docs/tutorials/01_introduction_and_fermionic_circuits.ipynb

{
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   "source": [
    "# Introduction & Fermionic Circuits\n",
    "\n",
    "In digital quantum computing, the fundamental unit of information is typically an addressable two-level quantum system called a qubit. Within the circuit model, each qubit is assigned a wire in the circuit. After _initialization_ in a well-defined state (e.g. the ground state 0), gates applied to these wires describe an _evolution_ of the state under a sequence of unitary operations. A _measurement_ on a wire then projects the corresponding unit of information onto one of its internal states (0 or 1 for qubits).\n",
    "\n",
    "Quantum simulation architectures based on cold atoms have been vastly explored for the simulation of condensed matter systems in the last two decades. [1] Their experimental control has advanced to a point where they now offer varying degrees of programmability making them strong candidates for a novel kind of quantum information processor.\n",
    "Similar to the qubit circuits described above, experiments run on cold atomic quantum simulators are also commonly described by an _initialization_ in some easy-to-prepare state, a subsequent _evolution_ of the state under programmable unitary operations and finally a _measurement_ yielding information about the quantum state of the atoms such as location, momentum or spin. \n",
    "\n",
    "Due to these similarities between the qubits and cold atomic quantum systems we can abstract quantum computations and simulations run on cold atomic systems in quantum circuits where the wires represent the internal degrees of freedom of the atoms which are accessed by the measurement. \n",
    "\n",
    "Qiskit's cold atom module explores such circuit-based descriptions of cold atomic experiments, leveraging the existing Qiskit control stack and building upon functionality such as circuits, backends, gates, providers etc.  \n",
    "\n",
    "Specifically, this module enables two different settings:  \n",
    "\n",
    "1.  A \"fermionic\" setting where the individual units of information are the occupations of fermionic modes realized by trapped fermionic atoms as described in this tutorial. \n",
    "2. A \\\"spin\\\" setting where the individual units of information are orientations of long spins as realized by trapped Bose-Einstein-Condensates. This is introduced in the [spin circuits tutorial](./02_spin_circuits.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "304f8244",
   "metadata": {},
   "source": [
    "## Fermionic setting\n",
    "\n",
    "In a fermionic setting, the wires of a quantum circuit describe the occupations of individual fermionic modes. Due to the Pauli exclusion principle, a fermionic mode can either be empty, i.e. in the \"vacuum state\" $\\left| 0 \\right>$ or occupied $\\left| 1 \\right>$. However, no two particles can occupy the same mode. We assign one wire to each fermionic mode in the quantum circuit describing such systems.\n",
    "\n",
    "Before applying gates to this fermionic register, we need to initialize some modes with particles, which is done with a `load` instruction. Importing the `qiskit_cold_atom.fermions` module will add this instruction to the `QuantumCircuit` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1ebfe70b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from qiskit_cold_atom.fermions import FermionSimulator\n",
    "\n",
    "# initialize the generic fermionic simulator backend\n",
    "backend = FermionSimulator()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2b635ce0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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WjzlslJQX873/WMqK4kksLHRw96PJVo8kg7D9B+VVV1eTn5+P2+0mKiqK9PR0mpqa2Lx5MydPnqSlpQWArKwsawcdRp589WGiI2OZ8rnr6Ohss3ocuQRbR+zxeFi8eDFut5u1a9eyfv16oqOjAdi4cSPr1q0jNDQUh8NBRkaGxdMOH888dLLvQ9/v23Qtnd3tFk8kg7H16fTq1atxuVwUFBSwadOmvoABioqKyMzMpKenh+TkZGJiYiycdHi5ELCYwbYR19TUUFpaSlxcHMXFxQPuM3v2bAAyMzP7tr3wwgt85StfISkpicjISKZNm8a3v/1t2tt1NJLhybYRl5SU4PV6Wb58OWPHjh1wn4iICMA/4k2bNjFq1CgeffRRXn31Ve6//35++tOfctNNN+H16su8ZPix7XPi8vJyAHJzcy+6j8vlAvwj3rlzJ/Hx8X2/nj9/PvHx8Sxfvpw333yTefPmBWlikcDYNuKGhgYAkpKSBlzv6elh7969gH/EfxrwBdnZ2QA0NjYGNEt2djZut/vSOw6RsNAIthecsHoMS0xJm0J3T6fVY/TjdDqprKwM6La2jbijowOAzs6B/4OVlpbi8XiIjo4mJSVl0Pvas2cPANOnTw9oFrfbHfBfAMEQPjrS6hEs09zURNf5D60e4zNl24idTietra1UVVWRk5Pjt9bc3ExhYSEAGRkZOByOi95PY2Mj3/nOd7jpppsCfi3Z6XQGdLtgCQuNsHoEy0y45ppheyQOlG0jzsvLo6amhg0bNrBw4ULS0tIAOHDgACtWrMDj8QCDv8mjvb2dm2++mbCwMJ588smAZwn0NClYRvIXqp04fsJ2X6hm24iLiop49tlnOX36NDNmzGDatGl0dXVRW1tLfn4+ycnJ7N692+/58J/q7Oxk8eLFnDp1ioqKCiZMmDDEj8A6v37nPzjT+tE1hbaO9+np7ebnv/k+AFeNT2Lh7BVWjicfY9uIExISqKiooLCwkDfeeIP6+nrS09PZtm0b9913H5MnTwYYMOLz589z++23U1lZyWuvvUZ6evpQj2+pX+7/N35f94bftqd2fweAjEnzFfEwMyK/n7i9vZ2YmBgcDgfnzp0jMvL/L/R4vV7uuusuduzYwSuvvMKCBQssnDQ4RvLptB2/n9i2R+LBHD58GJ/PR1paml/AAKtWreL555/noYceIjIykn379vWtTZ48ecCXoESsZNt3bA3m0KFDwMCn0q+++ioAjz32GDk5OX7/lJWVDemcIp/EiDwSDxZxfX39EE8j8unoSCxiuBF5JL7wvmoROxiRR2IRO1HEIoZTxCKGU8QihlPEIoZTxCKGU8QihlPEIoZTxCKGU8QihlPEIoYbkR8KMNL5fOA9b/UU1ggZDYN8LqKRFLGI4XQ6LWI4RSxiOEUsYjhFLGI4RSxiOEUsYjhFLGI4RSxiOEUsYjhFLGI4RSxiOEUsYjhFLGI4RSxiOEUsYjhFLGI4RSxiOEUsYjhFLGI4RSxiOEUsYjhFLGI4RSxiOEUsYjhFLGI4RSxiOEUsYjhFLGI4RSxiOEUsYjhFLGI4RSxiuBERscfjoaioiNTUVMLDw0lMTGTNmjV0dHSwcuVKHA4HW7dutXpMkYCEWj1AsFVXV5Ofn4/b7SYqKor09HSamprYvHkzJ0+epKWlBYCsrCxrBxUJkMPn8/msHiJYPB4Ps2bNwuVysXbtWtavX090dDQAGzduZN26dYSGhtLb20tbWxsxMTEWTyxy+Wwd8bJlyygpKaGgoIAtW7b0W8/KyuLgwYOkpKRQV1dnwYQin55tnxPX1NRQWlpKXFwcxcXFA+4ze/ZsADIzM/u2VVRUkJeXx4QJExgzZgwJCQnceeed1NTUDMncIpfLts+JS0pK8Hq9LF++nLFjxw64T0REBOAfcWtrKzNnzuTrX/86V111FS6Xi+LiYnJycnj33XdJSEgYkvlFPinbRlxeXg5Abm7uRfdxuVyAf8RLlixhyZIlfvvNmTOHqVOn8uKLL7JmzZogTCsSONtG3NDQAEBSUtKA6z09Pezduxfwj3ggV155JQChoYH9cWVnZ+N2uwO6rYwMTqeTysrKgG5r24g7OjoA6OzsHHC9tLQUj8dDdHQ0KSkp/dZ7e3vxer00NDTwrW99C6fTyR133BHQLG63m8bGxoBuK3Ipto3Y6XTS2tpKVVUVOTk5fmvNzc0UFhYCkJGRgcPh6Hf7+fPn9x2pU1NTKS8vJz4+PuBZRAbzqX5GfDb1wAMP+ABfYmKi79ixY33b9+/f75s6dapv9OjRPsC3atWqAW9/9OhR3759+3wlJSW+6667zpeQkOBraGgYqvFFPjHbvk7scrnIysri7NmzhIaGMm3aNLq6uqitrSU/Px+v18vu3bvZvn07991336D31dbWRnJyMnfffbfeninDjm1fJ05ISKCiooJFixYRHh5OfX09sbGxbNu2jbKyMo4fPw5c+qIWwLhx40hNTaW2tjbYY4tcNtseiQfT3t5OTEwMDoeDc+fOERkZOej+Z86cYfLkydxzzz08/vjjQzSlyCdj2wtbgzl8+DA+n4+0tLR+Ad99992kpqaSlZXFuHHjOHHiBD/84Q8JDQ3lwQcftGhikYsbkREfOnQIGPhU+oYbbuCZZ57hxz/+MV1dXSQmJpKbm8vDDz980decRaykiD+moKCAgoKCoR5JJGC2vbA1mMEiFjHNiLywJWInI/JILGIniljEcIpYxHCKWMRwiljEcIpYxHCKWMRwiljEcIpYxHCKWMRwiljEcIpYxHCKWMRwiljEcIpYxHCKWMRwiljEcIpYxHCKWMRwiljEcIpYxHCKWMRwiljEcIpYxHCKWMRwiljEcIpYxHCKWMRwiljEcIpYxHCKWMRwiljEcIpYxHCKWMRwiljEcIpYxHCKWMRwiljEcP8HahMXS9fslJoAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 287.496x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "\n",
    "circ1 = QuantumCircuit(4)  # Create a quantum circuit describing four fermionic modes.\n",
    "\n",
    "circ1.fload([1, 2])  # Load fermions into modes 1 and 2.\n",
    "\n",
    "circ1.draw(output=\"mpl\", style=\"clifford\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6ddfa98",
   "metadata": {},
   "source": [
    "A measurement will yield the occupations of each wire. Let's run the circuit on the `FermionSimulator` backend and confirm this. Calling `backend.run()` will create an `AerJob` object from qiskit-aer which comes with the same functionality to handle jobs familiar from the Aer simulation backends, such as a `.result()` method to retrieve the results. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1554f160",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'0110': 1000}\n"
     ]
    }
   ],
   "source": [
    "circ1.measure_all()\n",
    "\n",
    "job = backend.run(circ1)  # defaults to 1000 shots taken\n",
    "\n",
    "print(job.result().get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "000aa9a9",
   "metadata": {},
   "source": [
    "A fermionic register can also be created directly from a list of initial occupations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "901334f8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 321.874x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circ2 = backend.initialize_circuit([1, 0, 1])\n",
    "\n",
    "circ2.draw(output=\"mpl\", style=\"clifford\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4ceeafa",
   "metadata": {},
   "source": [
    "Observe that the first quantum circuit has a register named `q` while the second circuit has a register named `fer_mode` to emphasize that the wires are fermionic in nature. This does not affect the instructions that can be added to a circuit and reminds us of the different nature of the wires. Circuits with registers labeled `fer_mode` can be conveniently obtained from the cold atom backend instances using the `initialize_circuit` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d45c1471",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First circuit's register: [QuantumRegister(4, 'q')]\n",
      "Second circuit's register: [QuantumRegister(3, 'fer_mode')]\n"
     ]
    }
   ],
   "source": [
    "print(f\"First circuit's register: {circ1.qregs}\")\n",
    "print(f\"Second circuit's register: {circ2.qregs}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "363cc277",
   "metadata": {},
   "source": [
    "## Fermionic Gates\n",
    "\n",
    "Quantum gates define the unitary operations that are carried out on the system. The gate unitary $U$ can be uniquely identified by the hermitian Hamiltonian $H$ that generates the evolution of the state (see [Qiskit textbook](https://github.com/Qiskit/textbook/blob/main/notebooks/ch-gates/proving-universality.ipynb)) as $U = e^{-i H}$.\n",
    "The dynamics of cold atomic quantum simulators is commonly described by the Hamiltonian implemented by the system. The Qiskit Cold Atom module therefore defines fermionic gates using their generating Hamiltonians.\n",
    "\n",
    "As a formal language to describe fermionic Hamiltonians, we utilize the \n",
    "`FermionicOp` from Qiskit Nature. Gates are then defined as instances or subclasses of the `FermionicGate` class which inherits from Qiskit's original `Gate` class. \n",
    "\n",
    "In order for the `FermionSimulator` to run a circuit, each gate of the circuit needs to have its generating Hamiltonian given as a `FermionicOp`.  \n",
    "\n",
    "As a first example, let's define a gate $U_{\\text{swap}} = e^{-i H_{\\text{swap}}}$ which takes one particle from mode $i$ to another mode $j$ (and vice versa). In second quantization, the generating Hamiltonian is given as \n",
    "$$ H_{\\text{swap}} = \\frac{\\pi}{2} (f^\\dagger_{i} f_{j} + f^\\dagger_{j} f_{i}) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b1e95045",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from qiskit_nature.second_q.operators import FermionicOp\n",
    "import numpy as np\n",
    "\n",
    "# define the Hamiltonian as a FermionicOp\n",
    "H_swap = np.pi / 2 * FermionicOp({\"+_0 -_1\": 1, \"-_0 +_1\": -1}, num_spin_orbitals=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c1feaeb",
   "metadata": {},
   "source": [
    "For details on the syntax of how to define a `FermionicOp` please see the FermionicOp documentation.\n",
    "\n",
    "We can now define the fermionic gate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1a0f48c5",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from qiskit_cold_atom.fermions import FermionicGate\n",
    "\n",
    "swap_fermions = FermionicGate(name=\"swap_fermion\", num_modes=2, generator=H_swap)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d96abc4c",
   "metadata": {},
   "source": [
    "Let's use this gate to define and run a circuit on the simulator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "22c29095",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "circ = backend.initialize_circuit([1, 0, 1, 0])\n",
    "\n",
    "circ.append(swap_fermions, qargs=[0, 1])\n",
    "circ.append(swap_fermions, qargs=[2, 3])\n",
    "circ.append(swap_fermions, qargs=[1, 2])\n",
    "\n",
    "circ.measure_all()\n",
    "# circ.draw(output='mpl', scale=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d59f3c9e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'0011': 1000}\n"
     ]
    }
   ],
   "source": [
    "job = backend.run(circ)\n",
    "\n",
    "print(job.result().get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8df93cea",
   "metadata": {},
   "source": [
    "The fermions initialized at positions 0 and 2 got moved to position 2 and 3. Therefore, the outcome '0011' is always measured at each shot."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6be328de",
   "metadata": {},
   "source": [
    "### Superposition\n",
    "\n",
    "With the SWAP gate only, the system will always stay in a computational basis state. To create a superposition we define a similar gate which lets a particle tunnel from mode $i$ to mode $j$. This is achieved by applying the same Hamiltonian $H_{\\text{swap}}$ for half the time, i.e. with a prefactor half as large.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "aa3fa92b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# define a gate which will create superposition in the circuit\n",
    "split_fermions = FermionicGate(name=\"split_fermion\", num_modes=2, generator=H_swap / 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8b710f09",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 926.388x294.311 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_sup = backend.initialize_circuit([1, 0, 0])\n",
    "\n",
    "qc_sup.append(split_fermions, qargs=[0, 1])\n",
    "qc_sup.append(swap_fermions, qargs=[1, 2])\n",
    "\n",
    "qc_sup.measure_all()\n",
    "qc_sup.draw(output=\"mpl\", style=\"clifford\", scale=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f0a6fe2f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.visualization import plot_histogram\n",
    "\n",
    "job_sup = backend.run(qc_sup)\n",
    "\n",
    "plot_histogram(job_sup.result().get_counts(), figsize=(5, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c32fc0a0",
   "metadata": {},
   "source": [
    "We now see that the single particle in the register is found either in mode 0 or mode 2 with equal probability."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e0f6d27",
   "metadata": {},
   "source": [
    "## The fermionic simulator backend\n",
    "\n",
    "We have already seen above how to use the `FermionSimulator` to simulate measurements of the occupation of the fermionic modes. Internally, this backend simulates the evolution of the circuit by exact diagonalization and therefore also has access to the statevector and unitary of the system in the familiar way of `result.get_statevector()` and `result.get_unitary()`. If there is a final measurement in the circuit, the returned state and unitary of the circuit are those just prior to measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "8e52792e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "counts : {'1010': 1, '0011': 1, '1100': 5, '0101': 3}\n",
      "\n",
      "memory : ['0011', '1010', '0101', '1100', '1100', '0101', '0101', '1100', '1100', '1100']\n",
      "\n",
      "statevector : [0.-0.5j 0.+0.5j 0.+0.j  0.+0.j  0.+0.5j 0.-0.5j]\n",
      "\n",
      "circuit unitary : \n",
      " [[ 0. +0.j   0.5+0.j   0. +0.5j  0. -0.5j  0.5+0.j   0. +0.j ]\n",
      " [ 0. +0.j   0.5+0.j   0. +0.5j  0. +0.5j -0.5+0.j   0. +0.j ]\n",
      " [ 0. +0.j   0. +0.j   0. +0.j   0. +0.j   0. +0.j   0. +1.j ]\n",
      " [ 0. -1.j   0. +0.j   0. +0.j   0. +0.j   0. +0.j   0. +0.j ]\n",
      " [ 0. +0.j  -0.5+0.j   0. +0.5j  0. +0.5j  0.5+0.j   0. +0.j ]\n",
      " [ 0. +0.j  -0.5+0.j   0. +0.5j  0. -0.5j -0.5+0.j   0. +0.j ]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1492.43x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = backend.initialize_circuit([1, 0, 0, 1])\n",
    "\n",
    "qc.append(split_fermions, qargs=[0, 1])\n",
    "qc.append(swap_fermions, qargs=[2, 3])\n",
    "qc.append(swap_fermions, qargs=[0, 1])\n",
    "qc.append(split_fermions, qargs=[2, 3])\n",
    "qc.append(swap_fermions, qargs=[0, 2])\n",
    "\n",
    "qc.measure_all()\n",
    "\n",
    "job = backend.run(qc, shots=10, seed=1234)\n",
    "\n",
    "# access the counts\n",
    "print(\"counts :\", job.result().get_counts())\n",
    "\n",
    "# access the memory of individual outcomes\n",
    "print(\"\\nmemory :\", job.result().get_memory())\n",
    "\n",
    "# access the statevector\n",
    "print(\"\\nstatevector :\", job.result().get_statevector())\n",
    "\n",
    "# accedd the unitary\n",
    "print(\"\\ncircuit unitary : \\n\", job.result().get_unitary())\n",
    "\n",
    "qc.draw(output=\"mpl\", style=\"clifford\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9847181",
   "metadata": {},
   "source": [
    "Note that the statevector and unitary are defined in a Hilbert space of dimension six. This is because the simulator checks for the conservation of the total number of particles under the applied gates. If all gates conserve the total particle number, the simulation will only be carried out in the relevant subspace. In order to see which index in this basis belongs to which state, the basis of the simulation of a circuits can be accessed as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "deeade90",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " 0.   |0, 0, 1, 1>\n",
      " 1.   |0, 1, 0, 1>\n",
      " 2.   |0, 1, 1, 0>\n",
      " 3.   |1, 0, 0, 1>\n",
      " 4.   |1, 0, 1, 0>\n",
      " 5.   |1, 1, 0, 0>\n"
     ]
    }
   ],
   "source": [
    "print(backend.get_basis(qc))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab4ff80c",
   "metadata": {},
   "source": [
    "### Measuring observables\n",
    "\n",
    "The fermionic backends come with a method to sample the expectation value of observables which are diagonal in the occupation number basis. \n",
    "Like the gate Hamiltonians, these observables are given as a `FermionicOp`.\n",
    "\n",
    "For example, we can measure the correlation of the occupations of two sites in the above circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4af1fd5f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.484]\n"
     ]
    }
   ],
   "source": [
    "corr = FermionicOp({\"+_0 -_0 +_2 -_2\": 1}, num_spin_orbitals=4) + FermionicOp(\n",
    "    {\"-_0 +_0 -_2 +_2\": 1}, num_spin_orbitals=4\n",
    ")\n",
    "\n",
    "exp_val = backend.measure_observable_expectation(qc, observable=corr, shots=1000)\n",
    "\n",
    "print(exp_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50133e51",
   "metadata": {},
   "source": [
    "### Further remarks\n",
    "\n",
    "The `FermionSimulator` is a general simulator backend in the sense that it accepts any `FermionicGate` with a well-defined fermionic generator. Similar to the `qasm_simulator` for qubits, there are no coupling maps or further restrictions posed on the applicable gates. \n",
    "\n",
    "To see how fermionic circuits can describe a concrete experimental system of ultracold fermionic atoms with the gateset and coupling map of a real device please see the [fermionic tweezer hardware tutorial](./03_fermionic_tweezer_hardware.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aecfd238",
   "metadata": {},
   "source": [
    "## The ffsim backend\n",
    "\n",
    "Qiskit Cold Atom includes a fermion simulator backend based on [ffsim](https://github.com/qiskit-community/ffsim), a software library for fast simulations of fermionic circuits. This backend is implemented as `FfsimBackend`, and it can be used instead of the `FermionSimulator` backend for significantly improved performance.\n",
    "\n",
    "The ffsim simulator is not supported on Windows, and in order\n",
    "for it to be available, Qiskit Cold Atom must be installed with the `ffsim` extra, e.g.\n",
    "```\n",
    "pip install \"qiskit-cold-atom[ffsim]\"\n",
    "```\n",
    "\n",
    "Unlike the `FermionSimulator` backend, the ffsim backend does not compute the full unitary of the circuit, since doing so is exceedingly expensive at modest system sizes.\n",
    "\n",
    "The ffsim backend can be used to simulate the circuits we created earlier in this tutorial, which were constructed from fermionic gates defined directly in terms of their generators. However, the efficiency advantage of the ffsim backend is most apparent when simulating specific gates from the gate library, such as the `Hop`, `Interaction`, `Phase` gates. The following code cell shows how to use the ffsim backend to simulate a circuit with these gates. Because these gates individually conserve the numbers of spin up and spin down electrons, we set `num_species=2` when running the circuit so that the simulator exploits this symmetry. In this example, our circuit simulates a system with 8 spatial orbitals, with 2 particles of spin up and 2 particles of spin down. The total dimension of the Hilbert space is ${8 \\choose 2}^2 = 784.$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d0336727",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "counts : {'1100000011000000': 3, '1010000010100000': 1, '1001000011000000': 3, '1010000001100000': 2, '0110000010100000': 1}\n",
      "\n",
      "memory : ['1100000011000000', '1010000010100000', '1100000011000000', '1001000011000000', '1010000001100000', '0110000010100000', '1001000011000000', '1010000001100000', '1100000011000000', '1001000011000000']\n",
      "\n",
      "statevector length : 784\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "from qiskit_cold_atom.fermions import (\n",
    "    FfsimBackend,\n",
    "    Hop,\n",
    "    Interaction,\n",
    "    Phase,\n",
    ")\n",
    "\n",
    "# initialize the ffsim backend\n",
    "backend = FfsimBackend()\n",
    "\n",
    "# set the number of orbitals and occupancies\n",
    "norb = 8\n",
    "nocc = norb // 4\n",
    "nvrt = norb - nocc\n",
    "occ_a = [1] * nocc + [0] * nvrt\n",
    "occ_b = [1] * nocc + [0] * nvrt\n",
    "occupations = [occ_a, occ_b]\n",
    "\n",
    "# set parameters for fermionic gates\n",
    "hopping = np.ones(norb - 1)\n",
    "interaction = 1.0\n",
    "mu = np.ones(norb)\n",
    "\n",
    "# construct a circuit with some fermionic gates\n",
    "circuit = backend.initialize_circuit(occupations)\n",
    "circuit.append(Hop(2 * norb, hopping), list(range(2 * norb)))\n",
    "circuit.append(Interaction(2 * norb, interaction), list(range(2 * norb)))\n",
    "circuit.append(Phase(2 * norb, mu), list(range(2 * norb)))\n",
    "circuit.measure_all()\n",
    "\n",
    "# run the circuit and retrieve the measurement counts\n",
    "job = backend.run(circuit, shots=10, seed=1234, num_species=2)\n",
    "\n",
    "# access the counts\n",
    "print(\"counts :\", job.result().get_counts())\n",
    "\n",
    "# access the memory of individual outcomes\n",
    "print(\"\\nmemory :\", job.result().get_memory())\n",
    "\n",
    "# print the length of the statevector\n",
    "print(\"\\nstatevector length :\", len(job.result().get_statevector()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed9a2bfc",
   "metadata": {},
   "source": [
    "## References\n",
    "[1] Gross, Christian and Bloch, Immanuel *Quantum simulations with ultracold atoms in optical lattices*, Science, 357, 995-1001, 2017"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0e22aa30",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
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       "<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_nature</code></td><td>0.7.1</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_aer</code></td><td>0.12.2</td></tr><tr><th colspan='2'>System information</th></tr><tr><td>Python version</td><td>3.10.12</td></tr><tr><td>Python compiler</td><td>GCC 13.1.1 20230429</td></tr><tr><td>Python build</td><td>main, Jun 11 2023 18:49:26</td></tr><tr><td>OS</td><td>Linux</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>29.104999542236328</td></tr><tr><td colspan='2'>Mon Jan 29 16:19:47 2024 EST</td></tr></table>"
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       "<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": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import qiskit.tools.jupyter\n",
    "\n",
    "%qiskit_version_table\n",
    "%qiskit_copyright"
   ]
  }
 ],
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   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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