Three CNOTs#

This notebook shows the construction and simulation results of three logical CNOT gates between three logical qubits with lattice surgery [Horsman et al.[1]].

Construction#

The three CNOT gates are applied in the following order:

circuit_diagram

tqec provides builtin functions tqec.gallery.three_cnots to construct three logical CNOT gates compressed in spacetime.

[1]:

from tqec.gallery import three_cnots

graph = three_cnots()
graph.view_as_html()

[1]:

The three logical CNOTs has six independent stabilizer flow generators: XXI -> XIX, IXI -> IXX, IIX -> IIX, ZII -> ZII, ZZI -> IZI, IZZ -> IIZ. Here we show the correlation surfaces for the generators.

[2]:

correlation_surfaces = graph.find_correlation_surfaces()

`XXI -> XIX`#

[3]:

graph.view_as_html(
    pop_faces_at_direction="-Y",
    show_correlation_surface=correlation_surfaces[0],
)

[3]:

`IXI -> IXX`#

[4]:

graph.view_as_html(
    pop_faces_at_direction="-Y",
    show_correlation_surface=correlation_surfaces[4],
)

[4]:

`IIX -> IIX`#

[5]:

graph.view_as_html(
    pop_faces_at_direction="-Y",
    show_correlation_surface=correlation_surfaces[5],
)

[5]:

`ZII -> ZII`#

[6]:

graph.view_as_html(
    pop_faces_at_direction="+Z",
    show_correlation_surface=correlation_surfaces[1],
)

[6]:

`ZZI -> IZI`#

[7]:

graph.view_as_html(
    pop_faces_at_direction="+X",
    show_correlation_surface=correlation_surfaces[2],
)

[7]:

`IZZ -> IIZ`#

[8]:

graph.view_as_html(
    pop_faces_at_direction="+X",
    show_correlation_surface=correlation_surfaces[3],
)

[8]:

Example Circuit#

Here we show an example circuit of three logical CNOTs with \(d=3\) surface code that is initialized and measured in X basis. You can download the circuit here or view it in Crumble.

[9]:

from tqec import Basis, NoiseModel, compile_block_graph

graph = three_cnots(Basis.X)
compiled_graph = compile_block_graph(graph)
circuit = compiled_graph.generate_stim_circuit(
    k=1, noise_model=NoiseModel.uniform_depolarizing(p=0.001)
)

Simulation#

Here we show the simulation results for all the six observables under uniform depolarizing noise model.

Click to show the full code used for simulation

from multiprocessing import cpu_count
from pathlib import Path

import matplotlib.pyplot as plt
import numpy
import sinter

from tqec.gallery import three_cnots
from tqec import NoiseModel
from tqec.simulation.plotting.inset import plot_observable_as_inset
from tqec.simulation.simulation import start_simulation_using_sinter
from tqec.utils.enums import Basis

SAVE_DIR = Path("results")


def generate_graphs(support_observable_basis: Basis) -> None:
    block_graph = three_cnots(support_observable_basis)
    zx_graph = block_graph.to_zx_graph()

    correlation_surfaces = block_graph.find_correlation_surfaces()

    stats = start_simulation_using_sinter(
        block_graph,
        range(1, 4),
        list(numpy.logspace(-4, -1, 10)),
        NoiseModel.uniform_depolarizing,
        manhattan_radius=2,
        observables=correlation_surfaces,
        num_workers=cpu_count(),
        max_shots=1_000_000,
        max_errors=5_000,
        decoders=["pymatching"],
        print_progress=True,
        # note that save_resume_filepath and database_path can help reduce the time taken
        # by the simulation after the database and result statistics have been saved to
        # the chosen path
        save_resume_filepath=Path(
            f"../_examples_database/three_cnots_stats_{support_observable_basis.value}.csv"
        ),
        database_path=Path("../_examples_database/database.pkl"),
    )

    for i, stat in enumerate(stats):
        fig, ax = plt.subplots()
        sinter.plot_error_rate(
            ax=ax,
            stats=stat,
            x_func=lambda stat: stat.json_metadata["p"],
            failure_units_per_shot_func=lambda stat: stat.json_metadata["d"],
            group_func=lambda stat: stat.json_metadata["d"],
        )
        plot_observable_as_inset(ax, zx_graph, correlation_surfaces[i])
        ax.grid(axis="both")
        ax.legend()
        ax.loglog()
        ax.set_title("Three CNOTs Error Rate")
        ax.set_xlabel("Physical Error Rate")
        ax.set_ylabel("Logical Error Rate(per round)")
        fig.savefig(
            SAVE_DIR
            / f"three_cnots_result_{support_observable_basis}_observable_{i}.png"
        )


def main():
    SAVE_DIR.mkdir(exist_ok=True)
    generate_graphs(Basis.Z)
    generate_graphs(Basis.X)


if __name__ == "__main__"
    main()