Generating_IonIon_Couplings.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2d4f5058-3514-4d98-b943-0d1fb19ef23e",
   "metadata": {},
   "source": [
    "# Generating Ion-Ion Couplings"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68501139-f62b-4aec-ab6b-28dc9fa372f4",
   "metadata": {},
   "source": [
    "## Code setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "166e0062-1fef-4938-b2c4-9a7739368d5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import sin, cos, exp, sqrt, angle\n",
    "import scipy.integrate as integrate\n",
    "import scipy.linalg as linalg\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d2ae43ac-2190-49da-9bdc-22f4d002ec02",
   "metadata": {},
   "outputs": [],
   "source": [
    "import importlib\n",
    "import sys, os\n",
    "from pathlib import Path\n",
    "sys.path.append('tools/')\n",
    "import IonChainTools as ict\n",
    "import MSFidelityEstimation as msfe\n",
    "importlib.reload(msfe)\n",
    "from MSFidelityEstimation import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35711daa-ae36-49ad-8d36-77b50d430694",
   "metadata": {},
   "source": [
    "## Intro"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51e9dc9c-bfc0-40ce-b335-b9c9cdda5b13",
   "metadata": {},
   "source": [
    "A particular mode $m$ of a string of $N$ ions is described a vector $\\eta^m$ where $\\eta^m_i$ is the participation of ion $i$ in mode $m$.\n",
    "\n",
    "In an MS-type operation, the displacement of a particular motional in phase space generates a state-dependent phase (in the $X$ basis of the qubits). Assuming that the motional mode is returned to its original state at the end of the operation, the unitary acting on the qubits is $U=J_m^2$ where $J=\\sum_i \\eta^m_i X_i$. (Note that more generally we could have some pauli operator that is a superposition of $X_i$ and $Y_i$, but we'll just use $X_i$ for simplicity.)\n",
    "\n",
    "If we excite multiple motional modes and they each generate a phase $\\chi_m$, then the unitary becomes $U = \\sum_m \\chi_m J_m^2$. Importantly, we do *not* have $U=\\sum_m (\\chi_m J_m)^2$. While the vectors $\\eta^m$ fully span the space of real $N$-vectors, the matrices $\\eta^m(\\eta^m)^\\text{T}$ do not span the full space of real $N\\times N$ matrices. This means that even if we could get arbitrary contributions from each motional mode, we could not generate arbitrary couplings between each ion. This is simply a matter of algebra: with $N$ values of $\\chi_m$, we cannot control all $(N^2-N)/2$ couplings between ions.\n",
    "\n",
    "This prohibits doing an arbitrary two-qubit gate with a global drive, but obviosly does not prohibit doing so with individual addressing. If we only address the qubits that we want to operate on, then all couplings that involve other ions are never used."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac75ed74-3d98-4c71-9c5e-43f1b874bb77",
   "metadata": {},
   "source": [
    "## Trying to generate couplings using global drives"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3758e530-f5a8-43ce-818d-1df55c1eead4",
   "metadata": {},
   "source": [
    "We know that we cannot get arbitrary couplings between ions just from a linear combination of the couplings generated by each mode, but we can still try to get some useful couplings."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27a6afda-ced5-4832-a338-f888ce471641",
   "metadata": {},
   "source": [
    "### Nearest-Neighbor $XX$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "637ff056-87e9-4aa3-8037-f4f23cc18aef",
   "metadata": {},
   "source": [
    "We are trying to generate the unitary $U=\\sum_{i}^{N-1} X_i X_{i+1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66417ab3-b803-4e8d-8ccf-38d8b284fb26",
   "metadata": {},
   "source": [
    "The coupling can be visually presented as the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7407a5f8-2ef9-4ad5-9502-17697e65af21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 12\n",
    "A = np.zeros((N,N))\n",
    "for i in range(N-1):\n",
    "    A[i][i+1] = 1\n",
    "    A[i+1][i] = 1\n",
    "sb.heatmap(A, vmin=-1, vmax=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44709623-0beb-43ac-b191-0a167a9814d8",
   "metadata": {},
   "source": [
    "The couplings generated by each motional mode look like the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2903068b-4806-4170-8661-9d8aeebab265",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x2000 with 24 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "modes = ict.calcAxialModes(N)\n",
    "mvecs = [m[1] for m in modes]\n",
    "fig, axs = plt.subplots(int(N/2), 2, figsize=(10,20))\n",
    "axs_flat = [ax for axrow in axs for ax in axrow]\n",
    "for ax, mvec in zip(axs_flat, mvecs):\n",
    "    sb.heatmap(np.outer(mvec, mvec), ax=ax, vmin=-0.5, vmax=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e2f6649-e2d4-4ce6-8501-e1152c725a4b",
   "metadata": {},
   "source": [
    "We can try to combine the above couplings into a uniform nearest neighbor coupling by vectorizing the coupling matrices and projecting the nearest neighbor coupling vector onto the space spanned by the mode-generated coupling vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4c42ef00-bddb-4ec5-9ec0-11f755d845c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalize(vec):\n",
    "    return vec/np.linalg.norm(vec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "11779cf5-8b33-4aac-a7b1-92b5f6256ece",
   "metadata": {},
   "outputs": [],
   "source": [
    "modes = ict.calcAxialModes(N)\n",
    "mvecs = [mode[1] for mode in modes]\n",
    "B = np.stack([normalize(np.outer(mvec,mvec).flatten()) for mvec in mvecs]).T\n",
    "A_vec = A.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "32234560-598d-4acc-9d03-0850dde3467e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_1207308/214715069.py:1: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  mode_contribs, residual, _, _ = np.linalg.lstsq(B, A_vec)\n"
     ]
    }
   ],
   "source": [
    "mode_contribs, residual, _, _ = np.linalg.lstsq(B, A_vec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e8270fc9-3983-4900-a11a-3cb99f9de463",
   "metadata": {},
   "outputs": [],
   "source": [
    "A_vec_regenerated = np.sum([normalize(np.outer(mvec,mvec).flatten())*mode_contrib for mvec,mode_contrib in zip(mvecs, mode_contribs)], axis=0)\n",
    "A_regenerated = np.reshape(A_vec_regenerated, (N,N))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "69cfcff2-894e-40cf-96d7-18b970018c14",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sb.heatmap(A_regenerated, vmin=-1, vmax=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9773f8ea-ed42-4e2e-afcf-41493bcf3cf8",
   "metadata": {},
   "source": [
    "This result is pretty bad. Maybe it's possible to just use the center of the string? I don't know how the Ozeri group got good results in \"PHYSICAL REVIEW A 101, 032330 (2020) Theory of robust multiqubit nonadiabatic gates for trapped ions\". They likewise simply do a least squares method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "99bbc554-36de-420c-abf6-76225e35f937",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}