including assets

Bloqade_Python_Tutorial/1_Basics/chap_I_complete.ipynb

@@ -120,15 +120,7 @@
    "id": "d39e739b-aacc-4ae5-b05d-96806eac6262",
    "metadata": {},
    "source": [
-    "* *Exercise*: Let's compare the 5S ground and 70S Rydberg states. For a hydrogenoid atom (atoms with a single valence electron, like Rb), the mean value of the electron's radial coordinate $|\\vec{r}|$ scales as $\\langle|\\vec{r}|\\rangle \\propto n^2 a_0$, with $a_0= 0.5 \\AA$ the Bohr radius. Estimate the ratio $\\langle|\\vec{r}|\\rangle_{70S}/\\langle|\\vec{r}|\\rangle_{5S}$. How many times larger is the Rydberg state atom relative to when it is in its ground state? What is the typical length scale of the excited atom?"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7418541e",
-   "metadata": {},
-   "source": [
-    "*ans: ~200x bigger. $0.1 \\mu m$ scale.*"
+    "* *exercise 1.1*"
    ]
   },
   {
@@ -164,14 +156,6 @@
     "We will save gate-based quantum computing for future lessons and get started with the analog architecture.\n"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "6cf5d20c",
-   "metadata": {},
-   "source": [
-    "* *Exercise*?"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "6f58fc58",
@@ -210,7 +194,7 @@
    "id": "aa25fb0f",
    "metadata": {},
    "source": [
-    "* *Exercise*: provide a geometry of atoms in each state and get reader to tell corresponding bitstring"
+    "* *Exercise 1.2*"
    ]
   },
   {
@@ -437,7 +421,7 @@
    "id": "0804eff9",
    "metadata": {},
    "source": [
-    "* *Exercise*: depending on the orientation, a geometric configuration may satisfy geometric constraints more or less easily, impacting possible register sizes and performance. Given a hexagonal lattice, which orientation should be most performant between \"vertical\" and \"horizontal\"? How many rows of atoms would fit inside the user region in each case? ($a_{minv}=8\\mu m$ 9 rows, $a_{minh}=8/ \\sqrt{3} \\mu m$ 16 rows) [draw figure]"
+    "* *Exercise 1.3a*"
    ]
   },
   {
@@ -511,32 +495,6 @@
     "This interaction imparts a positive energy cost to the Hamiltonian, and thus a repulsive interaction between qubits. Since $V_{ij}$, decays with the distance between the qubits to the 6th power, qubits that are too close can contribute unbearably high-energies to the system if they happen to be both excited at once (i.e. when $\\hat{n}_i \\hat{n}_j = 1 \\times 1 = 1$). This is the source for entanglement in the quantum computing dynamics, and allows for conditional excitations (and thus is somewhat related to controlled logic quantum gates, like $CZ$ gates, in gate-based quantum computing).\n"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "15e8cb2e",
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-   "source": [
-    "> #### Derivation of the atomic Hamiltonian in the presence of a laser [worth doing, but this is not enough]\n",
-    ">\n",
-    "> Consider an atom described by a Hamiltonian with two electronic energy levels $|a \\rangle$ and $|b \\rangle$. There are two terms in the Hamiltonian: \n",
-    ">\n",
-    ">The first is the coupling term from the diapole moment $d$ between states caused by the time-dependent electric field\n",
-    "$E(t) = E_0 cos(\\omega_0 t + \\phi)$ of the laser operating.\n",
-    ">\n",
-    ">\n",
-    ">Here $\\omega_0$ is the angular frequency, and the product of the dipole moment is typically denoted by $-E_0d = \\Omega$, the **Rabi frequency**.\n",
-    ">\n",
-    ">The second is the difference in the energies $\\omega_a$ and $\\omega_b$ of the states, typically measured as the ionization energy of the electron (in eV or MHz).\n",
-    ">\n",
-    ">Through a number of steps of derivation, the Hamiltonian becomes:\n",
-    ">\n",
-    "> $$\n",
-    "> H = \\frac{\\Omega}{2}e^{i\\phi}|a\\rangle\\langle b| +\\frac{\\Omega}{2}e^{i\\phi}|b\\rangle\\langle a| + (\\omega_b - \\omega_a - \\omega_0)|b\\rangle\\langle b|\n",
-    "> $$\n",
-    ">\n",
-    ">The **Rabi frequency $\\Omega$** is the charactistic frequency at which the atom is driven between states $|𝑎\\rangle$ and $|𝑏\\rangle$. Thevalue $\\omega_b − \\omega_a  − \\omega_0  = −\\Delta$, which represents how off-resonant the laser is from the atomic energy transition, is called the detuning $\\Delta$. The value $\\phi$, which is set by the time offset of the laser drive, is called the **phase $\\phi$** and can always be set to zero at the beginning of the quantum evolution by 𝑈(1) symmetry. While this derivation was done in a time-independent setting for only two states of one atom, it naturally extends to more states, atoms, and timedependent parameters $\\Omega$, $\\Delta$, $\\phi$ under reasonable assumptions on the laser modulation bandwidth."
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "81584bea",
@@ -689,7 +647,7 @@
    "id": "b6c40745-55b3-471f-8daa-859d9705be77",
    "metadata": {},
    "source": [
-    "* *Exercise*: Estimate the maximum value one can achieve in $\\Omega$ in the shortest possible ramp allowed by hardware constraints"
+    "* *Exercise 1.3b*"
    ]
   }
  ],