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# SPDX-License-Identifier: Apache-2.0
from __future__ import annotations
import re
import jax
import jax.numpy as jnp
import numpy as np
from jaxtyping import Array, Float, Int
def _edge_relation_tags(mask: Array, bmask: Array) -> Int[Array, "n n"]:
n = mask.shape[0]
idx = jnp.arange(n, dtype=jnp.int32)
ii = idx[:, None]
jj = idx[None, :]
real_i = mask.astype(bool)[:, None]
real_j = mask.astype(bool)[None, :]
ctx_i = bmask.astype(bool)[:, None]
ctx_j = bmask.astype(bool)[None, :]
ctx_pair = ctx_i & ctx_j
real_real = real_i & real_j
empty_i = (~real_i) & ctx_i
empty_j = (~real_j) & ctx_j
self_pair = ii == jj
tag = jnp.zeros((n, n), dtype=jnp.int32)
tag = jnp.where(real_real & self_pair, 1, tag)
tag = jnp.where(empty_i & empty_j & self_pair, 2, tag)
tag = jnp.where(empty_i & empty_j & (~self_pair), 3, tag)
tag = jnp.where(empty_i & real_j, 4, tag)
tag = jnp.where(real_i & empty_j, 5, tag)
return jnp.where(ctx_pair, tag, jnp.asarray(-1, dtype=jnp.int32))
def _quantized_hash(x: Array, coeff: Array, tol: float) -> Int[Array, "..."]:
q = jnp.rint(
jnp.real(x).astype(jnp.float32) / jnp.asarray(tol, dtype=jnp.float32)
).astype(jnp.int32)
return jnp.sum(q * coeff.astype(jnp.int32), axis=-1).astype(jnp.int32)
def _canonical_hermitian_j(J_full: Float[Array, "n n 3 3"]) -> Float[Array, "n n 3 3"]:
return 0.5 * (J_full + jnp.transpose(J_full, (1, 0, 3, 2)))
def _j_pair_hash(
J_full: Float[Array, "n n 3 3"],
*,
tol: float,
) -> Int[Array, "n n"]:
n = J_full.shape[0]
coeff = jnp.asarray(
[
1_000_003,
1_009_003,
1_021_009,
1_033_013,
1_049_009,
1_061_009,
1_073_003,
1_087_009,
1_093_013,
1_109_009,
1_117_001,
1_123_003,
1_129_009,
1_151_003,
1_159_013,
1_171_009,
1_181_003,
1_187_009,
],
dtype=jnp.int32,
)
J_key = _canonical_hermitian_j(J_full)
pair = jnp.concatenate(
[
J_key.reshape(n, n, 9),
jnp.transpose(J_key, (1, 0, 2, 3)).reshape(n, n, 9),
],
axis=-1,
)
return _quantized_hash(pair, coeff, tol)
def _j_diag_hash(
J_full: Float[Array, "n n 3 3"],
*,
tol: float,
) -> Int[Array, "n"]:
n = J_full.shape[0]
coeff = jnp.asarray(
[
1_000_003,
1_009_003,
1_021_009,
1_033_013,
1_049_009,
1_061_009,
1_073_003,
1_087_009,
1_093_013,
],
dtype=jnp.int32,
)
J_key = _canonical_hermitian_j(J_full)
idx = jnp.arange(n)
diag = J_key[idx, idx].reshape(n, 9)
return _quantized_hash(diag, coeff, tol)
def route_quotient_keys(
J_full: Float[Array, "n n 3 3"],
h: Float[Array, "n 3"],
mask: Int[Array, "n"] | Array,
bmask: Int[Array, "n"] | Array,
*,
tol: float = 1e-6,
) -> tuple[Int[Array, "n"], Int[Array, "n n"]]:
real = mask.astype(bool)
context = bmask.astype(bool)
h_coeff = jnp.asarray([1_000_003, 1_009_003, 1_021_009], dtype=jnp.int32)
h_key = _quantized_hash(h, h_coeff, tol)
node_key = jnp.where(
real,
h_key
+ _j_diag_hash(J_full, tol=tol) * jnp.asarray(131_063, dtype=jnp.int32)
+ jnp.asarray(17_071, dtype=jnp.int32),
jnp.asarray(-313_037, dtype=jnp.int32),
)
node_key = jnp.where(context, node_key, jnp.asarray(-1, dtype=jnp.int32))
edge_hash = _j_pair_hash(J_full, tol=tol)
tags = _edge_relation_tags(mask, bmask)
edge_hash = jnp.where(tags == 1, jnp.asarray(0, dtype=jnp.int32), edge_hash)
edge_key = edge_hash + tags * jnp.asarray(131_071, dtype=jnp.int32)
edge_key = jnp.where(context[:, None] & context[None, :], edge_key, 0)
return node_key, edge_key
def conditional_orbit_ids_from_keys(
node_key: Int[Array, "n"],
edge_key: Int[Array, "n n"],
valid_mask: Int[Array, "n"] | Array,
context_mask: Int[Array, "n"] | Array,
prefix_ids: Int[Array, "n"],
prefix_len,
*,
max_rounds: int | None = None,
) -> Int[Array, "n"]:
n = node_key.shape[0]
if max_rounds is None:
max_rounds = n
idx = jnp.arange(n, dtype=jnp.int32)
prefix_len_i = jnp.asarray(prefix_len, dtype=jnp.int32)
context = context_mask.astype(bool)
valid = valid_mask.astype(bool) & context
prefix_active = (idx < prefix_len_i) & context[prefix_ids]
prefix_pos = jnp.max(
jnp.where(
prefix_active[:, None] & (prefix_ids[:, None] == idx[None, :]),
idx[:, None],
jnp.asarray(-1, dtype=jnp.int32),
),
axis=0,
)
is_prefix = prefix_pos >= 0
valid = valid & (~is_prefix)
prefix_color = jnp.asarray(
2_000_000_000, dtype=jnp.int32
) - prefix_pos * jnp.asarray(1_000_003, dtype=jnp.int32)
colors0 = jnp.where(is_prefix, prefix_color, node_key)
colors0 = jnp.where(context, colors0, jnp.asarray(-1, dtype=jnp.int32))
big = jnp.asarray(n + 1, dtype=jnp.int32)
def body(colors, _):
pair_key = edge_key + colors[None, :] * jnp.asarray(1_310_719, dtype=jnp.int32)
pair_key = jnp.where(
context[None, :], pair_key, jnp.asarray(0, dtype=jnp.int32)
)
sorted_keys = jnp.sort(pair_key, axis=1)
same_sig = (
context[:, None]
& context[None, :]
& (colors[:, None] == colors[None, :])
& jnp.all(sorted_keys[:, None, :] == sorted_keys[None, :, :], axis=-1)
)
new_colors = jnp.min(jnp.where(same_sig, idx[None, :], big), axis=1)
new_colors = jnp.where(is_prefix, prefix_color, new_colors)
return jnp.where(context, new_colors, jnp.asarray(-1, dtype=jnp.int32)), None
colors, _ = jax.lax.scan(body, colors0, None, length=int(max_rounds))
same_valid = valid[:, None] & valid[None, :] & (colors[:, None] == colors[None, :])
reps = jnp.min(jnp.where(same_valid, idx[None, :], big), axis=1)
return jnp.where(valid, reps, jnp.asarray(-1, dtype=jnp.int32))
def conditional_orbit_pair_ids_from_keys(
node_key: Int[Array, "n"],
edge_key: Int[Array, "n n"],
valid_mask: Int[Array, "n"] | Array,
context_mask: Int[Array, "n"] | Array,
prefix_ids: Int[Array, "n"],
prefix_len,
) -> Int[Array, "n"]:
n = int(node_key.shape[0])
idx = jnp.arange(n, dtype=jnp.int32)
pidx = jnp.arange(n * n, dtype=jnp.int32)
nn = jnp.asarray(n * n, dtype=jnp.int32)
big = jnp.asarray(n * n, dtype=jnp.int32)
prefix_len_i = jnp.asarray(prefix_len, dtype=jnp.int32)
context = context_mask.astype(bool)
valid = valid_mask.astype(bool) & context
prefix_active = (idx < prefix_len_i) & context[prefix_ids]
prefix_pos = jnp.max(
jnp.where(
prefix_active[:, None] & (prefix_ids[:, None] == idx[None, :]),
idx[:, None],
jnp.asarray(-1, dtype=jnp.int32),
),
axis=0,
)
is_prefix = prefix_pos >= 0
valid = valid & (~is_prefix)
prefix_color = jnp.asarray(
2_000_000_000, dtype=jnp.int32
) - prefix_pos * jnp.asarray(1_000_003, dtype=jnp.int32)
node_colors = jnp.where(is_prefix, prefix_color, node_key)
node_colors = jnp.where(context, node_colors, jnp.asarray(-1, dtype=jnp.int32))
cc = (context[:, None] & context[None, :]).reshape(-1)
def _canon(components):
same = cc[:, None] & cc[None, :]
for s in components:
sf = s.reshape(-1)
same = same & (sf[:, None] == sf[None, :])
reps = jnp.min(jnp.where(same, pidx[None, :], big), axis=1)
return jnp.where(cc, reps, jnp.asarray(-1, dtype=jnp.int32)).reshape(n, n)
ni = jnp.broadcast_to(node_colors[:, None], (n, n))
nj = jnp.broadcast_to(node_colors[None, :], (n, n))
pc0 = _canon([ni, nj, edge_key, jnp.transpose(edge_key)])
base_a = jnp.asarray(1_000_003, dtype=jnp.int32)
base_b = jnp.asarray(1_300_021, dtype=jnp.int32)
if n > 1:
pow_a = jnp.concatenate(
[
jnp.ones((1,), jnp.int32),
jnp.cumprod(jnp.full((n - 1,), base_a, jnp.int32)),
]
)
pow_b = jnp.concatenate(
[
jnp.ones((1,), jnp.int32),
jnp.cumprod(jnp.full((n - 1,), base_b, jnp.int32)),
]
)
else:
pow_a = jnp.ones((1,), jnp.int32)
pow_b = jnp.ones((1,), jnp.int32)
ctx_k = context[None, None, :]
off = jnp.asarray(7, dtype=jnp.int32)
neutral = jnp.asarray(-1, dtype=jnp.int32)
def _body(pc, _):
a = pc[:, None, :]
b = jnp.transpose(pc)[None, :, :]
code = jnp.where(ctx_k, a * nn + b, neutral)
sc = jnp.sort(code, axis=-1)
ph_a = jnp.sum((sc + off) * pow_a[None, None, :], axis=-1)
ph_b = jnp.sum((sc + off) * pow_b[None, None, :], axis=-1)
return _canon([pc, ph_a, ph_b]), None
pc, _ = jax.lax.scan(_body, pc0, None, length=n)
diag = jnp.diagonal(pc)
same_valid = valid[:, None] & valid[None, :] & (diag[:, None] == diag[None, :])
reps = jnp.min(jnp.where(same_valid, idx[None, :], big), axis=1)
return jnp.where(valid, reps, jnp.asarray(-1, dtype=jnp.int32))
_WL1_BREAKER_PATTERN = re.compile(r"wl1|srg|paley|shrikhande|rook", re.IGNORECASE)
_WL1_BREAKER_CATEGORY = "13_wl1_breaking"
def _tag_forces_fwl2(
*,
category: str | None = None,
tag: str | None = None,
topology_class: str | None = None,
j_class: str | None = None,
) -> bool:
if category is not None and str(category) == _WL1_BREAKER_CATEGORY:
return True
for value in (tag, topology_class, j_class):
if value is not None and _WL1_BREAKER_PATTERN.search(str(value)):
return True
return False
def system_needs_fwl2(
J_full,
h,
n_spins: int,
*,
category: str | None = None,
tag: str | None = None,
topology_class: str | None = None,
j_class: str | None = None,
tol: float = 1e-6,
) -> bool:
if _tag_forces_fwl2(
category=category,
tag=tag,
topology_class=topology_class,
j_class=j_class,
):
return True
n = int(n_spins)
J_arr = jnp.asarray(np.asarray(J_full, dtype=np.float64))
h_arr = jnp.asarray(np.asarray(h, dtype=np.float64))
mask = jnp.ones((n,), dtype=jnp.int32)
bmask = jnp.ones((n,), dtype=jnp.int32)
idx = jnp.arange(n, dtype=jnp.int32)
prefix_len = jnp.int32(0)
node_key, edge_key = route_quotient_keys(J_arr, h_arr, mask, bmask, tol=tol)
wl1 = conditional_orbit_ids_from_keys(
node_key, edge_key, mask, bmask, idx, prefix_len
)
fwl2 = conditional_orbit_pair_ids_from_keys(
node_key, edge_key, mask, bmask, idx, prefix_len
)
return bool(not jnp.array_equal(wl1, fwl2))
__all__ = [
"conditional_orbit_ids_from_keys",
"conditional_orbit_pair_ids_from_keys",
"route_quotient_keys",
"system_needs_fwl2",
]
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