Add explanatory reference to PiecewiseChebychev (#8393)

* Add explanatort reference to ``PiecewiseChebychev``

and update other locations with published version

* fix name

* Fix links

Co-authored-by: Matthew Treinish <mtreinish@kortar.org>

Co-authored-by: Matthew Treinish <mtreinish@kortar.org>
Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>

qiskit/algorithms/linear_solvers/hhl.py

@@ -87,12 +87,12 @@ class HHL(LinearSolver):
     References:
 
         [1]: Harrow, A. W., Hassidim, A., Lloyd, S. (2009).
-        Quantum algorithm for linear systems of equations.
-        `Phys. Rev. Lett. 103, 15 (2009), 1–15. <https://doi.org/10.1103/PhysRevLett.103.150502>`_
+             Quantum algorithm for linear systems of equations.
+             `Phys. Rev. Lett. 103, 15 (2009), 1–15. <https://doi.org/10.1103/PhysRevLett.103.150502>`_
 
-        [2]: Carrera Vazquez, A., Hiptmair, R., & Woerner, S. (2020).
-        Enhancing the Quantum Linear Systems Algorithm using Richardson Extrapolation.
-        `arXiv:2009.04484 <http://arxiv.org/abs/2009.04484>`_
+        [2]: Carrera Vazquez, A., Hiptmair, R., & Woerner, S. (2022).
+             Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation.
+             `ACM Transactions on Quantum Computing 3, 1, Article 2 <https://doi.org/10.1145/3490631>`_
 
     """
 

qiskit/circuit/library/arithmetic/piecewise_chebyshev.py

@@ -29,7 +29,8 @@ class PiecewiseChebyshev(BlueprintCircuit):
     polynomial Chebyshev approximation on :math:`n` qubits to :math:`f(x)` on the given intervals.
     All the polynomials in the approximation are of degree :math:`d`.
 
-    The values of the parameters are calculated according to [1].
+    The values of the parameters are calculated according to [1] and see [2] for a more
+    detailed explanation of the circuit construction and how it acts on the qubits.
 
     Examples:
 
@@ -51,6 +52,9 @@ class PiecewiseChebyshev(BlueprintCircuit):
         [1]: Haener, T., Roetteler, M., & Svore, K. M. (2018).
              Optimizing Quantum Circuits for Arithmetic.
              `arXiv:1805.12445 <http://arxiv.org/abs/1805.12445>`_
+        [2]: Carrera Vazquez, A., Hiptmair, H., & Woerner, S. (2022).
+             Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation.
+             `ACM Transactions on Quantum Computing 3, 1, Article 2 <https://doi.org/10.1145/3490631>`_
     """
 
     def __init__(

qiskit/circuit/library/arithmetic/piecewise_polynomial_pauli_rotations.py

@@ -81,9 +81,9 @@ class PiecewisePolynomialPauliRotations(FunctionalPauliRotations):
              Optimizing Quantum Circuits for Arithmetic.
              `arXiv:1805.12445 <http://arxiv.org/abs/1805.12445>`_
 
-        [2]: Carrera Vazquez, A., Hiptmair, R., & Woerner, S. (2020).
+        [2]: Carrera Vazquez, A., Hiptmair, R., & Woerner, S. (2022).
              Enhancing the Quantum Linear Systems Algorithm using Richardson Extrapolation.
-             `arXiv:2009.04484 <http://arxiv.org/abs/2009.04484>`_
+             `ACM Transactions on Quantum Computing 3, 1, Article 2 <https://doi.org/10.1145/3490631>`_
     """
 
     def __init__(