Week1_Rydberg/Calculations/task1_calculations.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d2f72f99",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Bloqade\n",
    "using PythonCall\n",
    "using KrylovKit\n",
    "using SparseArrays\n",
    "using Yao, YaoPlots\n",
    "plt = pyimport(\"matplotlib.pyplot\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b31f3783",
   "metadata": {},
   "source": [
    "## Task 1: Adiabatic state preparation with Bloqade\n",
    "\n",
    "First, we prepare the $\\mathbb{Z_2}$ state. When considering open-boundary conditions, only 1D chains with an odd number of atoms can be prepared in the $\\mathbb{Z_2}$ state. We found that all chains will have excitations at the endpoints, which is due to the repulsive nature of the excited states. If the number of atoms in the chain is even, then it is not possible to have excitations at the endpoints and still obtain the $\\mathbb{Z_2}$ state. Thus, we investigate only chains with odd numbers of atoms in this analysis and start with the state preparation of 9 atoms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e9698bee",
   "metadata": {},
   "outputs": [],
   "source": [
    "# specify a 1D chain of 9 atoms with open boundary conditions\n",
    "nsites = 9\n",
    "atoms = generate_sites(ChainLattice(), nsites, scale = 5.72); # atom separation of 5.72 um\n",
    "\n",
    "# specify the adiabatic pulse sequence for Rabi frequency by using the built-in waveform function\n",
    "total_time = 3.0; Ω_max = 2π * 4;\n",
    "# piecewise_linear function creates a linear waveform\n",
    "Ω = piecewise_linear(clocks = [0.0, 0.1, 2.1, 2.2, total_time], values = [0.0, Ω_max, Ω_max, 0, 0]);\n",
    "\n",
    "# specify detuning sequence:\n",
    "U1 = -2π * 10; U2 = 2π * 10;\n",
    "Δ = piecewise_linear(clocks = [0.0, 0.6, 2.1, total_time], values = [U1, U1, U2, U2]);\n",
    "\n",
    "# generate time-dependent Hamiltonian:\n",
    "h = rydberg_h(atoms; Δ, Ω);\n",
    "\n",
    "# specify all atoms to be in the |0> state initially\n",
    "reg = zero_state(nsites);\n",
    "# and set up the emulation problem by choosing an ODE solver:\n",
    "prob = SchrodingerProblem(reg, total_time, h);\n",
    "integrator = init(prob, Vern8());\n",
    "\n",
    "# TimeChoiceIterator is used to measure the Rydberg density on each site at various times:\n",
    "densities = []\n",
    "for _ in TimeChoiceIterator(integrator, 0.0:1e-3:total_time)\n",
    "    push!(densities, rydberg_density(reg))\n",
    "end\n",
    "D = hcat(densities...);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "963eae6a",
   "metadata": {},
   "source": [
    "Next, we are interested in the 9-qubit state as it evolves in time according to the specified Hamiltonian. We plot the average occupation on each site as a function of time (Rydberg density == \\<n\\>)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4747d344",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "\u001b[0m\u001b[1mPython Figure: \u001b[22m<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# plot Rydberg density for each site as a function of time:\n",
    "fig, ax = plt.subplots(figsize = (10, 4))\n",
    "shw = ax.imshow(real(D), interpolation = \"nearest\", aspect = \"auto\", extent = [0, total_time, 0.5, nsites + 0.5])\n",
    "ax.set_xlabel(\"time (μs)\")\n",
    "ax.set_ylabel(\"site\")\n",
    "ax.set_xticks(0:0.2:total_time)\n",
    "ax.set_yticks(1:nsites)\n",
    "bar = fig.colorbar(shw, label=\"Rydberg density\")\n",
    "#fig.savefig(\"state_prep.png\", bb_inches=\"tight\")\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7adc79db",
   "metadata": {},
   "source": [
    "We see that the Rydberg densities converge towards the $\\mathbb{Z_2}$ ordered state. Unfortunately, it appears that the excited states in the middle of the chain are not prepared to the ideal target state. Plotting the bitstring distribution at the final time also shows that state preparations is not ideal:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b69d6dc6",
   "metadata": {},
   "outputs": [
    {
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       "\u001b[0m\u001b[1mPython Figure: \u001b[22m<Figure size 640x480 with 1 Axes>"
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     "execution_count": 4,
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   "source": [
    "bitstring_hist(reg; nlargest = 20)"
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    "It is interesting to calculate the expectation value of $\\langle \\sigma^x_i \\rangle$ for our prepared state. For both the ground and excited states, the expectation value of the Pauli X operator is equal to zero. Thus, we expect that the non-ideal preparation of each site will result in non-zero expectation values. This is confirmed by the following plot:"
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  {
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   "execution_count": 5,
   "id": "92606232",
   "metadata": {
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   "outputs": [
    {
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       "\u001b[0m\u001b[1mPython Figure: \u001b[22m<Figure size 800x400 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate the expectation value of pauli_x matrix, for each of the 9 sites.\n",
    "sigma_x_i = []\n",
    "for i in 1:nsites\n",
    "    append!(sigma_x_i, abs(expect(put(nsites,i=>X), reg)))\n",
    "end\n",
    "\n",
    "# plot the expectation value of pauli_x matrix for each site\n",
    "fig, ax = plt.subplots(figsize = (8, 4))\n",
    "ax.grid()\n",
    "ax.scatter(collect(1:nsites)[1:2:end], sigma_x_i[1:2:end], c=\"b\", label=\"|r>\", zorder=2)\n",
    "ax.scatter(collect(1:nsites)[2:2:end], sigma_x_i[2:2:end], c=\"r\", label=\"|g>\", zorder=2)\n",
    "\n",
    "ax.set_xlabel(\"Site \\$i\\$\")\n",
    "ax.set_ylabel(\"<\\$\\\\sigma_i^x > \\$\")\n",
    "ax.legend(title=\"Target state\", loc = \"upper right\", title_fontsize=15, fontsize=15)\n",
    "#fig.savefig(\"expectation_value.png\")\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0574494e",
   "metadata": {},
   "source": [
    "Just as we saw in the analysis of how the state evolves in time, the above plot shows that state preparation is better at the endpoints and decreases in fidelity as we consider states towards the middle of the chain. We also see that state preparation of the even numbered sites is better as compared to the excited state. This is not surprising since both the initial and target states of the even numbered sites are the ground state.\n",
    "\n",
    "Finally, we wish to determine the viability of the adiabatic protocol for quantum computing based on Rydberg atom arrays. The abiabatic condition states that the system is evolved slow enough such that the atoms stay in the ground state [1]. The lower-bound for the time required to evolve the Rydberg atom system and stay within the adiabatic protocol is given by the inverse square of the energy-splitting between the ground and excited states $\\Delta E\\,$ [1], i.e.,\n",
    "$$ t >> \\frac{1}{(\\Delta E/2\\pi)^2 s} , $$\n",
    "where $t$ is the time evolution of the system. Thus, the smaller the energy splitting, the longer the time required to evolve the system. We can determine the minimum energy splitting as a function of the detuning, for a fixed Rabi frequency:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d54e73a9",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum energy-splitting = 1.6106045555850368/2π MHz\n",
      "Minimum time = 0.38549802170561753\n"
     ]
    },
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       "\u001b[0m\u001b[1mPython Figure: \u001b[22m<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
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   "source": [
    "deltaE = zeros(0) # array will store the energy splitting for values of pulse detuning\n",
    "Ω = 2π * 4\n",
    "Δ_step = 30\n",
    "Δ = LinRange(-2π * 10, 2π * 10, Δ_step);\n",
    "\n",
    "for ii in 1:Δ_step\n",
    "    h_ii = rydberg_h(atoms; Δ = Δ[ii], Ω) # create the Rydberg Hamiltonian\n",
    "    h_m = mat(h_ii) # convert the Hamiltonian into a matrix\n",
    "    vals, vecs, info = KrylovKit.eigsolve(h_m, 2, :SR) # find the ground state eigenvalue and eigenvector\n",
    "    append!(deltaE, vals[2]-vals[1])\n",
    "end\n",
    "\n",
    "min_dE = minimum(deltaE)/(2π)\n",
    "println(\"Minimum energy-splitting = \", min_dE, \"/2π MHz\")\n",
    "println(\"Minimum time = \", 1/(min_dE)^2)\n",
    "\n",
    "# plot deltaE as a function of the pulse detuning\n",
    "fig, ax = plt.subplots(figsize = (10, 4))\n",
    "plt.axhline(y=minimum(deltaE)/(2π), color='r', linestyle=\"dashed\")\n",
    "ax.plot(Δ / 2π, deltaE / 2π)\n",
    "ax.set_xlabel(\"Δ/2π (MHz) \")\n",
    "ax.set_ylabel(\"ΔE/2π (MHz)\")\n",
    "ax.grid()\n",
    "#fig.savefig(\"deltaE_vs_detuning.png\", bb_inches=\"tight\")\n",
    "fig"
   ]
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   "id": "eebcb136",
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   "source": [
    "For the 9 atom 1D chain and a Rabi frequency of $\\Omega = 2\\pi \\times 4$ MHz, the minimum time evolution is\n",
    "$$ t >> \\frac{\\text{MHz}}{(1.61 \\text{ MHz})^2} = 0.39 \\mu s . $$\n",
    "Next, it would be interesting to determine the dependence of the calculation time on the number of atoms. To that end, we calculate the energy splitting and the minimum evolution time for chains with an increasing number of atoms:"
   ]
  },
  {
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   "execution_count": 7,
   "id": "70f607be",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "calc_deltaE calculates the minimum energy splitting between the ground and first-excited state\n",
    "params:\n",
    "    nsites: number of atoms in 1D chain (int)\n",
    "returns:\n",
    "    minimum energy splitting (real)\n",
    "\"\"\"\n",
    "function calc_deltaE(nsites)\n",
    "    atoms = generate_sites(ChainLattice(), nsites, scale = 5.72);\n",
    "    deltaE = zeros(0)\n",
    "    Ω = 2π * 4\n",
    "    Δ_step = 30\n",
    "    Δ = LinRange(-2π * 10, 2π * 10, Δ_step);\n",
    "\n",
    "    for ii in 1:Δ_step\n",
    "        h_ii = rydberg_h(atoms; Δ = Δ[ii], Ω) # create the Rydberg Hamiltonian\n",
    "        h_m = mat(h_ii) # convert the Hamiltonian into a matrix\n",
    "        vals, vecs, info = KrylovKit.eigsolve(h_m, 2, :SR) # find the ground state eigenvalue and eigenvector\n",
    "        append!(deltaE, (vals[2]-vals[1])/(2π))\n",
    "    end\n",
    "    return minimum(deltaE)\n",
    "end\n",
    "\n",
    "# calculate minimum deltaE for 1D chains with 1,3,...,15 atoms\n",
    "deltaE = []\n",
    "for i in collect(1:15)[1:2:end]\n",
    "    append!(deltaE, calc_deltaE(i))\n",
    "end"
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  },
  {
   "cell_type": "markdown",
   "id": "ce070677",
   "metadata": {},
   "source": [
    "Plot both energy splitting and the minimum time evolution associated with 1D chains with 1,3,...,15 atoms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "05c97b04",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "\u001b[0m\u001b[1mPython Figure: \u001b[22m<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
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    }
   ],
   "source": [
    "xs = LinRange(0.1, 15, 100)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(ncols = 2, figsize = (12, 4))\n",
    "ax1.scatter(collect(1:15)[1:2:end], deltaE.^2, zorder=2, label=\"1D Chain\", c=\"black\")\n",
    "ax1.grid()\n",
    "ax1.set_xlabel(\"Number of atoms (n)\")\n",
    "ax1.set_ylabel(\"ΔE/2π (MHz)\")\n",
    "ax1.legend(loc = \"upper right\", fontsize=15)\n",
    "ax1.set_ylim(0,20)\n",
    "\n",
    "ax2.set_yscale(\"log\")\n",
    "ax2.scatter(collect(1:15)[1:2:end], (deltaE.^2).^(-1), zorder=2, label=\"1D Chain\", c=\"black\")\n",
    "ax2.plot(xs, xs.^2, zorder=2, label=\"O(\\$ n^2 \\$)\", c=\"navy\")\n",
    "ax2.plot(xs, 2 .^xs, zorder=2, label=\"O(\\$ 2^n \\$)\", c=\"firebrick\")\n",
    "ax2.grid()\n",
    "ax2.set_xlabel(\"Number of atoms (n)\")\n",
    "ax2.set_ylabel(\"t (us)\")\n",
    "ax2.legend(loc = \"upper left\", fontsize=15)\n",
    "\n",
    "#fig.savefig(\"deltaE_and_time.png\", bb_inches=\"tight\")\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20a89d18",
   "metadata": {},
   "source": [
    "The plot on the left shows that even for a small number of qubits, the adiabatic protocol requires a relatively small energy separation between the ground and excited states. This becomes problematic when considering a larger number of atoms, as it becomes increasingly difficult to drive the system while ensuring that it remains in the ground state as required by the adiabatic protocol.\n",
    "\n",
    "The plot on the right shows how the minimum time required to complete the protocol scales with the number of atoms. An advantage of this protocol is that the runtime is $O(2^n)$, which demonstrates that the quantum computation is indeed an advantage over its classical counterpart. \n",
    "\n",
    "Our analysis indicates that despite a speedup in the runtime, excuting the adiabatic protocol is likely infeasible for a large number of qubits. We have seen that state preparation with high-fidelity is difficult for a large number of qubits, and the ability to adhere to the adiabatic requirements in terms of driving the system without exciting the state becomes increasingly difficult for a large number of atoms."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72103f8e",
   "metadata": {},
   "source": [
    "# References\n",
    "[1] Albash, Tameem, and Daniel A. Lidar. \"Adiabatic quantum computation.\" Reviews of Modern Physics 90.1 (2018): 015002."
   ]
  }
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