change name PEA -> QPE, IPEA -> IQPE

Author: DavitKhach

README.md

@@ -9,12 +9,13 @@
 This is a collection of tutorials for quantum algorithms. 
 Here is the list of the tutorials (existing and planned).
 
-* [Iterative phase estimation algorithm (IPEA)](https://github.com/DavitKhach/quantum-algorithms-tutorials/blob/master/iterative_phase_estimation.ipynb)
+* [Iterative quantum phase estimation algorithm (IQPE or IPEA)](https://github.com/DavitKhach/quantum-algorithms-tutorials/blob/master/iterative_quantum_phase_estimation.ipynb)
+
+* [Quantum phase estimation algorithm (QPE or PEA)](https://github.com/DavitKhach/quantum-algorithms-tutorials/blob/master/quantum_phase_estimation.ipynb)
 
 * [Variational quantum eigensolver (VQE)](https://github.com/DavitKhach/quantum-algorithms-tutorials/blob/master/variational_quantum_eigensolver.ipynb)
 
-* *Phase estimation algorithm (PEA)* (next)
-* *HHL algorithm* (planed)
+* *HHL algorithm* (next)
 * *Simon's algorithm* (planed)
 * *Shor's quantum factoring algorithm* (planed)
 * ...

iterative_phase_estimation.ipynb renamed to iterative_quantum_phase_estimation.ipynb

@@ -7,10 +7,10 @@
     "<img src=\"images/quantum_algorithms_tutorials.png\" alt=\"drawing\" width=\"100\" align=\"left\"/>\n",
     "\n",
     "<h1 align=\"center\">\n",
-    "\tIterative phase estimation algorithm\n",
+    "Iterative quantum phase estimation\n",
     "</h1>\n",
     "\n",
-    "The iterative phase estimation algorithm is a quantum algorithm for estimating the phase (or eigenvalue) of an eigenvector of a unitary operator [[1](https://en.wikipedia.org/wiki/Quantum_phase_estimation_algorithm), [2](https://www.tandfonline.com/doi/abs/10.1080/00268976.2011.552441)]. One of the main applications of the algorithm is to estimate eigenvalues (energies) of some molecule's $H$ Hamiltonian. Because $H$ is a Hermitian operator, not unitary, (the algorithm works only with unitary operators) we can't estimate directly its eigenvalues. Instead, we create some unitary operator from $H$ and estimate not the eigenvalues of $H$, but something different (the phase). From the estimated phase one can obtain the corresponding eigenvalue of $H$. So, in the end, we are not only estimating the phase but, what is more important, the desired eigenvalue. Here are the main steps of the algorithm:\n",
+    "The iterative quantum phase estimation (IQPE, also known as IPEA) algorithm is a quantum algorithm for estimating the phase (or eigenvalue) of an eigenvector of a unitary operator [[1](https://en.wikipedia.org/wiki/Quantum_phase_estimation_algorithm), [2](https://www.tandfonline.com/doi/abs/10.1080/00268976.2011.552441)]. One of the main applications of the algorithm is to estimate eigenvalues (energies) of some molecule's $H$ Hamiltonian. Because $H$ is a Hermitian operator, not unitary, (the algorithm works only with unitary operators) we can't estimate directly its eigenvalues. Instead, we create some unitary operator from $H$ and estimate not the eigenvalues of $H$, but something different (the phase). From the estimated phase one can obtain the corresponding eigenvalue of $H$. So, in the end, we are not only estimating the phase but, what is more important, the desired eigenvalue. Here are the main steps of the algorithm:\n",
     "\n",
     "1) Create unitary operator $U$ from given $H$: \n",
     "$$U = e^{iHt}.$$ \n",

quantum_phase_estimation.ipynb

@@ -27,7 +27,7 @@
     "\n",
     "where $E_1$ and $E_2$ are the eigenvalues of the $\\hat{H}$, $\\varphi_2 = \\frac{E_2 t}{2 \\pi}$ is the phase that the algorithm is capable to estimate. Note that $U = e^{i H t}$ is a unitary operator and in the code, we will name it as ```unitary```.\n",
     "\n",
-    "The code and the algorithm is similar to the [IPEA](https://github.com/DavitKhach/quantum-algorithms-tutorials/blob/master/iterative_phase_estimation.ipynb) algorithm, which tutorial we also have covered. IPEA actually is a modification of QPE algorithm. So, that's why some parts/explanations are omitted here and more details are provided about the parts of QPE that are different from IPEA.\n",
+    "The code and the algorithm is similar to the [IQPE](https://github.com/DavitKhach/quantum-algorithms-tutorials/blob/master/iterative_quantum_phase_estimation.ipynb) algorithm, which tutorial we also have covered. IPEA actually is a modification of QPE algorithm. So, that's why some parts/explanations are omitted here and more details are provided about the parts of QPE that are different from IQPE.\n",
     "\n",
     "In the first code, all necessary packages are imported and the diagonal matrix is created:"
    ]
@@ -371,7 +371,7 @@
     "\n",
     "How you have seen we did the job of the algorithm without SWAP gates and obtained the result. The SWAP gates don't add anything to this algorithm and we can omit them. Not only they increase the gate number of the circuit, but also they add errors. So, that is why we are avoiding SWAP gates.\n",
     "\n",
-    "They are some details about Trotterization, the $t$ parameter in the $U = e^{iHt}$, what should we do when the eigenvalue is negative that we don't cover here. If you interested in these topics you can check our [IPEA](https://github.com/DavitKhach/quantum-algorithms-tutorials/blob/master/iterative_phase_estimation.ipynb) tutorial, that is a modification of QPE algorithm. There are two main differences between QPE and IPEA algorithms. QPE demands $n$ ancillary qubits for $n$ bit phase estimation, IPEA demands only one ancillary qubit for any $n$ bit phase estimation. The second difference is that QPE applies inverse QFT, and IPEA applies inverse QFT iteratively ($R_z$ rotations are applied iteratively)."
+    "They are some details about Trotterization, the $t$ parameter in the $U = e^{iHt}$, what should we do when the eigenvalue is negative that we don't cover here. If you interested in these topics you can check our [IQPE](https://github.com/DavitKhach/quantum-algorithms-tutorials/blob/master/iterative_quantum_phase_estimation.ipynb) tutorial, that is a modification of QPE algorithm. There are two main differences between QPE and IQPE algorithms. QPE demands $n$ ancillary qubits for $n$ bit phase estimation, IQPE demands only one ancillary qubit for any $n$ bit phase estimation. The second difference is that QPE applies inverse QFT, and IQPE applies inverse QFT iteratively ($R_z$ rotations are applied iteratively)."
    ]
   },
   {