Reproduce Table 1 of arXiv:2404.18809

[perlinm]

@jmlarson1 let's discuss this sometime

[perlinm]

1. Your reading is correct, there is only a partial search over placement strategies for the right partition.
2. It is certainly possible to do a complete search for the right partition as well. I avoid this (as we did in arXiv:2404.18809 for the [288, 12, 18] code) because it generally takes very long. If you want to perform this search, you should search over

orders_l = code.get_order(vecs_l[0]), code.get_order(vecs_l[1])
for vecs_r in lattice_vectors:
    orders_r = code.get_order(vecs_r[0]), code.get_order(vecs_r[1])
    if orders_r == orders_l[::-1]
        vecs_r = vecs_r[::-1]
    elif orders_r != orders_l:  # required for L/R qubits to be placed on the same rectangular grid
        continue

3. The "left" and "right" partitions correspond to L-type and R-type data qubits. See Figure 1 on page 4 of arXiv:2308.07915.
4. There is no guarantee of optimality anywhere I can see 🙂

[perlinm]

By the way, if you want to play around with qubit placements, you can do something like

code = qldpc.codes.BBCode(
    {x: 6, y: 6},
    x**3 + y + y**2,
    y**3 + x + x**2,
)
folded_layout = True

vecs_l, vecs_r, shift_r, optimal_distance = get_optimal_layout_params(code, folded_layout, cheat=True)
get_qubit_pos = get_qubit_pos_func(code, folded_layout, vecs_l, vecs_r, shift_r)

Now you can get the position of node = qldpc.objects.Node(...) with get_qubit_pos(node.index, node.is_data).

[jmlarson1]

Since there is no search for optimality, should we rename the function get_optimal_layout_params to get_best_known_layout_params?

[perlinm]

get_best_known_layout_params doesn't sound right either, because get_optimal_layout_params does optimize over some search space (as long as cheat=False).

Maybe rather than having a boolean cheat flag, I can split off get_best_known_layout_params from get_optimal_layout_params. Is there a better name for get_optimal_layout_params when it only finds an optimum over a restricted search space?

[jmlarson1]

1. I think the "split" is a good idea.
2. How about the name search_for_layout_params since there is some search space. ("optimal" suggests "best-possible" to me.)

[perlinm]

@jmlarson1 done. What do you think of the current version?