https://iopscience.iop.org/article/10.1088/1751-8113/41/15/155302>`__.
+#     `arXiv:quant-ph/0701193 <https://doi.org/10.48550/arXiv.quant-ph/0701193>`__,
+#     `J. Phys. A: Math. Theor. 41 155302 <https://iopscience.iop.org/article/10.1088/1751-8113/41/15/155302>`__.
 #
 # .. [#Shende_Minimal]
 #
 #     Vivek V Shende, Igor L Markov, Stephen S Bullock (2003) *Minimal Universal Two-qubit
 #     Quantum Circuits.*
-#     arXiv preprint `quant-ph/0308033 <https://doi.org/10.48550/arXiv.quant-ph/0308033>`__.
-#     Phys. Rev. A **69**, 062321.
+#     `arXiv:quant-ph/0308033 <https://doi.org/10.48550/arXiv.quant-ph/0308033>`__,
+#     `Phys. Rev. A 69, 062321 <https://doi.org/10.1103/PhysRevA.69.062321>`__.
 #
 # Appendix: Gate counts
 # ---------------------