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"source": [
"# Example from *Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus*\n",
"\n",
"This notebook shows how the circuit that is used as a demonstration in the paper https://arxiv.org/abs/1902.03178 is generated and simplified."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First we need to important the standard things"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import sys; sys.path.append('..')\n",
"import random\n",
"import pyzx as zx\n",
"%config InlineBackend.figure_format = 'svg'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we generate the circuit. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Circuit on 4 qubits with 350 gates.\n",
" 4 is the T-count\n",
" 346 Cliffords among which \n",
" 109 2-qubit gates and 0 Hadamard gates.\n"
]
}
],
"source": [
"random.seed(1344) # Make sure the same circuit is generated\n",
"g = zx.generate.cliffordT(4,350,p_t=0.010) # Generate the circuit as a ZX-diagram\n",
"c = zx.Circuit.from_graph(g) # Convert it to a sequence-of-gates representation\n",
"print(c.stats())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This circuit contains many more gates then the one used in the paper. This is because ``generate.clifordT`` generates a lot of single qubit gate strings that can trivially be simplified. Before processing it with our ZX-simplification routine, we therefore process it trough the ``optimize.basic_optimization`` routine to show that our simplification routine is actually doing non-trivial simplifications."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Circuit on 4 qubits with 195 gates.\n",
" 4 is the T-count\n",
" 191 Cliffords among which \n",
" 86 2-qubit gates and 43 Hadamard gates.\n"
]
}
],
"source": [
"c2 = zx.optimize.basic_optimization(c.split_phase_gates())\n",
"print(c2.stats())"
]
},
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"execution_count": 4,
"metadata": {},
"outputs": [
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"source": [
"g = c2.to_graph()\n",
"zx.d3.draw(g)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we simplify our circuit"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"spider_simp: 58. 37. 17. 11. 4. 5 iterations\n",
"id_simp: 1. 1 iterations\n",
"spider_simp: 8. 1. 2 iterations\n",
"pivot_simp: 15. 6. 2. 2. 4 iterations\n",
"lcomp_simp: 33. 12. 11. 6. 6. 4. 4. 4. 3. 1. 1. 1. 1. 13 iterations\n"
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"source": [
"zx.simplify.clifford_simp(g) # This does the simplification routine from the paper\n",
"g.normalise() # This simply puts the circuit in a more compact format, that allows easy visualisation\n",
"zx.d3.draw(g)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally we extract a circuit from this diagram."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Circuit on 4 qubits with 41 gates.\n",
" 4 is the T-count\n",
" 37 Cliffords among which \n",
" 21 2-qubit gates and 12 Hadamard gates.\n"
]
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"source": [
"c = zx.extract.streaming_extract(g.copy())\n",
"print(c.to_basic_gates().stats())\n",
"zx.d3.draw(c.to_graph())"
]
},
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