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"source": [
"# Decomposing Qiskit circuits"
]
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"source": [
"In this notebook, we show how Qiskit circuits can be converted into Perceval circuits. To do so, we take the example of a simple gate-based circuit (a circuit producing GHZ states) and we show the translation to a linear optical circuit. We also show the equivalence between the two circuits."
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"source": [
"As usual we start by imported the useful libraries. Note that this notebook requires the installation of Qiskit (which can be easiliy done with `pip install qiskit`)."
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"source": [
"import perceval as pcvl\n",
"import perceval.lib.phys as phys\n",
"from perceval.converters import QiskitConverter\n",
"\n",
"from qiskit import QuantumCircuit\n",
"from qiskit.quantum_info import Statevector"
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"source": [
"## GHZ State generation in Qiskit"
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"We first define the circuit generating GHZ states of 3 qubits with Qiskit. To do so, we first act with a Hadamard gate on qubit 0 to put in superposition of state $|0\\rangle$ and $|1\\rangle$. Then we perform two CNOT gates using qubit 0 as control and qubits 1 and 2 as targets."
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"text/plain": " ┌───┐ \nq_0: ┤ H ├──■────■──\n └───┘┌─┴─┐ │ \nq_1: ─────┤ X ├──┼──\n └───┘┌─┴─┐\nq_2: ──────────┤ X ├\n └───┘",
"text/html": "
┌───┐ \nq_0: ┤ H ├──■────■──\n └───┘┌─┴─┐ │ \nq_1: ─────┤ X ├──┼──\n └───┘┌─┴─┐\nq_2: ──────────┤ X ├\n └───┘
"
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"source": [
"# Create a Quantum Circuit acting on the q register\n",
"circuit = QuantumCircuit(3)\n",
"\n",
"# Add a H gate on qubit 0\n",
"circuit.h(0)\n",
"\n",
"# Add CX (CNOT) gates on control qubit 0 and target qubits 1 and 2\n",
"circuit.cx(0, 1)\n",
"circuit.cx(0, 2)\n",
"\n",
"# Draw the circuit\n",
"circuit.draw()"
],
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"source": [
"We display the final state when starting from the input state $|000\\rangle$."
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"text/latex": "$$\\frac{\\sqrt{2}}{2} |000\\rangle+\\frac{\\sqrt{2}}{2} |111\\rangle$$"
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
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"source": [
"# Set the initial state of the simulator to the ground state using from_int\n",
"state = Statevector.from_int(0, 2**3)\n",
"\n",
"# Evolve the state by the quantum circuit\n",
"state = state.evolve(circuit)\n",
"\n",
"#draw using latex\n",
"state.draw('latex')"
],
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"cell_type": "markdown",
"source": [
"## Conversion to Perceval"
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"cell_type": "markdown",
"source": [
"With the use of `QiskitConverter`, we can transform the Qiskit circuit into a Perceval circuit. It uses 2 modes per qubit and additional modes for ancillary photons to perform deterministically two-qubit gates. Below the first six modes correspond to the three logical qubits (see the 'Spatial Modes encoding' paragraph in the 'Basics' section of the documentation) of the gate-based circuit above.\n",
"\n",
"The other modes are used to successfully implement two-qubit gates via heralding or post-selection. Heralding employs [4 ancillary modes](https://doi.org/10.1073/pnas.1018839108) while post-selection employs [2 ancillary modes](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.65.062324). With the option `heralded=True` in the method `.convert` on a `QiskitConverter` object, every CNOT but the last is implemented with a heralding scheme. Here it means that it would add $4+2$ ancillary modes. The option `heralded=True` only implements post-selected CNOTs. Here it would mean $2+2$ ancillary modes. A cautionary warning: post-selected CNOTs do not compose generally."
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"source": [
"qiskit_converter = QiskitConverter(phys)\n",
"quantum_processor = qiskit_converter.convert(circuit, heralded=True)\n",
"pcvl.pdisplay(quantum_processor, recursive=True)"
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"source": [
"With this converted circuit, we can now check that the resulting state is the same as before the conversion."
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