Generating Lattices

We have several functions in the qse.lattices submodule to directly generate known lattices and geometries.

import numpy as np
import qse

One Dimensional Chain

qchain = qse.lattices.chain(lattice_spacing=3, repeats=10)
qchain.draw(radius="nearest", equal_aspect=False)

Ring geometry

qring = qse.lattices.ring(spacing=2.0, nqbits=12)
qring.draw(radius="nearest")

Square lattice

qsquare = qse.lattices.square(1, repeats_x=6, repeats_y=6)
qsquare.set_centroid(0.0)
qsquare.draw(radius=2)

Triangular lattice

qtriangle = qse.lattices.triangular(1, repeats_x=6, repeats_y=5)
qtriangle.draw(radius="nearest")

Hexagonal lattice

qhexagon = qse.lattices.hexagonal(1, repeats_x=5, repeats_y=5)
qhexagon.draw(radius="nearest", show_labels=True)

del qhexagon[[0, 49]]
qhexagon.draw(radius="nearest")

Kagome lattice

qkagome = qse.lattices.kagome(1, repeats_x=5, repeats_y=5)
qkagome.set_centroid(0.0)
qkagome.draw(radius=3)

Constructing lattices via lattice vectors

Rectangluar lattice

spacing = 1.0
cell = spacing * np.array([[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 0.0]])

# qbits object with one qubit at origin
q_unit = qse.Qbits(positions=np.zeros((1, 3)), cell=cell)

# now repeat the pattern to get lattice of desired size
qrectangle = q_unit.repeat((5, 5, 1))
qrectangle.draw(radius=2)

Simple Cubic lattice

spacing = 1.0
cell = spacing * np.array([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]])

# qbits object with one qubit at origin
q_unit = qse.Qbits(positions=np.zeros((1, 3)), cell=cell)

# now repeat the pattern to get lattice of desired size
qsquare = q_unit.repeat((5, 5, 5))
qsquare.draw(radius="nearest")

Some special geometries

Torus geometry

qtorus = qse.lattices.torus(n_outer=15, n_inner=15, inner_radius=2.0, outer_radius=6.0)
qtorus.draw(radius=2.0)

Version

qse.utils.print_environment()

Python version: 3.12.13
qse version: 1.1.13