{
"cells": [
{
"cell_type": "markdown",
"id": "fff49b9d-0934-43b9-bceb-f7b8c7d52b7f",
"metadata": {},
"source": [
"# Move Rotation\n",
"\n",
"This notebook demonstrates moving and rotating the spatial boundary of a logical qubit. Rotating the boundary types of a logical qubit is a crucial operation in lattice surgery. For instance, merging two logical qubits requires their boundary types to be aligned. Therefore, performing such boundary-type rotations is often essential to facilitate seamless lattice merging."
]
},
{
"cell_type": "markdown",
"id": "0e48152b-79c3-452b-b03a-dc8b4615065b",
"metadata": {},
"source": [
"### Construction\n",
"\n",
"`tqec` provides builtin function `tqec.gallery.move_rotation` to construct it."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "5ce9f004-70ba-4cb0-a20e-4a73c74d5426",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from tqec import Basis\n",
"from tqec.gallery import move_rotation\n",
"\n",
"graph = move_rotation()\n",
"graph.view_as_html()"
]
},
{
"cell_type": "markdown",
"id": "f4e3ebd4-2338-4222-b08a-630394abd13a",
"metadata": {},
"source": [
"This operation rotates the orientation of the logical observable through a spatial L-shape junction. As shown below, the correlation surface initially aligns with the Y-axis and finally aligns with X-axis."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "cdab68b5-378f-4db2-aba2-c5e3db242dfc",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"correlation_surfaces = graph.find_correlation_surfaces()\n",
"graph.view_as_html(\n",
" pop_faces_at_direction=\"-Y\",\n",
" show_correlation_surface=correlation_surfaces[0],\n",
")"
]
},
{
"cell_type": "markdown",
"id": "1455147e-e169-4c06-b488-70e3a1929052",
"metadata": {},
"source": [
"### Example Circuit\n",
"\n",
"Here we show an example circuit of move rotation with $d=3$ surface code that is initialized and measured in X basis. You can download the circuit [here](../media/gallery/move_rotation/circuit.stim) or view it in [Crumble](https://algassert.com/crumble#circuit=Q(0,4)0;Q(0,8)1;Q(0,12)2;Q(1,1)3;Q(1,3)4;Q(1,5)5;Q(1,7)6;Q(1,9)7;Q(1,11)8;Q(1,13)9;Q(2,0)10;Q(2,2)11;Q(2,4)12;Q(2,6)13;Q(2,8)14;Q(2,10)15;Q(2,12)16;Q(2,14)17;Q(3,1)18;Q(3,3)19;Q(3,5)20;Q(3,7)21;Q(3,9)22;Q(3,11)23;Q(3,13)24;Q(4,2)25;Q(4,4)26;Q(4,6)27;Q(4,8)28;Q(4,10)29;Q(4,12)30;Q(5,1)31;Q(5,3)32;Q(5,5)33;Q(5,7)34;Q(5,9)35;Q(5,11)36;Q(5,13)37;Q(6,2)38;Q(6,6)39;Q(6,10)40;Q(6,12)41;Q(6,14)42;Q(7,9)43;Q(7,11)44;Q(7,13)45;Q(8,8)46;Q(8,10)47;Q(8,12)48;Q(9,9)49;Q(9,11)50;Q(9,13)51;Q(10,10)52;Q(10,12)53;Q(10,14)54;Q(11,9)55;Q(11,11)56;Q(11,13)57;Q(12,8)58;Q(12,10)59;Q(12,12)60;Q(13,9)61;Q(13,11)62;Q(13,13)63;Q(14,12)64;RX_0_3_4_5_10_11_12_18_19_20_25_26_27_31_32_33_38;TICK;CX_12_4_25_18_27_20;CZ_11_3_26_19_38_31;TICK;CX_12_19_25_31_27_33;CZ_0_4;TICK;CX_10_3_12_5_25_19;CZ_11_4_26_20_38_32;TICK;CZ_11_18_26_32;TICK;CX_10_18_12_20_25_32;CZ_0_5_11_19_26_33;TICK;MX_0_10_11_12_25_26_27_38;DT(2,0,0)rec[-7];DT(2,4,0)rec[-5];DT(4,2,0)rec[-4];DT(4,6,0)rec[-2];TICK;RX_0_10_11_12_25_26_27_38;TICK;CX_12_4_25_18_27_20;CZ_11_3_26_19_38_31;TICK;CX_12_19_25_31_27_33;CZ_0_4;TICK;CX_10_3_12_5_25_19;CZ_11_4_26_20_38_32;TICK;CZ_11_18_26_32;TICK;CX_10_18_12_20_25_32;CZ_0_5_11_19_26_33;TICK;MX_0_10_11_12_25_26_27_38;DT(0,4,1)rec[-8]_rec[-16];DT(2,0,1)rec[-7]_rec[-15];DT(2,2,1)rec[-6]_rec[-14];DT(2,4,1)rec[-5]_rec[-13];DT(4,2,1)rec[-4]_rec[-12];DT(4,4,1)rec[-3]_rec[-11];DT(4,6,1)rec[-2]_rec[-10];DT(6,2,1)rec[-1]_rec[-9];TICK;RX_0_10_11_12_25_26_27_38;TICK;CX_12_4_25_18_27_20;CZ_11_3_26_19_38_31;TICK;CX_12_19_25_31_27_33;CZ_0_4;TICK;CX_10_3_12_5_25_19;CZ_11_4_26_20_38_32;TICK;CZ_11_18_26_32;TICK;CX_10_18_12_20_25_32;CZ_0_5_11_19_26_33;TICK;MX_0_10_11_12_25_26_27_38;DT(0,4,2)rec[-8]_rec[-16];DT(2,0,2)rec[-7]_rec[-15];DT(2,2,2)rec[-6]_rec[-14];DT(2,4,2)rec[-5]_rec[-13];DT(4,2,2)rec[-4]_rec[-12];DT(4,4,2)rec[-3]_rec[-11];DT(4,6,2)rec[-2]_rec[-10];DT(6,2,2)rec[-1]_rec[-9];TICK;RX_0_1_2_6_7_8_9_10_11_12_13_14_15_16_17_21_22_23_24_25_26_27_28_29_30_34_35_36_37_38_39_40_41_42_43_44_45_46_47_48_49_50_51_52_53_54_55_56_57_58_59_60_61_62_63_64;TICK;CX_12_4_14_6_16_8_25_18_27_20_29_22_41_36_47_43_53_50_59_55_64_62;CZ_11_3_13_5_15_7_17_9_26_19_28_21_30_23_38_31_39_33_40_35_42_37_48_44_52_49_54_51_60_56;TICK;CX_12_19_14_21_25_31_27_33_29_35;CZ_0_4_1_6_2_8_17_24_30_36_40_43_42_45_48_50_52_55_54_57_60_62;TICK;CX_10_3_12_5_14_7_16_9_25_19_27_21_29_23_41_37_47_44_53_51_59_56_64_63;CZ_11_4_13_6_15_8_26_20_28_22_30_24_38_32_39_34_40_36_46_43_48_45_52_50_58_55_60_57;TICK;CX_16_23_41_44_47_49_53_56_59_61;CZ_11_18_13_20_15_22_26_32_28_34;TICK;CX_10_18_12_20_14_22_16_24_25_32_27_34_29_36_41_45_47_50_53_57_59_62;CZ_0_5_1_7_2_9_11_19_13_21_15_23_26_33_28_35_30_37_40_44_46_49_48_51_52_56_58_61_60_63;TICK;MX_0_1_2_10_11_12_13_14_15_16_17_25_26_27_28_29_30_38_39_40_41_42_46_47_48_52_53_54_58_59_60_64;DT(0,4,3)rec[-32]_rec[-40];DT(2,0,3)rec[-29]_rec[-39];DT(2,2,3)rec[-28]_rec[-38];DT(2,4,3)rec[-27]_rec[-37];DT(2,8,3)rec[-25];DT(2,12,3)rec[-23];DT(4,2,3)rec[-21]_rec[-36];DT(4,4,3)rec[-20]_rec[-35];DT(4,6,3)rec[-19]_rec[-34];DT(4,10,3)rec[-17];DT(6,2,3)rec[-15]_rec[-33];DT(6,12,3)rec[-12];DT(8,10,3)rec[-9];DT(10,12,3)rec[-6];DT(12,10,3)rec[-3];DT(14,12,3)rec[-1];TICK;RX_0_1_2_10_11_12_13_14_15_16_17_25_26_27_28_29_30_38_39_40_41_42_46_47_48_52_53_54_58_59_60_64;TICK;CX_12_4_14_6_16_8_25_18_27_20_29_22_41_36_47_43_53_50_59_55_64_62;CZ_11_3_13_5_15_7_17_9_26_19_28_21_30_23_38_31_39_33_40_35_42_37_48_44_52_49_54_51_60_56;TICK;CX_12_19_14_21_25_31_27_33_29_35;CZ_0_4_1_6_2_8_17_24_30_36_40_43_42_45_48_50_52_55_54_57_60_62;TICK;CX_10_3_12_5_14_7_16_9_25_19_27_21_29_23_41_37_47_44_53_51_59_56_64_63;CZ_11_4_13_6_15_8_26_20_28_22_30_24_38_32_39_34_40_36_46_43_48_45_52_50_58_55_60_57;TICK;CX_16_23_41_44_47_49_53_56_59_61;CZ_11_18_13_20_15_22_26_32_28_34;TICK;CX_10_18_12_20_14_22_16_24_25_32_27_34_29_36_41_45_47_50_53_57_59_62;CZ_0_5_1_7_2_9_11_19_13_21_15_23_26_33_28_35_30_37_40_44_46_49_48_51_52_56_58_61_60_63;TICK;MX_0_1_2_10_11_12_13_14_15_16_17_25_26_27_28_29_30_38_39_40_41_42_46_47_48_52_53_54_58_59_60_64;DT(0,4,4)rec[-32]_rec[-64];DT(0,8,4)rec[-31]_rec[-63];DT(0,12,4)rec[-30]_rec[-62];DT(2,0,4)rec[-29]_rec[-61];DT(2,2,4)rec[-28]_rec[-60];DT(2,4,4)rec[-27]_rec[-59];DT(2,6,4)rec[-26]_rec[-58];DT(2,8,4)rec[-25]_rec[-57];DT(2,10,4)rec[-24]_rec[-56];DT(2,12,4)rec[-23]_rec[-55];DT(2,14,4)rec[-22]_rec[-54];DT(4,2,4)rec[-21]_rec[-53];DT(4,4,4)rec[-20]_rec[-52];DT(4,6,4)rec[-19]_rec[-51];DT(4,8,4)rec[-18]_rec[-50];DT(4,10,4)rec[-17]_rec[-49];DT(4,12,4)rec[-16]_rec[-48];DT(6,2,4)rec[-15]_rec[-47];DT(6,6,4)rec[-14]_rec[-46];DT(6,10,4)rec[-13]_rec[-45];DT(6,12,4)rec[-12]_rec[-44];DT(6,14,4)rec[-11]_rec[-43];DT(8,8,4)rec[-10]_rec[-42];DT(8,10,4)rec[-9]_rec[-41];DT(8,12,4)rec[-8]_rec[-40];DT(10,10,4)rec[-7]_rec[-39];DT(10,12,4)rec[-6]_rec[-38];DT(10,14,4)rec[-5]_rec[-37];DT(12,8,4)rec[-4]_rec[-36];DT(12,10,4)rec[-3]_rec[-35];DT(12,12,4)rec[-2]_rec[-34];DT(14,12,4)rec[-1]_rec[-33];TICK;RX_0_1_2_10_11_12_13_14_15_16_17_25_26_27_28_29_30_38_39_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]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "82de0598-5163-4bce-845c-3d94cfc08cf8",
"metadata": {},
"outputs": [],
"source": [
"from tqec import NoiseModel, compile_block_graph\n",
"\n",
"graph = move_rotation(Basis.X)\n",
"compiled_graph = compile_block_graph(graph)\n",
"circuit = compiled_graph.generate_stim_circuit(\n",
" k=1, noise_model=NoiseModel.uniform_depolarizing(p=0.001)\n",
")"
]
},
{
"cell_type": "markdown",
"id": "07a68266-b81c-4d02-8c34-63f6e270cb8f",
"metadata": {},
"source": [
"### Simulation\n",
"\n",
"Here we show the simulation results of both X-basis and Z-basis experiments under **uniform depolarizing** noise model.\n",
"\n",
"Click to show the full code used for simulation
\n",
"\n",
"```py\n",
"from pathlib import Path\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import numpy\n",
"import sinter\n",
"\n",
"from tqec.gallery.memory import memory\n",
"from tqec.gallery.move_rotation import move_rotation\n",
"from tqec import NoiseModel\n",
"from tqec.simulation.plotting.inset import plot_observable_as_inset\n",
"from tqec.simulation.simulation import start_simulation_using_sinter\n",
"from tqec.utils.enums import Basis\n",
"\n",
"SAVE_DIR = Path(\"results\")\n",
"\n",
"\n",
"def generate_graphs(support_observable_basis: Basis) -> None:\n",
" block_graph = move_rotation(support_observable_basis)\n",
" zx_graph = block_graph.to_zx_graph()\n",
"\n",
" correlation_surfaces = block_graph.find_correlation_surfaces()\n",
"\n",
" stats = start_simulation_using_sinter(\n",
" block_graph,\n",
" range(1, 4),\n",
" list(numpy.logspace(-4, -1, 10)),\n",
" NoiseModel.uniform_depolarizing,\n",
" manhattan_radius=2,\n",
" observables=correlation_surfaces,\n",
" num_workers=20,\n",
" max_shots=10_000_000,\n",
" max_errors=5_000,\n",
" decoders=[\"pymatching\"],\n",
" print_progress=True,\n",
" )\n",
"\n",
" for i, stat in enumerate(stats):\n",
" fig, ax = plt.subplots()\n",
" sinter.plot_error_rate(\n",
" ax=ax,\n",
" stats=stat,\n",
" x_func=lambda stat: stat.json_metadata[\"p\"],\n",
" failure_units_per_shot_func=lambda stat: stat.json_metadata[\"d\"],\n",
" group_func=lambda stat: stat.json_metadata[\"d\"],\n",
" )\n",
" plot_observable_as_inset(ax, zx_graph, correlation_surfaces[i])\n",
" ax.grid(axis=\"both\")\n",
" ax.legend()\n",
" ax.loglog()\n",
" ax.set_title(\"Move Rotation Error Rate\")\n",
" ax.set_xlabel(\"Physical Error Rate\")\n",
" ax.set_ylabel(\"Logical Error Rate(per round)\")\n",
" fig.savefig(\n",
" SAVE_DIR\n",
" / f\"move_rotation_result_{support_observable_basis}_observable_{i}.png\"\n",
" )\n",
"\n",
"\n",
"def main():\n",
" SAVE_DIR.mkdir(exist_ok=True)\n",
" generate_graphs(Basis.Z)\n",
" generate_graphs(Basis.X)\n",
"\n",
"\n",
"if __name__ == \"__main__\":\n",
" main()\n",
"\n",
"\n",
"```\n",
"\n",
"