docs/tutorials/04_collective_spin_hardware.ipynb

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    "# Collective Spin Hardware"
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    "## Experimental system\n",
    "\n",
    "In this tutorial, we show how the spin circuit setting, introduced in the [second tutorial](./02_spin_circuits.ipynb), can describe a realistic cold atomic experimental setup based on spins as a backend in Qiskit-cold-atom. We call this setting the \"collective spin hardware\"."
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    "Collective spins can be experimentally realized by trapping a cloud of bosonic atoms with two internal states (denoted $\\uparrow$ and $\\downarrow$) i.e. effective spin-$\\frac{1}{2}$-systems in a Bose-Einstein-Condensate (BEC) [1]. Due to their bosonic indistinguishability, the state of $N$ such spin-$\\frac{1}{2}$ particles can be described as the state of one long angular momentum (or \"spin\") of length $L=\\frac{N}{2}$ [1]. This so-called \"collective spin\" has $2L+1$ internal states which are the eigenstates of the projection onto the quantization axis $L_z$. \n",
    "\n",
    "\n",
    "Multiple collective spins can be realized by having atoms trapped in multiple lattice sites or optical tweezers, where the atoms in each tweezer form a BEC. If all atoms are spin-$\\uparrow$, their collective spin will be at its maximal value $L_z = \\frac{N}{2}$, whereas if all atoms are spin-$\\downarrow$, their collective spin will be at is minimal value $L_z = -\\frac{N}{2}$. The value of $L_z$ thus corresponds to the value of half the number of atoms in the $\\uparrow$-state minus half the number of atoms in the $\\downarrow$-state: $L_z = \\frac{N_\\uparrow - N_\\downarrow}{2}$. \n",
    "This is shown schematically in the figure below where each dot corresponds to an atom whose internal state is indicated by the color.\n",
    "\n",
    "<img src=\"aux_files/collective_spin_array.png\" width=\"800\">"
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    "The arrows below the tweezers indicate the \"orientation\" of the spin which can take one of the $N+1$ discrete values indicated by the dashed lines. \n",
    "\n",
    "By tuning the number of atoms loaded into each tweezer in the state preparation step, the length of the collective spin $L$ can be controlled. "
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    "## Circuit description\n",
    "\n",
    "Each collective spin will be assigned one wire in the circuit. \n",
    "\n",
    "### Initialization\n",
    "Instead of labeling the individual states from $ \\left| -\\frac{N}{2} \\right>$ to $\\left| \\frac{N}{2} \\right>$, we label them from $\\left| 0 \\right>$ to $\\left| N+1 \\right>$ which is closer to the language used in quantum information. \n",
    "\n",
    "Similar to qubits, the state of the individual collective spins is initialized in $\\left| 0 \\right>$, that is all individual atoms are aligned in the $\\uparrow$-direction. \n",
    "\n",
    "The [ColdAtomProvider](./05_cold_atom_provider.ipynb) includes the backend to simulate the collective spins hardware:"
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    "from qiskit_cold_atom.providers import ColdAtomProvider\n",
    "\n",
    "provider = ColdAtomProvider()\n",
    "backend = provider.get_backend(\"collective_spin_simulator\")"
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    "### Readout\n",
    "\n",
    "Upon readout, each wire is projected onto the eigenstates of $L_z$. Experimentally, this is accomplished by counting the number of atoms found in each of the two spin states $N_\\uparrow$ and $N_\\downarrow$.  "
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    "### Gates and dynamics\n",
    "\n",
    "As laid out in the introductory notebook, within Qiskit-cold-atom, the unitary gates available in the hardware are described by their generating Hamiltonian.\n",
    "\n",
    "#### Single-spin gates\n",
    "The physical dynamics of the individual collective spins in this hardware are described by a so-called _one-axis-twisting_ Hamiltonian [2]:\n",
    "\n",
    "$$ H_{\\text{OAT}}(\\chi, \\Delta, \\omega) = \\sum_{i=1}^3 \\chi_i L_{z, i}^2 + \\Delta_i L_{z, i} + \\Omega_i L_{x, i}$$"
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    "Here, $i$ indexes the tweezer mode. \n",
    "\n",
    "- The first term parameterized by the couplings $\\chi$ stems from the interactions of the particles which can be switched on and off.\n",
    "- The second term generates rotations of the long spin around the $z$-axis which can be controlled by a magnetic field through the parameter $\\Delta$.\n",
    "- The third term arises from a Rabi coupling $\\Omega$ of the two internal spin states of the atoms, generating a rotation around the x-axis of the collective spin.\n",
    "\n",
    "Having individual control over the parameters $\\chi, \\Delta, \\Omega$ allows to generate all single-spin unitaries [1]. \n",
    "We can thus use this Hamiltonian to define a set of unitary quantum gates on a single wire. By choosing specific values $\\{\\chi_i, \\Delta_i, \\Omega_i\\}$, the unitary of the gate is defined as $U_{\\text{OAT}} = e^{-i H_{\\text{OAT}}(\\chi_i, \\Delta_i, \\Omega_i)}$.\n",
    "\n",
    "Let's look at a first example circuit where a one-axis-twisting gate is applied to a single collective spin:"
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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "from qiskit_cold_atom.spins.spins_gate_library import OATGate\n",
    "from qiskit.visualization import plot_histogram\n",
    "\n",
    "qc = QuantumCircuit(1)\n",
    "\n",
    "qc.append(OATGate(chi=0.4, delta=-1., omega=2.), qargs=[0])\n",
    "\n",
    "# alternatively append the OAT gate directly:\n",
    "# qc.oat(chi=0.4, delta=-1., omega=2., wire=0)\n",
    "\n",
    "qc.measure_all()\n",
    "\n",
    "# simulate the circuit with a spin length L=5\n",
    "counts = backend.run(qc, spin=5).result().get_counts()\n",
    "# convert counts to integers for better formatting\n",
    "plot_histogram({int(k):v for k,v in counts.items()})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bff0cae2-8c6d-4eee-bbe1-22614e6e3cdb",
   "metadata": {},
   "source": [
    "This gate creates a complicated superposition of the individual levels of the collective spin.\n",
    "\n",
    "Similar to the [fermionic gateset](./03_fermionic_tweezer_hardware.ipynb) built up from Fermi-Hubbard interactions, we can separate the different terms in the one-axis-twisting Hamiltonian to define gates with a more refined behaviour:\n",
    "\n",
    "- An `RLXGate` with unitary $U_{\\text{LX}}(\\Omega) = U_{\\text{OAT}}(\\chi=0, \\Delta=0, \\Omega)$ describing rotations around the collective spin's x-axis\n",
    "- A `RLZGate` with unitary $U_{\\text{LZ}}(\\Delta) = U_{\\text{OAT}}(\\chi=0, \\Delta, \\Omega=0)$ describing rotations around the collective spin's z-axis\n",
    "- A `RLZ2Gate` with unitary $U_{\\text{LZ2}}(\\chi) = U_{\\text{OAT}}(\\chi, \\Delta=0, \\Omega=0)$ describing a non-linear \"spin-squeezing\" dynamic"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99f0ee8d-3734-44dc-adb0-9b22963e0c5f",
   "metadata": {},
   "source": [
    "These gates are available as `SpinGates` from the `spin_gate_library`. As detailed in the introduction notebook, these gates have their generating Hamiltonians defined as a `SpinOp`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b9d4f41c-0299-4646-90ae-c2e4d388227d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LX generator: \n",
      " Spin Operator\n",
      "spin=1/2, number spins=1, number terms=1\n",
      "  0.5 * ( X_0 )\n",
      "LZ generator: \n",
      " Spin Operator\n",
      "spin=1/2, number spins=1, number terms=1\n",
      "  1.0 * ( Z_0 )\n",
      "LZ2 generator: \n",
      " Spin Operator\n",
      "spin=1/2, number spins=1, number terms=1\n",
      "  1.5 * ( Z_0^2 )\n"
     ]
    }
   ],
   "source": [
    "from qiskit_cold_atom.spins.spins_gate_library import RLXGate, RLZGate, RLZ2Gate\n",
    "print(\"LX generator: \\n\", RLXGate(0.5).generator)\n",
    "print(\"LZ generator: \\n\", RLZGate(1.).generator)\n",
    "print(\"LZ2 generator: \\n\", RLZ2Gate(1.5).generator)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6dd826b1-3735-4397-864d-b9f337d56c84",
   "metadata": {},
   "source": [
    "#### Rabi oscillations:\n",
    "\n",
    "The `LXGate` is sufficient to generate Rabi-oscillations of individual collective spins. For Rabi oscilattions, we create a list of circuits with increasing angles $\\Omega$ in the LX-gate used above. These can be sent to the backend in a single job:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d7bbb041-e811-4b27-8b18-f63e89fe20ff",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qiskit.circuit import Parameter\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# lenght of spin for the simulation\n",
    "spin = 20\n",
    "\n",
    "# sample at 50 angles between 0 and 4*pi\n",
    "vals = 50\n",
    "angles = np.linspace(0, 4*np.pi, vals)\n",
    "\n",
    "omega = Parameter(\"omega\")\n",
    "# create list of circuits\n",
    "circuit = QuantumCircuit(1, 1)\n",
    "circuit.rlx(omega, 0)\n",
    "circuit.measure(0, 0)\n",
    "\n",
    "rabi_list = [circuit.assign_parameters([angle]) for angle in angles]\n",
    "\n",
    "job_rabi = backend.run(rabi_list, shots = 10, spin = spin, seed=5462)\n",
    "result_rabi = job_rabi.result()\n",
    "\n",
    "outcomes = np.array([np.array(result_rabi.get_memory(i), dtype=float) for i in range(vals)])\n",
    "plt.errorbar(angles, np.mean(outcomes, axis=1), yerr=np.std(outcomes, axis=1), fmt='o', color=\"#4589ff\")\n",
    "plt.title(f\"Rabi oscillations for a single collective spin of length L = {spin}\")\n",
    "plt.ylabel(\"measurement outcome\")\n",
    "plt.xlabel(\"angle of x-rotation\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbfc8567-202e-4100-8fab-40378294ac1c",
   "metadata": {},
   "source": [
    "The `LXGate` takes the collective spin from its initial position at $\\left| 0 \\right>$ all the way to its maximum value $\\left| 2L \\right>$ and back. In between, the errorbars on the measurement outcomes are larger indicating a larger spread in the measurement distributions. As we saw in the introduction to spin circuits tutorial, this is due to the binomial distribution of measurement outcomes generated by a single rotation. \n",
    "\n",
    "This spread can be decreased by a phenomenom called [spin squeezing](https://en.wikipedia.org/wiki/Spin_squeezing), which can be engineered with the `LZ2Gate2`. In a spin-squeezed state, the variance in one spin projection is reduced at the cost of increasing the spread in another spin direction. This can be useful for quantum metrology applications [3]. \n",
    "\n",
    "#### Spin squeezing\n",
    "\n",
    "To observe spin squeezing, we implement the following sequence: \n",
    "- The state is rotated onto the y-axis by the LX gate. \n",
    "- This state is spin-squeezed by applying LZ2.\n",
    "- To \"see\" the squeezing in the computational ($L_z$) basis we rotate the squeezed state along the y-axis which is done by a z- and x-rotation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "24a3043a-0a49-4174-920e-d1877106fb11",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 519.897x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# circuit with spin squeezing\n",
    "squeez_circ = QuantumCircuit(1, 1)\n",
    "squeez_circ.rlx(-np.pi/2, 0)\n",
    "squeez_circ.rlz2(0.3, 0)\n",
    "squeez_circ.rlz(-np.pi/2, 0)\n",
    "squeez_circ.rlx(-0.15, 0)\n",
    "squeez_circ.measure(0, 0)\n",
    "\n",
    "job_squeez = backend.run(squeez_circ, shots = 1000, spin=20, seed=14)\n",
    "\n",
    "squeez_circ.draw(output='mpl', style=\"clifford\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c02f4e8b-e7ee-4909-90b1-35dd16bdb98c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for comparison: circuit with a single rotation\n",
    "circ_x = QuantumCircuit(1, 1)\n",
    "circ_x.rlx(np.pi/2, 0)\n",
    "circ_x.measure_all()\n",
    "\n",
    "job_x = backend.run(circ_x, shots = 1000, spin=20, seed=14)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(2, figsize=(10,8))\n",
    "fig.tight_layout(pad=5.0)\n",
    "ax1.set_title(\"spin squeezing circuit\")\n",
    "ax2.set_title(\"single rotation circuit\")\n",
    "\n",
    "plot_histogram(job_squeez.result().get_counts(), ax=ax1, color=\"#9f1853\") #, number_to_keep=10)\n",
    "plot_histogram(job_x.result().get_counts(), ax=ax2) #, number_to_keep=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "811ff2c8-8747-4347-87be-410d075d73a7",
   "metadata": {},
   "source": [
    "The spin squeezing generated by the $LZ2$-gate is a vital tool in this architecture to amplify the amplitude of a target state, such as \"20\" in the above example. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e23a95a-9447-492f-93ab-417d0f17d68e",
   "metadata": {},
   "source": [
    "#### Multiple-spin gates\n",
    "\n",
    "Interactions between the collective spins in the individual tweezers can be mediated through collisions with a second species of atoms present in an overlapping trap [1]. In the setting we employ here, this results in an interaction which implements the spin-analogue of a ZZ-rotation with a generating Hamiltonian\n",
    "\n",
    "$$ H_{int}(\\gamma) = \\gamma L_{z, i} L_{z, j} $$\n",
    "\n",
    "where $i$ and $j$ are the indices of the coupled tweezers. This can be used to create entanglement between two collective spins:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c41a2e9f-23e2-48b0-b13a-789a3887bd29",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit_cold_atom.spins.spins_gate_library import RLZLZGate\n",
    "\n",
    "qc = QuantumCircuit(2)\n",
    "\n",
    "qc.rlx(np.pi/2, [0, 1])\n",
    "qc.rlzlz(np.pi, [0, 1])\n",
    "qc.rlx(np.pi/2, [0, 1])\n",
    "\n",
    "qc.measure_all()\n",
    "\n",
    "plot_histogram(backend.run(qc, spin=2).result().get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a2128be-81ef-4cc3-8ad0-2fbda0d79d27",
   "metadata": {},
   "source": [
    "The state we have created here can be seen as the generalization of a Bell state of two qubits, which we can verify if we run the simulation with a single atom, i.e. spin length $\\frac{1}{2}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "14cdb96e-7647-4cbc-b124-7d7ee8eb63a9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(backend.run(qc, spin=1/2).result().get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "432fc57e-7ef9-49e5-a6a6-36dbdf8ce1dd",
   "metadata": {},
   "source": [
    "## Description as a backend\n",
    "\n",
    "The framework describing the collective spin hardware is implemented as a dedicated _backend_.\n",
    "\n",
    "We could have also run the circuits above on the generic `SpinSimulator` backend. However, by defining a specific `CollectiveSpinSimulator` backend, we have a direct way of describing the accepted gates, size and other settings of this specific system in the backend's _configuration_. \n",
    "\n",
    "The backend configuration explicitly states which instructions are accepted and in what way these instructions can be applied to the spin register. The latter is achieved through _coupling maps_ which define the accepted wiring for all gates. For reference, here is the entire configuration of the `CollectiveSpinSimulator`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "40beeccc-aec9-4f96-93f1-4717ec9165bc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'atomic_species': ['na'],\n",
      " 'backend_name': 'collective_spin_simulator',\n",
      " 'backend_version': '0.0.1',\n",
      " 'basis_gates': ['rlx', 'rly', 'rlz', 'rlz2', 'OAT', 'rlzlz', 'rlxly'],\n",
      " 'cold_atom_type': 'spin',\n",
      " 'conditional': False,\n",
      " 'coupling_map': None,\n",
      " 'description': 'simulator of a collective hardware. Each wire in the circuit '\n",
      "                'denotes the orientation of one collective spin in the '\n",
      "                'hardware',\n",
      " 'dynamic_reprate_enabled': False,\n",
      " 'gates': [{'coupling_map': [[0], [1], [2]],\n",
      "            'description': 'local rotation of the coherent spin around x',\n",
      "            'name': 'rlx',\n",
      "            'parameters': ['omega'],\n",
      "            'qasm_def': 'gate rlx(omega) {}'},\n",
      "           {'coupling_map': [[0], [1], [2]],\n",
      "            'description': 'local rotation of the coherent spin around y',\n",
      "            'name': 'rly',\n",
      "            'parameters': ['delta'],\n",
      "            'qasm_def': 'gate rly(delta) {}'},\n",
      "           {'coupling_map': [[0], [1], [2]],\n",
      "            'description': 'local rotation of the coherent spin around z',\n",
      "            'name': 'rlz',\n",
      "            'parameters': ['delta'],\n",
      "            'qasm_def': 'gate rlz(delta) {}'},\n",
      "           {'coupling_map': [[0], [1], [2]],\n",
      "            'description': 'local spin evolution generated by one-axis '\n",
      "                           'twisting Hamiltonian Lz^2',\n",
      "            'name': 'rlz2',\n",
      "            'parameters': ['chi'],\n",
      "            'qasm_def': 'gate rlz2(chi) {}'},\n",
      "           {'coupling_map': [[0], [1], [2]],\n",
      "            'description': 'local spin evolution generated by (chi*Lz^2 + '\n",
      "                           'delta*Lz + omega*Lx)',\n",
      "            'name': 'oat',\n",
      "            'parameters': ['chi', 'delta', 'omega'],\n",
      "            'qasm_def': 'gate rot(chi, delta, omega) {}'},\n",
      "           {'coupling_map': [[0, 1], [1, 2], [1, 0], [2, 1]],\n",
      "            'description': 'ZZ-interaction coupling two collective spins',\n",
      "            'name': 'rlzlz',\n",
      "            'parameters': ['gamma'],\n",
      "            'qasm_def': 'gate rlzlz(gamma) {}'},\n",
      "           {'coupling_map': [[0, 1], [1, 2], [1, 0], [2, 1]],\n",
      "            'description': 'LXLY-interaction coupling two collective spins',\n",
      "            'name': 'rlxly',\n",
      "            'parameters': ['gamma'],\n",
      "            'qasm_def': 'gate rlxly(gamma) {}'}],\n",
      " 'local': True,\n",
      " 'max_experiments': 10,\n",
      " 'max_shots': 1000000.0,\n",
      " 'memory': True,\n",
      " 'n_qubits': 3,\n",
      " 'open_pulse': False,\n",
      " 'simulator': True,\n",
      " 'supported_instructions': ['rlz',\n",
      "                            'rlx',\n",
      "                            'rly',\n",
      "                            'rlz2',\n",
      "                            'OAT',\n",
      "                            'rlzlz',\n",
      "                            'rlxly',\n",
      "                            'measure',\n",
      "                            'barrier']}\n"
     ]
    }
   ],
   "source": [
    "from pprint import pprint\n",
    "\n",
    "collective_spins_configuration = backend.configuration().to_dict()\n",
    "\n",
    "pprint(collective_spins_configuration)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64fa14f2-9b53-40bc-9fc4-74bc96967f73",
   "metadata": {},
   "source": [
    "Note how each gate has a custom coupling map which defines the allowed wire indices with which the gate can be added to the circuit.\n",
    "\n",
    "Apart from that, the `CollectiveSpinSimulator` inherits all functionality of the generic `SpinSimulator` such as retrieving the statevector and the unitary."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f9a7dc1-cc4d-4977-b62d-190e90d5b517",
   "metadata": {},
   "source": [
    "## Outlook\n",
    "\n",
    "The collective spin simulator backend can be used as a tool to study what kind of quantum computations can be performed in a realistic experimental hardware based on spins as the carriers of quantum information. This collective spin setting is particularly interesting as its gateset forms a universal set on the Hilbert space of the collective spins and could implement error correction when encoding a qubit in each collective spin [2].\n",
    "\n",
    "The supported functionality for spin circuits in Qiskit-cold-atom can in principle be utilized to describe a larger class of spin setups, i.e. other trap- or lattice-based architectures that can deterministically prepare, manipulate and measure individual spins encoded in bosonic atoms. Such experiments might have different underlying Hamiltonian dynamics, number of atomic species, available gates and coupling maps. \n",
    "\n",
    "This tutorial is just one example showing how Qiskit can be used to build a backend for a specific experimental setting that greatly differs from superconducting-qubit-based quantum computers. \n",
    "\n",
    "Interested users are encouraged to explore spin circuits and backend configurations for other setups."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d27bd054-76a9-4708-86f4-27286b82d5ce",
   "metadata": {},
   "source": [
    "## References\n",
    "[1] Gross, Christian *Spin squeezing, entanglement and quantum metrology with Bose–Einstein condensates* Journal of Physics B: Atomic, Molecular and Optical Physics. 45 (10):103001\n",
    "\n",
    "[2] Kasper, Valentin et al., *Universal quantum computation and quantum error correction with ultracold atomic mixtures*, arXiv preprint arXiv:2010.15923, 2020\n",
    "\n",
    "[3] Strobel, Helmut et al. *Fisher information and entanglement of non-Gaussian spin states*, Science, 345(6195):424–427, 2014"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "06923ad1-9327-41eb-8d3e-a23e30539b16",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h3>Version Information</h3><table><tr><th>Software</th><th>Version</th></tr><tr><td><code>qiskit</code></td><td>0.45.1</td></tr><tr><td><code>qiskit_algorithms</code></td><td>0.2.1</td></tr><tr><td><code>qiskit_cold_atom</code></td><td>0.1.0</td></tr><tr><td><code>qiskit_nature</code></td><td>0.7.1</td></tr><tr><td><code>qiskit_aer</code></td><td>0.12.0</td></tr><tr><th colspan='2'>System information</th></tr><tr><td>Python version</td><td>3.9.16</td></tr><tr><td>Python compiler</td><td>MSC v.1916 64 bit (AMD64)</td></tr><tr><td>Python build</td><td>main, Jan 11 2023 16:16:36</td></tr><tr><td>OS</td><td>Windows</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>63.724937438964844</td></tr><tr><td colspan='2'>Tue Jan 09 11:28:37 2024 W. Europe Standard Time</td></tr></table>"
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      "text/plain": [
       "<IPython.core.display.HTML object>"
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     "metadata": {},
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      "text/html": [
       "<div style='width: 100%; background-color:#d5d9e0;padding-left: 10px; padding-bottom: 10px; padding-right: 10px; padding-top: 5px'><h3>This code is a part of Qiskit</h3><p>&copy; Copyright IBM 2017, 2024.</p><p>This code is licensed under the Apache License, Version 2.0. You may<br>obtain a copy of this license in the LICENSE.txt file in the root directory<br> of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.<p>Any modifications or derivative works of this code must retain this<br>copyright notice, and modified files need to carry a notice indicating<br>that they have been altered from the originals.</p></div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
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   ],
   "source": [
    "import qiskit.tools.jupyter\n",
    "%qiskit_version_table\n",
    "%qiskit_copyright"
   ]
  },
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