def glue_logops():
m = argv.get("m", 4)
n = argv.get("n", m + m + 1)
dist = argv.get("dist", 3)
N = argv.get("N", 2)
M = argv.get("M", N)
p = argv.get("p", 0.03)
weight = argv.weight
codes = []
code = None
for i in range(N):
Hx, Hz = make_quantum(n, m, dist, weight)
#Hx, Hz = make_surface()
print("Hx, Hz:")
print(shortstrx(Hx, Hz))
c = CSSCode(Hx=Hx, Hz=Hz)
codes.append(c)
code = c if code is None else code + c
A, B = codes
code = A + B
print(code)
print("Lx, Lz:")
print(shortstrx(code.Lx, code.Lz))
print("Hx, Hz:")
print(shortstrx(code.Hx, code.Hz))
print()
#Hx = cat((code.Lx, code.Hx))
Hx = code.Hx
Hz = cat((code.Lz, code.Hz))
idxs = list(range(2 * n))
idxs.sort(key=lambda i: (-code.Lz[:, i].sum(), ))
Hx = Hx[:, idxs]
Hz = Hz[:, idxs]
print(shortstrx(Hx, Hz))
i0 = argv.get("i0")
i1 = argv.get("i1")
if i0 is None:
return
# code = code.glue(0, n)
# print(code)
# print(shortstrx(code.Hx, code.Hz))
Hx, Hz = glue1_quantum(Hx, Hz, i0, i1)
print("Hx, Hz:")
print(shortstrx(Hx, Hz))
def find_logops():
Hz = parse("""
11111.........................
1....1111.....................
.1.......1111.................
..1..1.......111..............
...1..1..1......11............
....1.....1..1....11..........
...........1....1...111.......
............1.....1.1..11.....
..............1....1...1.11...
.......1.......1.........1.11.
........1........1...1.....1.1
......................1.1.1.11
""")
Hx = parse("""
11......1..1.........1........
.....11..11..1................
...11...........1.1.1.........
.........1..1....1......1....1
....................11.1.1.1..
..........11.......1..1...1...
.............1.1..1.....1...1.
..11...........1.1.........1..
.....1..1.....1...........1..1
.11.........1.1........1......
1...1..1...........1.....1....
......11........1.....1.....1.
""")
Hz = remove_dependent(Hz)
Hx = remove_dependent(Hx)
mx, n = Hx.shape
mz, n = Hz.shape
print(n, mx, mz)
Hz = parse("1.111... .111.1.. 1...1.11")
Hx = parse("111...1. 11.1...1 ..1.111.")
from qupy.ldpc.css import CSSCode
code = CSSCode(Hx=Hx, Hz=Hz)
print("Lx:")
print(shortstr(code.Lx))
print("Lz:")
print(shortstr(code.Lz))
def find_homology_2(g, f, *dims):
print("find_homology")
print(dims[2], "--f-->", dims[1], "--g-->", dims[0])
F = numpy.zeros((dims[1], dims[2]))
for row, col in list(f.keys()):
v = f[row, col]
F[row, col] = v % 2
#print shortstr(F.transpose())
#print
G = numpy.zeros((dims[0], dims[1]))
for row, col in list(g.keys()):
v = g[row, col]
G[row, col] = v % 2
#print shortstr(G)
if argv.ldpc:
from qupy.ldpc.css import CSSCode
code = CSSCode(Hx=F.transpose(), Hz=G)
code.build()
code = code.prune_deadbits()
print(code)
name = argv.get("name")
if name.endswith(".ldpc"):
print("saving", name)
code.save(name)
if argv.logops:
L = find_logops(G, F.transpose())
w = min([v.sum() for v in L])
print("logops weight:", w)
L = find_logops(F, G.transpose())
w = min([v.sum() for v in L])
print("logops weight:", w)
GF = numpy.dot(G, F) % 2
#print shortstr(GF)
assert numpy.abs(GF).sum() == 0
F = F.astype(numpy.int32)
G = G.astype(numpy.int32)
print("rank(f)=%d, rank(g)=%d" % (rank(F), rank(G)))
if g:
kerg = find_kernel(G)
print("ker(g):", len(kerg))
def test_flow():
seed(3)
m, n = argv.get("m", 3), argv.get("n", 3)
cx = Complex()
if argv.disc:
cx.build_surface((0, 0), (m, n))
k = 0
elif argv.surface:
cx.build_surface((0, 0), (m, n), open_top=True, open_bot=True)
k = 0
elif argv.torus:
cx.build_torus(m, n)
k = 2
else:
cx.build_torus(m, n)
k = 2
#print(cx)
for trial in range(10):
flow = Flow(cx)
flow.build()
if argv.render:
flow.render(name="output")
break
chain = flow.morse_homology(1)
A, B = chain
BA = B * A
for key, v in BA.elements.items():
assert v % 2 == 0
#print(BA.todense())
Hzt = A.todense() % 2
Hz = Hzt.transpose()
Hx = B.todense() % 2
assert dot2(Hx, Hzt).sum() == 0
code = CSSCode(Hx=Hx, Hz=Hz)
#print("k =", code.k)
assert code.k == k, (code.k, k)
def __call__(self, other):
assert isinstance(other, CSSCode)
assert other.n * 2 == self.n
Lx, Lz, Hx, Tz, Hz, Tx, Gx, Gz = (other.Lx, other.Lz, other.Hx,
other.Tz, other.Hz, other.Tx,
other.Gx, other.Gz)
assert Gx is None
assert Gz is None
A = self.A.transpose()
LxLz = dot2(cat((Lx, Lz), axis=1), A)
HxTz = dot2(cat((Hx, Tz), axis=1), A)
TxHz = dot2(cat((Tx, Hz), axis=1), A)
n = self.n // 2
Lx, Lz = LxLz[:, :n], LxLz[:, n:]
Hx, Tz = HxTz[:, :n], HxTz[:, n:]
Tx, Hz = TxHz[:, :n], TxHz[:, n:]
code = CSSCode(Lx=Lx, Lz=Lz, Hx=Hx, Tz=Tz, Hz=Hz, Tx=Tx)
return code
def get_code(self):
self.check()
keys = self.keys
keymap = self.keymap
x_ops, z_ops = self.get_stabs()
n = len(keys)
mx = len(x_ops)
mz = len(z_ops)
Hx = zeros2(mx, n)
Hz = zeros2(mz, n)
for idx, stab in enumerate(x_ops):
for key in stab:
Hx[idx, keymap[key]] = 1
for idx, stab in enumerate(z_ops):
for key in stab:
Hz[idx, keymap[key]] = 1
code = CSSCode(Hx=Hx, Hz=Hz)
return code
def get_code(self, idx=0, build=True, check=True):
#print "get_code"
Hs = self.Hs
Hx = Hs[idx]
write("li:")
Hx = solve.linear_independent(Hx)
Hz = Hs[idx + 1].transpose()
write("li:")
Hz = solve.linear_independent(Hz)
#print(Hx.shape, Hz.shape)
if self.Ls:
Lz = self.Ls[idx]
#print "get_code:", Lz.shape
else:
Lz = None
#print shortstr(dot(Hx, Hz.transpose()))
#print "Hz:"
#print shortstr(Hz)
#print "Hx:"
#print shortstr(Hx)
from qupy.ldpc.css import CSSCode
code = CSSCode(Hx=Hx, Hz=Hz, Lz=Lz, build=build, check=check)
return code
def is_422_cat_selfdual(Hz, Hx, perm):
"concatenate with the [[4,2,2]] code and see if we get a self-dual code"
from numpy import alltrue, zeros, dot
import qupy.ldpc.solve
import bruhat.solve
qupy.ldpc.solve.int_scalar = bruhat.solve.int_scalar
from bruhat.solve import shortstrx, zeros2, dot2, array2, solve
from qupy.ldpc.css import CSSCode
Cout = CSSCode(Hz=Hz, Hx=Hx)
#print(Cout)
#Cin = CSSCode(Hz=array2([[1,1,1,1]]), Hx=array2([[1,1,1,1]]))
#print(Cin)
pairs = []
singles = []
for i in range(Cout.n):
j = perm[i]
if j < i:
continue
if i == j:
singles.append(i)
else:
pairs.append((i, j))
#print(singles, pairs)
M = len(singles) + 4 * len(pairs)
# encoding matrices
enc_z = zeros2(M, Cout.n)
enc_x = zeros2(M, Cout.n)
row = 0
for col in singles:
enc_z[row, col] = 1
enc_x[row, col] = 1
row += 1
H = []
for (i, j) in pairs:
enc_z[row, i] = 1 # 1010
enc_z[row + 2, i] = 1
enc_z[row, j] = 1 # 1100
enc_z[row + 1, j] = 1
enc_x[row, i] = 1 # 1100
enc_x[row + 1, i] = 1
enc_x[row, j] = 1 # 1010
enc_x[row + 2, j] = 1
h = array2([0] * M)
h[row:row + 4] = 1
H.append(h)
row += 4
assert row == M
#print(shortstrx(enc_z, enc_x))
Hz = dot2(enc_z, Cout.Hz.transpose()).transpose()
Hx = dot2(enc_x, Cout.Hx.transpose()).transpose()
assert alltrue(dot2(Hz, Hx.transpose()) == 0)
Hz = numpy.concatenate((Hz, H))
Hx = numpy.concatenate((Hx, H))
assert alltrue(dot2(Hz, Hx.transpose()) == 0)
C = CSSCode(Hz=Hz, Hx=Hx)
assert C.k == Cout.k
#print(C)
lhs = (solve(Hz.transpose(), Hx.transpose()) is not None)
rhs = (solve(Hx.transpose(), Hz.transpose()) is not None)
return lhs and rhs
def even_code():
p = argv.get("p", 7)
#assert (p%8) in [1, 7]
# equivalent to "2 (binary!) is a quadratic _residue mod p"
# eg. 7 17 23 31 41 47 71 73 79 89 97
def neginv(i):
if i == 0:
return p
if i == p:
return 0
for j in range(1, p):
if (i * j) % p == 1:
break
else:
assert 0
return (-j) % p
nonresidues = set(range(1, p))
residues = set()
for i in range(1, p):
j = (i * i) % p
if j not in residues:
residues.add(j)
nonresidues.remove(j)
print("residues:", residues)
print("non-residues:", nonresidues)
# extended binary quadratic _residue code
N = p + 1
G = zeros2(N, N)
G[p, :] = 1
for u in range(p):
G[u, p] = 0 if (p - 1) % 8 == 0 else 1
for v in range(p):
if u == v:
i = 0
elif (v - u) % p in residues:
i = 1
else:
i = 0
G[u, v] = i
G = linear_independent(G)
print("G =")
print(shortstr(G))
from qupy.ldpc.css import CSSCode
from qupy.ldpc.gallagher import classical_distance
G = G.astype(numpy.int32)
code = CSSCode(Hx=G, Hz=G)
print(code)
from bruhat.codes import strong_morthogonal
for genus in range(1, 4):
print("genus:", genus, "strong_morthogonal:",
strong_morthogonal(G, genus))
def double(G):
M, N = G.shape
DG = zeros2(M + 1, 2 * N)
DG[1:, 0:N] = G
DG[1:, N:2 * N] = G
DG[0, 0:N] = 1
DG = DG.astype(numpy.int32)
return DG
DG = G
DG = DG.astype(numpy.int32)
print("distance:", classical_distance(DG))
for _ in range(2):
DG = double(DG)
DG = linear_independent(DG)
print(shortstr(DG))
for genus in range(1, 5):
print("genus:", genus, "strong_morthogonal:",
strong_morthogonal(DG, genus))
code = CSSCode(Hx=DG, Hz=DG)
print(code)
def hypergraph_product(C, D, check=False):
print("hypergraph_product:", C.shape, D.shape)
print("distance:", classical_distance(C))
c0, c1 = C.shape
d0, d1 = D.shape
E1 = identity2(c0)
E2 = identity2(d0)
M1 = identity2(c1)
M2 = identity2(d1)
Hx0 = kron(M1, D.transpose()), kron(C.transpose(), M2)
Hx = numpy.concatenate(Hx0, axis=1) # horizontal concatenate
Hz0 = kron(C, E2), kron(E1, D)
#print("Hz0:", Hz0[0].shape, Hz0[1].shape)
Hz = numpy.concatenate(Hz0, axis=1) # horizontal concatenate
assert dot2(Hz, Hx.transpose()).sum() == 0
n = Hx.shape[1]
assert Hz.shape[1] == n
# ---------------------------------------------------
# Build Lx
KerC = find_kernel(C)
#KerC = min_span(KerC) # does not seem to matter... ??
assert KerC.shape[1] == c1
K = KerC.transpose()
E = identity2(d0)
print(shortstr(KerC))
print()
Lxt0 = kron(K, E), zeros2(c0 * d1, K.shape[1] * d0)
Lxt0 = numpy.concatenate(Lxt0, axis=0)
assert dot2(Hz, Lxt0).sum() == 0
K = find_kernel(D).transpose()
assert K.shape[0] == d1
E = identity2(c0)
Lxt1 = zeros2(c1 * d0, K.shape[1] * c0), kron(E, K)
Lxt1 = numpy.concatenate(Lxt1, axis=0)
assert dot2(Hz, Lxt1).sum() == 0
Lxt = numpy.concatenate((Lxt0, Lxt1), axis=1) # horizontal concatenate
Lx = Lxt.transpose()
assert dot2(Hz, Lxt).sum() == 0
# These are linearly dependent, but
# once we add stabilizers it will be reduced:
assert rank(Lx) == len(Lx)
if 0:
# ---------------------------------------------------
print(shortstr(Lx))
k = get_k(Lx, Hx)
print("k =", k)
left, right = [], []
draw = Draw(c0, c1, d0, d1)
cols = []
for j in range(d0): # col
col = []
for i in range(len(KerC)): # logical
op = Lx[i * d0 + j]
col.append(op)
if j == i:
draw.mark_xop(op)
if j < d0 / 2:
left.append(op)
else:
right.append(op)
cols.append(col)
draw.save("output.2")
left = array2(left)
right = array2(right)
print(get_k(left, Hx))
print(get_k(right, Hx))
return
# ---------------------------------------------------
# Build Lz
counit = lambda n: unit2(n).transpose()
K = find_cokernel(D) # matrix of row vectors
#E = counit(c1)
E = identity2(c1)
Lz0 = kron(E, K), zeros2(K.shape[0] * c1, c0 * d1)
Lz0 = numpy.concatenate(Lz0, axis=1) # horizontal concatenate
assert dot2(Lz0, Hx.transpose()).sum() == 0
K = find_cokernel(C)
#E = counit(d1)
E = identity2(d1)
Lz1 = zeros2(K.shape[0] * d1, c1 * d0), kron(K, E)
Lz1 = numpy.concatenate(Lz1, axis=1) # horizontal concatenate
Lz = numpy.concatenate((Lz0, Lz1), axis=0)
assert dot2(Lz, Hx.transpose()).sum() == 0
overlap = 0
for lx in Lx:
for lz in Lz:
w = (lx * lz).sum()
overlap = max(overlap, w)
assert overlap <= 1, overlap
#print("max overlap:", overlap)
assert rank(Hx) == len(Hx)
assert rank(Hz) == len(Hz)
mx = len(Hx)
mz = len(Hz)
# ---------------------------------------------------
Lxs = []
for op in Lx:
op = (op + Hx) % 2
Lxs.append(op)
LxHx = numpy.concatenate(Lxs)
LxHx = row_reduce(LxHx)
print("LxHx:", len(LxHx))
assert LxHx.shape[1] == n
print(len(intersect(LxHx, Hx)), mx)
assert len(intersect(LxHx, Hx)) == mx
Lzs = []
for op in Lz:
op = (op + Hz) % 2
Lzs.append(op)
LzHz = numpy.concatenate(Lzs)
LzHz = row_reduce(LzHz)
print("LzHz:", len(LzHz))
assert LzHz.shape[1] == n
# ---------------------------------------------------
# Remove excess logops.
# print("remove_dependent")
#
# # -------- Lx
#
# Lx, Lx1 = mk_disjoint_logops(Lx, Hx)
#
# # -------- Lz
#
# Lz, Lz1 = mk_disjoint_logops(Lz, Hz)
# --------------------------------
# independent_logops for Lx
k = get_k(Lx, Hx)
idxs0, idxs1 = [], []
for j in range(d0): # col
for i in range(c1):
idx = j + i * d0
if j < d0 // 2:
idxs0.append(idx)
else:
idxs1.append(idx)
Lx0 = in_support(LxHx, idxs0)
Lx0 = independent_logops(Lx0, Hx)
k0 = (len(Lx0))
Lx1 = in_support(LxHx, idxs1)
Lx1 = independent_logops(Lx1, Hx)
k1 = (len(Lx1))
assert k0 == k1 == k, (k0, k1, k)
# --------------------------------
# independent_logops for Lz
idxs0, idxs1 = [], []
for j in range(d0): # col
for i in range(c1):
idx = j + i * d0
if i < c1 // 2:
idxs0.append(idx)
else:
idxs1.append(idx)
Lz0 = in_support(LzHz, idxs0)
Lz0 = independent_logops(Lz0, Hz)
k0 = (len(Lz0))
Lz1 = in_support(LzHz, idxs1)
Lz1 = independent_logops(Lz1, Hz)
k1 = (len(Lz1))
assert k0 == k1 == k, (k0, k1, k)
# ---------------------------------------------------
#
#assert eq2(dot2(Lz, Lxt), identity2(k))
assert mx + mz + k == n
print("mx = %d, mz = %d, k = %d : n = %d" % (mx, mz, k, n))
# ---------------------------------------------------
#
# if Lx1 is None:
# return
#
# if Lz1 is None:
# return
# ---------------------------------------------------
#
op = zeros2(n)
for lx in Lx0:
for lz in Lz0:
lxz = lx * lz
#print(lxz)
#print(op.shape, lxz.shape)
op += lxz
for lx in Lx1:
for lz in Lz1:
lxz = lx * lz
#print(lxz)
#print(op.shape, lxz.shape)
op += lxz
idxs = numpy.where(op)[0]
print("correctable region size = %d" % len(idxs))
#print(op)
#print(idxs)
Lx, Lz = Lx0, Lz0
Lxs = []
for op in Lx:
op = (op + Hx) % 2
Lxs.append(op)
LxHx = numpy.concatenate(Lxs)
LxHx = row_reduce(LxHx)
assert LxHx.shape[1] == n
Lzs = []
for op in Lz:
op = (op + Hz) % 2
Lzs.append(op)
LzHz = numpy.concatenate(Lzs)
LzHz = row_reduce(LzHz)
assert LzHz.shape[1] == n
if argv.draw:
do_draw(**locals())
good = is_correctable(n, idxs, LxHx, LzHz)
assert good
print("good")
# ---------------------------------------------------
#
if argv.code:
print("code = CSSCode()")
code = CSSCode(Hx=Hx,
Hz=Hz,
Lx=Lx,
Lz=Lz,
check=True,
verbose=False,
build=True)
print(code)
#print(code.weightstr())
if check:
U = solve(Lx.transpose(), code.Lx.transpose())
assert U is not None
#print(U.shape)
assert eq2(dot2(U.transpose(), Lx), code.Lx)
#print(shortstr(U))
if 0:
Lx, Lz = code.Lx, code.Lz
print("Lx:", Lx.shape)
print(shortstr(Lx))
print("Lz:", Lz.shape)
print(shortstr(Lz))
def main():
m = argv.get('m', 6) # constraints (rows)
n = argv.get('n', 16) # bits (cols)
j = argv.get('j', 3) # column weight (left degree)
k = argv.get('k', 8) # row weight (constraint weight; right degree)
#assert 2*m<=n, "um?"
max_iter = argv.get('max_iter', 200)
verbose = argv.verbose
check = argv.get('check', False)
strop = shortstr
Lx = None
Lz = None
Hx = None
Tz = None
Hz = None
Tx = None
build = argv.get('build', False)
logops_only = argv.get("logops_only", True)
code = None
if argv.code == 'ldpc':
H = ldpc(m, n, j, k)
code = CSSCode(Hz=H, Hx=zeros2(0, n))
elif argv.code == 'cycle':
#n = argv.get('n', 20)
#m = argv.get('m', 18)
row = str(argv.get('H', '1101'))
H = []
for i in range(n):
h = [0] * n
for j, c in enumerate(row):
h[(i + j) % n] = int(c)
H.append(h)
delta = n - m
for i in range(delta):
H.pop(i * n // delta - i)
# while len(H) > m:
# idx = randint(0, len(H)-1)
# H.pop(idx)
Hz = array2(H)
print(shortstr(Hz))
#print shortstr(solve.row_reduce(Hz))
# code = CSSCode(Hz=Hz)
# print
# print code
# print code.weightstr()
#
# decoder = StarDynamicDistance(code)
# L = decoder.find(verbose=verbose)
# print shortstr(L)
# print "distance:", L.sum()
# return
elif argv.code == "opticycle":
code = opticycle(m, n)
H = Hz = code.Hz
#return
elif argv.code == 'tree':
k = argv.get('k', 5)
n = 2**k + 1
code = build_tree(45)
print(code)
# graph = Graph()
# for i in range(H.shape[0]):
# edge = list(numpy.where(H[i])[0])
# #print edge,
# for i0 in edge:
# for i1 in edge:
# if i0!=i1:
# graph.add_edge(i0, i1)
#
# leaves = [idx for idx in range(n) if H[:, idx].sum()<=1]
# print leaves
#
#
# k = len(leaves)//2
# print graph.metric(leaves[1], leaves[k])
# return
# for i in range(k-1):
# #i0 = poprand(leaves)
# #i1 = poprand(leaves)
# u = zeros2(1, n)
# u[0, leaves[i]] = 1
# u[0, leaves[i+k]] = 1
# # what about picking three leaves?
# print (leaves[i], leaves[i+k]),
# H = append2(H, u)
# print
#
# # if we take all the leaves we get degenerate...
# leaves = [idx for idx in range(n) if H[:, idx].sum()<=1]
# print "leaves:", leaves
#
# #print shortstr(H)
# #print
# #print shortstr(solve.row_reduce(H))
# code = CSSCode(Hz=H)
# print code
# print code.weightstr()
# print numpy.where(code.Lx[3])
#
# return
elif argv.code == 'bicycle':
from qupy.ldpc.bicycle import Bicycle_LDPC
print("Bicycle_LDPC(%s, %s, %s, %s)" % (m, n, j, k))
b = Bicycle_LDPC(m, n, j, k)
Hx = Hz = b.H
elif argv.code == 'toric':
from qupy.ldpc.toric import Toric2D
l = argv.get('l', 8)
li = argv.get('li', l)
lj = argv.get('lj', l)
si = argv.get('si', 0)
sj = argv.get('sj', 0)
toric = Toric2D(li, lj, si, sj)
Hx, Hz = toric.Hx, toric.Hz
strop = toric.strop
#print("Hx:")
#print(shortstr(Hx))
#print("Lx:")
#print(shortstr(toric.Lx))
code = CSSCode(Hx=Hx, Hz=Hz, Lx=toric.Lx, Lz=toric.Lz)
elif argv.code == 'cylinder':
from qupy.ldpc.toric import Cylinder
l = argv.get('l', 8)
li = argv.get('li', l)
lj = argv.get('lj', l)
si = argv.get('si', 0)
sj = argv.get('sj', 0)
assert si == 0
surface = Cylinder(li, lj, sj)
Hx, Hz = surface.Hx, surface.Hz
strop = surface.strop
#print("Hx:")
#print(shortstr(Hx))
#print("Lx:")
#print(shortstr(surface.Lx))
code = CSSCode(Hx=Hx, Hz=Hz)
elif argv.code == 'torichie':
from qupy.ldpc.toric import Toric2DHie
l = argv.get('l', 8)
toric = Toric2DHie(l)
Hx, Hz = toric.Hx, toric.Hz
elif argv.code == 'surface':
from qupy.ldpc.toric import Surface
l = argv.get('l', 8)
si = argv.get('si', 0) # todo
sj = argv.get('sj', 0)
surface = Surface(l)
#Hx, Hz = surface.Hx, surface.Hz
#strop = surface.strop
#print shortstr(Hx)
code = surface.get_code()
elif argv.code == 'toric3':
from qupy.ldpc.toric import Toric3D
l = argv.get('l', 8)
toric = Toric3D(l)
Hx, Hz = toric.Hx, toric.Hz
strop = toric.strop
#print shortstr(Hx)
elif argv.code == 'gcolor':
from qupy.ldpc.gcolor import Lattice
l = argv.get('l', 1)
lattice = Lattice(l)
#code = lattice.build_code()
G = lattice.Hx
print(shortstr(G))
m, n = G.shape
G1 = zeros2(m + 1, n + 1)
G1[1:, 1:] = G
G1[0, :] = 1
print()
print(shortstr(G1))
for genus in range(1, 5):
print(genus, strong_morthogonal(G1, genus))
code = CSSCode(Hx=G1, Hz=G1)
elif argv.code == 'self_ldpc':
from qupy.ldpc.search import SelfContainingLDPC_Code
ldpc_code = SelfContainingLDPC_Code(m, n, j, k)
ldpc_code.search(max_step=argv.get('max_step', None), verbose=verbose)
#print ldpc_code
H = ldpc_code.H
print("H:")
print(shortstr(H))
H = solve.linear_independent(H)
Hx = Hz = H
code = CSSCode(Hx=Hx, Hz=Hz)
elif argv.code == 'cssldpc':
from qupy.ldpc.search import CSS_LDPC_Code
ldpc_code = CSS_LDPC_Code(m, n, j, k)
ldpc_code.search(max_step=argv.get('max_step', None), verbose=verbose)
#print ldpc_code
Hx, Hz = ldpc_code.Hx, ldpc_code.Hz
#print "Hx:"
#print shortstr(Hx)
Hx = solve.linear_independent(Hx)
Hz = solve.linear_independent(Hz)
#Hx = Hz = H
code = CSSCode(Hx=Hx, Hz=Hz)
elif argv.code == "hpack":
code = hpack(n, j=j, k=k, check=check, verbose=verbose)
elif argv.code == 'randldpc':
mz = argv.get('mz', n // 3)
rw = argv.get('rw', 12) # row weight
code = randldpc(n, mz, rw, check=check, verbose=verbose)
elif argv.code == 'randcss':
mx = argv.get('mx', n // 3)
mz = argv.get('mz', n // 3)
distance = argv.get("code_distance")
code = randcss(n,
mx,
mz,
distance=distance,
check=check,
verbose=verbose)
elif argv.code == 'sparsecss':
mx = argv.get('mx', n // 3)
mz = argv.get('mz', n // 3)
weight = argv.get('weight', 4)
code = sparsecss(n, mx, mz, weight, check=check, verbose=verbose)
elif argv.code == 'ensemble':
mx = argv.get('mx', n // 3)
mz = argv.get('mz', mx)
rw = argv.get('rw', 12) # row weight
maxw = argv.get('maxw', 4 * rw)
C = argv.get("C", 100)
code = ensemble.build(n,
mx,
mz,
rw,
maxw,
C,
check=check,
verbose=verbose)
elif argv.code == "rm" or argv.code == "reed_muller":
from qupy.ldpc import reed_muller
r = argv.get("r", 1)
m = argv.get("m", 4)
puncture = argv.puncture
cl_code = reed_muller.build(r, m, puncture)
G = cl_code.G
G = array2([row for row in G if row.sum() % 2 == 0])
code = CSSCode(Hx=G, Hz=G)
elif argv.code == "qrm":
from qupy.ldpc.gallagher import get_code, hypergraph_product
from qupy.ldpc import reed_muller
r = argv.get("r", 1)
m = argv.get("m", 4)
puncture = argv.puncture
cl_code = reed_muller.build(r, m, puncture)
H = cl_code.G
H = array2([row for row in H if row.sum() % 2 == 0])
print(shortstr(H))
m, n = 4, 4
J = zeros2(m, n)
for i in range(m):
J[i, i] = 1
J[i, (i + 1) % n] = 1
print()
print(shortstr(J))
Hx, Hz, Lx, Lz = hypergraph_product(J, H)
code = CSSCode(Hx=Hx, Hz=Hz, Lx=Lx, Lz=Lz)
#print(code.weightstr())
#print("Hz:")
#print(shortstr(code.Hz))
#print("Hx:")
#print(shortstr(code.Hx))
elif argv.code == "qgall":
from qupy.ldpc.gallagher import make_gallagher, hypergraph_product
l = argv.get("l", 3) # column weight
m = argv.get("m", 4) # row weight
n = argv.get("n", 8) # cols
r = argv.get("r", n * l // m) # rows
dist = argv.get("dist", 4) # distance
H = make_gallagher(r, n, l, m, dist)
#print(H)
rm = argv.get("rm", dist)
J = zeros2(rm, rm)
for i in range(rm):
J[i, i] = 1
J[i, (i + 1) % rm] = 1
#print(J)
Hx, Hz, Lx, Lz = hypergraph_product(J, H)
code = CSSCode(Hx=Hx, Hz=Hz, Lx=Lx, Lz=Lz)
#print(code.weightstr())
#print("Hz:")
#print(shortstr(code.Hz))
#print("Hx:")
#print(shortstr(code.Hx))
elif argv.code == "qr7":
H = parse("""
...1111
.11..11
1.1.1.1
""")
code = CSSCode(Hx=H, Hz=H)
elif argv.code == "golay" or argv.code == "qr23":
H = parse("""
1.1..1..11111..........
1111.11.1....1.........
.1111.11.1....1........
..1111.11.1....1.......
...1111.11.1....1......
1.1.1.111..1.....1.....
1111...1..11......1....
11.111...11........1...
.11.111...11........1..
1..1..11111..........1.
.1..1..11111..........1
""")
code = CSSCode(Hx=H, Hz=H)
elif argv.code == "dgolay": # double golay code (tri-orthogonal)
H = parse("""
111111111111111111111111........................
.1111.1.11..11..1.1....1.1111.1.11..11..1.1....1
..1111.1.11..11..1.1...1..1111.1.11..11..1.1...1
...1111.1.11..11..1.1..1...1111.1.11..11..1.1..1
....1111.1.11..11..1.1.1....1111.1.11..11..1.1.1
.....1111.1.11..11..1.11.....1111.1.11..11..1.11
1.....1111.1.11..11..1.11.....1111.1.11..11..1.1
.1.....1111.1.11..11..11.1.....1111.1.11..11..11
1.1.....1111.1.11..11..11.1.....1111.1.11..11..1
.1.1.....1111.1.11..11.1.1.1.....1111.1.11..11.1
..1.1.....1111.1.11..111..1.1.....1111.1.11..111
1..1.1.....1111.1.11..111..1.1.....1111.1.11..11
11..1.1.....1111.1.11..111..1.1.....1111.1.11..1
""")
code = CSSCode(Hx=H, Hz=H)
elif argv.code == "dham": # double hamming code (tri-orthogonal)
H = parse("""
11111111........
.11.1..1.11.1..1
..11.1.1..11.1.1
...11.11...11.11
1...11.11...11.1
""")
code = CSSCode(Hx=H, Hz=H)
elif argv.code == "ddham": # double double hamming code
H = parse("""
1111111111111111................
11111111........11111111........
.11.1..1.11.1..1.11.1..1.11.1..1
..11.1.1..11.1.1..11.1.1..11.1.1
...11.11...11.11...11.11...11.11
1...11.11...11.11...11.11...11.1
""")
code = CSSCode(Hx=H, Hz=H)
elif argv.code == "qr31":
H = parse("""
1..1..1.1...11.11..............
11.11.1111..1.11.1.............
11111111.11.1.....1............
.11111111.11.1.....1...........
..11111111.11.1.....1..........
...11111111.11.1.....1.........
1..111.1.1111.11......1........
11.111....11...........1.......
.11.111....11...........1......
..11.111....11...........1.....
...11.111....11...........1....
....11.111....11...........1...
1..1.1...11.11..............1..
.1..1.1...11.11..............1.
..1..1.1...11.11..............1
""")
code = CSSCode(Hx=H, Hz=H)
elif argv.code == "qr17":
# not self-dual
Hz = parse("""
.11.1...11...1.11
1.11.1...11...1.1
11.11.1...11...1.
.11.11.1...11...1
1.11.11.1...11...
.1.11.11.1...11..
..1.11.11.1...11.
...1.11.11.1...11
1...1.11.11.1...1
11...1.11.11.1...
.11...1.11.11.1..
..11...1.11.11.1.
...11...1.11.11.1
1...11...1.11.11.
.1...11...1.11.11
1.1...11...1.11.1
11.1...11...1.11.
""")
Hx = parse("""
...1.111..111.1..
11.1.....1.111..1
111..111.1.....1.
....1.111..111.1.
111.1.....1.111..
.111..111.1.....1
.....1.111..111.1
.111.1.....1.111.
1.111..111.1.....
1.....1.111..111.
..111.1.....1.111
.1.111..111.1....
.1.....1.111..111
1..111.1.....1.11
..1.111..111.1...
1.1.....1.111..11
11..111.1.....1.1
""")
Hz = solve.linear_independent(Hz)
Hx = solve.linear_independent(Hx)
code = CSSCode(Hx=Hx, Hz=Hz)
elif argv.code == "qr41":
# not self-dual
Hz = parse("""
.11.11..111.....1.1.11.1.1.....111..11.11
1.11.11..111.....1.1.11.1.1.....111..11.1
11.11.11..111.....1.1.11.1.1.....111..11.
.11.11.11..111.....1.1.11.1.1.....111..11
1.11.11.11..111.....1.1.11.1.1.....111..1
11.11.11.11..111.....1.1.11.1.1.....111..
.11.11.11.11..111.....1.1.11.1.1.....111.
..11.11.11.11..111.....1.1.11.1.1.....111
1..11.11.11.11..111.....1.1.11.1.1.....11
11..11.11.11.11..111.....1.1.11.1.1.....1
111..11.11.11.11..111.....1.1.11.1.1.....
.111..11.11.11.11..111.....1.1.11.1.1....
..111..11.11.11.11..111.....1.1.11.1.1...
...111..11.11.11.11..111.....1.1.11.1.1..
....111..11.11.11.11..111.....1.1.11.1.1.
.....111..11.11.11.11..111.....1.1.11.1.1
1.....111..11.11.11.11..111.....1.1.11.1.
.1.....111..11.11.11.11..111.....1.1.11.1
1.1.....111..11.11.11.11..111.....1.1.11.
.1.1.....111..11.11.11.11..111.....1.1.11
""")
Hx = parse("""
...1..11...11111.1.1..1.1.11111...11..1..
1111...11..1.....1..11...11111.1.1..1.1.1
111.1.1..1.1.11111...11..1.....1..11...11
....1..11...11111.1.1..1.1.11111...11..1.
11111...11..1.....1..11...11111.1.1..1.1.
1111.1.1..1.1.11111...11..1.....1..11...1
.....1..11...11111.1.1..1.1.11111...11..1
.11111...11..1.....1..11...11111.1.1..1.1
11111.1.1..1.1.11111...11..1.....1..11...
1.....1..11...11111.1.1..1.1.11111...11..
1.11111...11..1.....1..11...11111.1.1..1.
.11111.1.1..1.1.11111...11..1.....1..11..
.1.....1..11...11111.1.1..1.1.11111...11.
.1.11111...11..1.....1..11...11111.1.1..1
..11111.1.1..1.1.11111...11..1.....1..11.
..1.....1..11...11111.1.1..1.1.11111...11
1.1.11111...11..1.....1..11...11111.1.1..
...11111.1.1..1.1.11111...11..1.....1..11
1..1.....1..11...11111.1.1..1.1.11111...1
.1.1.11111...11..1.....1..11...11111.1.1.
""")
code = CSSCode(Hz=Hz, Hx=Hx)
elif argv.code == "qr47":
H = parse("""
1...11..11.11..1..1.1..11......................
11..1.1.1.11.1.11.1111.1.1.....................
111.1..11.....111111.111..1....................
11111......11...11.1..1....1...................
.11111......11...11.1..1....1..................
1.11..1.11.11111...111.1.....1.................
11.1.1.11.11.11.1.1..111......1................
111..11.......1..1111.1........1...............
.111..11.......1..1111.1........1..............
1.11.1.1.1.11..11.11.111.........1.............
11.1.11..111.1.11111..1...........1............
.11.1.11..111.1.11111..1...........1...........
1.111..1.1...1...1.1.1.1............1..........
11.1.....1111.11......11.............1.........
111..1..111..1..1.1.1.................1........
.111..1..111..1..1.1.1.................1.......
..111..1..111..1..1.1.1.................1......
...111..1..111..1..1.1.1.................1.....
1.....1.1..1.111.11...11..................1....
11..11.11..1..1.1..11......................1...
.11..11.11..1..1.1..11......................1..
..11..11.11..1..1.1..11......................1.
...11..11.11..1..1.1..11......................1
""")
code = CSSCode(Hx=H, Hz=H)
elif argv.code == "qr71":
H = parse("""
1.1.1.11.1...11..11.....1....1...1111..................................
1111111.111..1.1.1.1....11...11..1...1.................................
.1111111.111..1.1.1.1....11...11..1...1................................
..1111111.111..1.1.1.1....11...11..1...1...............................
1.11.1..1..11.1.11..1.1.1..111..1.11....1..............................
1111...1....1.11.....1.111..1.1...1......1.............................
.1111...1....1.11.....1.111..1.1...1......1............................
1..1.111.....1..1.1....11111.11.1111.......1...........................
111.....11...1....11.....1111111............1..........................
.111.....11...1....11.....1111111............1.........................
..111.....11...1....11.....1111111............1........................
...111.....11...1....11.....1111111............1.......................
....111.....11...1....11.....1111111............1......................
1.1.11...1.......1.....1.....1111................1.....................
.1.1.11...1.......1.....1.....1111................1....................
..1.1.11...1.......1.....1.....1111................1...................
...1.1.11...1.......1.....1.....1111................1..................
1.1....11.....1..11..1..1..1.1.......................1.................
.1.1....11.....1..11..1..1..1.1.......................1................
..1.1....11.....1..11..1..1..1.1.......................1...............
...1.1....11.....1..11..1..1..1.1.......................1..............
....1.1....11.....1..11..1..1..1.1.......................1.............
.....1.1....11.....1..11..1..1..1.1.......................1............
......1.1....11.....1..11..1..1..1.1.......................1...........
1.1.1.1......1.1.11..1...1..11.1.1.1........................1..........
1111111..1...1..11.1..1.1.1...1.11.1.........................1.........
11.1.1...11..1......1..111.1.1.1...1..........................1........
11.....1.111.1...11..1...11.111.1111...........................1.......
11..1.11111111...1.1..1.1.11..11................................1......
.11..1.11111111...1.1..1.1.11..11................................1.....
..11..1.11111111...1.1..1.1.11..11................................1....
...11..1.11111111...1.1..1.1.11..11................................1...
....11..1.11111111...1.1..1.1.11..11................................1..
1.1.11.1...11..11.....1....1...1111..................................1.
.1.1.11.1...11..11.....1....1...1111..................................1
""")
code = CSSCode(Hx=H, Hz=H)
elif argv.code == "rm_2_5_p":
H = parse("""
...11111111....................
.11..1111..11..................
1.1.1.11.1.1.1.................
11.1..1.11.1..1................
...1111........1111............
.11..11........11..11..........
1.1.1.1........1.1.1.1.........
11.1..1.........11.1..1........
.11111111......11......11......
1.111111.1.....1.1.....1.1.....
11.1111.11......11.....1..1....
111.1111...1...1...1...1...1...
1111.11.1..1....1..1...1....1..
11111.1..1.1.....1.1...1.....1.
111111.111.1...111.1...1......1
""")
code = CSSCode(Hx=H, Hz=H)
elif argv.code == "to_16_6": # triorthogonal
H = parse("""
........11111111
....1111....1111
11111111........
..11..11..11..11
.1.1.1.1.1.1.1.1
1..1.11..11.1..1
""") # distance = 4
code = CSSCode(Hx=H, Hz=H)
elif argv.code == "B11": # Pless 1971, punctured B12
H = parse("""
.1111......
...1111....
.....1111..
.......1111
1.1.1.1.1.1
""")
from qupy.ldpc.gallagher import classical_distance
print(classical_distance(H))
code = CSSCode(Hx=H, Hz=H)
elif argv.code == "glue_classical_self":
from qupy.ldpc.glue import glue_classical, glue_classical_self
H = glue_classical_self()
H = H.copy()
code = CSSCode(Hx=H, Hz=H)
#if argv.classical_distance:
# from qupy.ldpc.gallagher import classical_distance
# print("distance:", classical_distance(H))
elif argv.code == "randselfdual":
m = argv.get("m", 4)
n = argv.get("n", 8)
rw = argv.get("rw", 4)
code = randselfdual(m, n, rw)
else:
from qupy.ldpc.gallagher import get_code
code = get_code(argv.code)
if argv.truncate:
idx = argv.truncate
Hx = Hx[:idx]
Hz = Hz[:idx]
for arg in argv:
if arg.endswith('.ldpc'):
code = CSSCode.load(arg,
build=build,
check=check,
rebuild=argv.rebuild)
if argv.rebuild:
code.save(arg)
break
if code is None:
code = CSSCode(Lx,
Lz,
Hx,
Tz,
Hz,
Tx,
build=build,
check=check,
verbose=verbose,
logops_only=logops_only)
if argv.dual:
print("dual code...")
code = code.dual(build=build)
# take several copies of the code..
mul = argv.get("mul", 1)
code = mul * code
if argv.classical_product:
H1 = code.Hx
H2 = H1.transpose()
Hx, Hz = hypergraph_product(H1, H2)
code = CSSCode(Hx=Hx, Hz=Hz)
if argv.product:
codes = code.product(code.dual())
for _code in codes:
print(_code)
if _code.k:
_code.save(stem="prod")
if argv.verbose != 0:
print(code)
#print code.longstr()
#print code.weightstr()
print(code.weightsummary())
if argv.shorten:
code.shorten()
print(code)
print(code.weightsummary())
if argv.prune:
print("pruning:", argv.prune)
code.prune_xlogops(argv.prune)
print(code)
print(code.weightsummary())
if argv.split:
for i in range(4):
code = x_split(code, build=False)
print(code)
print(code.weightsummary())
code = code.dual()
code = x_split(code, build=False)
code = code.dual()
print(code)
print(code.weightsummary())
code.save(stem="split")
if argv.save:
code.save(argv.save)
if argv.symplectic:
i = randint(0, code.mz - 1)
j = randint(0, code.k - 1)
code.Lz[j] += code.Hz[i]
code.Lz[j] %= 2
code.Tx[i] -= code.Lx[j]
code.Tx[i] %= 2
code.do_check()
return
if argv.showcode:
print(code.longstr())
if argv.todot:
todot(code.Hz)
return
if argv.tanner:
Hx = code.Hx
graph = Tanner(Hx)
#graph.add_dependent()
depth = 3
graphs = [graph]
for i in range(depth):
_graphs = []
for g in graphs:
left, right = g.split()
_graphs.append(left)
_graphs.append(right)
graphs = _graphs
print("split", graphs)
k = code.Lx.shape[0]
op = code.Lx[1]
#op = (op + code.Tx[20])%2
print(strop(op), op.sum())
print()
for i in range(Hx.shape[0]):
if random() <= 0.5:
op = (op + Hx[i]) % 2
#print shortstr(op), op.sum()
print(strop(op), op.sum())
print()
#for graph in [left, right]:
for graph in graphs * 2:
#op = graph.minimize(op, verbose=True)
op = graph.localmin(op, verbose=True)
print(strop(op), op.sum())
print()
#op = graph.localmin(op)
#print strop(op), op.sum()
#print
#print shortstr(op), op.sum()
return
if argv.distance == 'star':
decoder = StarDynamicDistance(code)
L = decoder.find(verbose=verbose)
print(shortstr(L))
print("distance <=", L.sum())
elif argv.distance == 'stab':
d = random_distance_stab(code)
print("distance <=", d)
elif argv.distance == 'pair':
d = pair_distance(code)
print("distance <=", d)
elif argv.distance == 'free':
d = free_distance(code)
print("distance <=", d)
elif argv.distance == 'lookup':
d = lookup_distance(code)
if d <= 4:
print("distance =", d)
else:
print("distance <=", d)
if type(argv.distance) == str:
return
if argv.get('exec'):
exec(argv.get('exec'))
N = argv.get('N', 0)
p = argv.get('p', 0.01)
weight = argv.weight
#assert code.Tx is not None, "use code.build ?"
decoder = get_decoder(argv, argv.decode, code)
if decoder is None:
return
if argv.whack:
whack(code, decoder, p, N, argv.get("C0", 10),
argv.get("error_rate", 0.05), argv.get("mC", 1.2), verbose, argv)
return
if argv.noerr:
print("redirecting stderr to stderr.out")
fd = os.open("stderr.out", os.O_CREAT | os.O_WRONLY)
os.dup2(fd, 2)
decoder.strop = strop
print("decoder:", decoder.__class__.__name__)
n_ranks = numpy.zeros((code.n, ), dtype=numpy.float64)
n_record = []
k_ranks = numpy.zeros((code.k, ), dtype=numpy.float64)
k_record = []
failures = open(argv.savefail, 'w') if argv.savefail else None
if argv.loadfail:
loadfail = open(argv.loadfail)
errs = loadfail.readlines()
N = len(errs)
newHx = []
newHz = []
distance = code.n
count = 0
failcount = 0
nonuniq = 0
if argv.weight1:
# run through all weight=1 errors
N = code.n
if argv.weight2:
# run through all weight=1 errors
N = code.n**2
for i in range(N):
# We use Hz to look at X type errors (bitflip errors)
if argv.loadfail:
err_op = parse(errs[i])
err_op.shape = (code.n, )
elif argv.weight1:
err_op = zeros2(code.n)
err_op[i % code.n] = 1
elif argv.weight2:
err_op = zeros2(code.n)
ai = i % code.n
bi = (i // code.n)
err_op[ai] = 1
err_op[bi] = 1
elif weight is not None:
err_op = zeros2(code.n)
r = 0
while r < weight:
idx = randint(0, code.n - 1)
if err_op[idx] == 0:
err_op[idx] = 1
r += 1
#print err_op
else:
err_op = ra.binomial(1, p, (code.n, ))
err_op = err_op.astype(numpy.int32)
# err_op = parse("..............................")
# err_op.shape = (err_op.shape[1],)
write(str(err_op.sum()))
#print err_op.shape
s = dot2(code.Hz, err_op)
write(":s%d:" % s.sum())
op = decoder.decode(p, err_op, verbose=verbose, argv=argv)
c = 'F'
success = False
if op is not None:
op = (op + err_op) % 2
# Should be a codeword of Hz (kernel of Hz)
if dot2(code.Hz, op).sum() != 0:
print(dot2(code.Hz, op))
print("\n!!!!! BUGBUG !!!!!", sparsestr(err_op))
continue
write("%d:" % op.sum())
#print "is_stab:"
#print strop(op)
# Are we in the image of Hx ? If so, then success.
#success = code.is_stab(op)
success = dot2(code.Lz, op).sum() == 0
if success and op.sum():
nonuniq += 1
# print "\n", shortstr(err_op)
# return
c = '.' if success else 'x'
if argv.k_rank:
# XX this does not work very well...
a = dot2(code.Lz, op)
assert (a.sum() == 0) == success
if not success:
#r = -1. // (a.sum()**0.5) # sqrt ??
r = -1. / a.sum()
k_ranks += r * a
else:
#r = 1. / (code.k**0.5)
r = 1. / code.k
k_ranks += r * a
k_record.append((a, success))
if op.sum() and not success:
distance = min(distance, op.sum())
#if op.sum() == 2:
# print()
# print("main:")
# print(shortstr(op))
# print()
# print(strop(op))
if argv.minop and argv.minop >= op.sum():
a = dot2(code.Lz, op)
print()
print(sparsestr(a))
if not success and argv.addstabs and op.sum() <= argv.addstabs:
#write("%d"%op.sum())
print((sparsestr(op)))
newHx.append(op)
A = numpy.concatenate((code.Lx, code.Hx))
c = solve.solve(A.transpose(), op.transpose()).transpose()
cL = c[:code.k]
zstab = dot2(cL, code.Lz)
print(shortstr(zstab))
graph = Tanner(code.Hz)
zstab = graph.minimize(zstab, target=8, verbose=True)
print(shortstr(zstab))
newHz.append(zstab)
break
# Hz, Hx = code.Hz, append2(code.Hx, op)
# #if len(Hz) < len(Hx):
# # Hx, Hz = Hz, Hx
# print Hx.shape, Hz.shape
# code = CSSCode(Hx=Hx, Hz=Hz)
# if len(Hz) < len(Hx):
# code = code.dual()
# decoder = get_decoder(argv, argv.decode, code)
# print
# print code
# print code.weightsummary()
# code.save("addstabs_%d_%d_%d.ldpc"%(code.n, code.k, code.distance))
if not success and argv.showfail:
print()
print("FAIL:")
print(shortstr(err_op))
else:
failcount += 1
if failures:
print(shortstr(err_op), file=failures)
failures.flush()
if argv.n_rank:
r = 2. * int(success) - 1
#print "r =", r
if err_op.sum():
r /= err_op.sum()
#print r
#print r*err_op
n_ranks += r * err_op
n_record.append((err_op, success))
write(c + ' ')
count += success
if hasattr(decoder, 'fini'):
decoder.fini()
if N:
print()
print(datestr)
print(argv)
print("error rate = %.8f" % (1. - 1. * count / (i + 1)))
print("fail rate = %.8f" % (1. * failcount / (i + 1)))
print("nonuniq = %d" % nonuniq)
print("distance <= %d" % distance)
if argv.n_rank:
#n_ranks //= N
n_ranks = list(enumerate(n_ranks))
n_ranks.sort(key=lambda item: -item[1])
#print [r[0] for r in n_ranks]
print(' '.join('%d:%.2f' % r for r in n_ranks))
#print min(r[1] for r in n_ranks)
#print max(r[1] for r in n_ranks)
A = numpy.array([rec[0] for rec in n_record])
b = numpy.array([rec[1] for rec in n_record])
print(A.shape, b.shape)
sol = lstsq(A, b)
x, res, rk, s = sol
#print x
for i, val in enumerate(x):
if val < 0:
print(i, end=' ')
print()
if argv.k_rank:
#k_ranks //= N
k_ranks = list(enumerate(k_ranks))
k_ranks.sort(key=lambda item: -item[1])
#print [r[0] for r in k_ranks]
print(' '.join('%d:%.2f' % r for r in k_ranks))
#print ' '.join(str(r) for r in k_ranks)
#print min(r[1] for r in k_ranks)
#print max(r[1] for r in k_ranks)
A = numpy.array([rec[0] for rec in k_record])
b = numpy.array([rec[1] for rec in k_record])
#print A.shape, b.shape
sol = lstsq(A, b)
x, res, rk, s = sol
#print x
xs = list(enumerate(x))
xs.sort(key=lambda item: item[1])
print(' '.join('%d:%.2f' % item for item in xs))
if argv.addstabs and newHz:
Hz = append2(code.Hz, newHz[0])
code = CSSCode(Hx=code.Hx, Hz=Hz)
code.save(stem="addstabs")
print(code)
print(code.weightsummary())
elif argv.addstabs and newHx: # and newHx.shape[0]>code.Hx.shape[0]:
newHx = array2(newHx)
newHx = numpy.concatenate((code.Hx, newHx))
#print shortstr(newHx)
#print
Hx = solve.linear_independent(newHx)
#print shortstr(Hx)
#print
code = CSSCode(Hx=Hx, Hz=code.Hz)
code.save(stem="addstabs")
print(code)
print(code.weightsummary())
def test_symplectic():
n = 3
I = Matrix.identity(n)
for idx in range(n):
for jdx in range(n):
if idx == jdx:
continue
CN_01 = Matrix.cnot(n, idx, jdx)
CN_10 = Matrix.cnot(n, jdx, idx)
assert CN_01 * CN_01 == I
assert CN_10 * CN_10 == I
lhs = CN_10 * CN_01 * CN_10
rhs = Matrix.swap(n, idx, jdx)
assert lhs == rhs
lhs = CN_01 * CN_10 * CN_01
assert lhs == rhs
#print(Matrix.cnot(3, 0, 2))
#if 0:
cnot = Matrix.cnot
hadamard = Matrix.hadamard
n = 2
gen = [cnot(n, 0, 1), cnot(n, 1, 0), hadamard(n, 0), hadamard(n, 1)]
for A in gen:
assert A.is_symplectic()
Cliff2 = mulclose_fast(gen)
assert len(Cliff2) == 72 # index 10 in Sp(2, 4)
CZ = array2([[1, 0, 0, 0], [0, 1, 0, 0], [0, 1, 1, 0], [1, 0, 0, 1]])
CZ = Matrix(CZ)
assert CZ.is_symplectic()
assert CZ in Cliff2
n = 3
gen = [
cnot(n, 0, 1),
cnot(n, 1, 0),
cnot(n, 0, 2),
cnot(n, 2, 0),
cnot(n, 1, 2),
cnot(n, 2, 1),
hadamard(n, 0),
hadamard(n, 1),
hadamard(n, 2),
]
for A in gen:
assert A.is_symplectic()
assert len(mulclose_fast(gen)) == 40320 # index 36 in Sp(2,4)
if 0:
# cnot's generate GL(2, n)
n = 4
gen = []
for i in range(n):
for j in range(n):
if i != j:
gen.append(cnot(n, i, j))
assert len(mulclose_fast(gen)) == 20160
if 0:
n = 2
count = 0
for A in enum2(4 * n * n):
A.shape = (2 * n, 2 * n)
A = Matrix(A)
try:
assert A.is_symplectic()
count += 1
except:
pass
print(count) # 720 = |Sp(2, 4)|
return
for n in [1, 2]:
gen = []
for x in enum2(2 * n):
A = Matrix.transvect(x)
assert A.is_symplectic()
gen.append(A)
G = mulclose_fast(gen)
assert len(G) == [6, 720][n - 1]
n = 2
Sp = G
#print(len(Sp))
found = set()
for g in Sp:
A = g.A.copy()
A[:n, n:] = 0
A[n:, :n] = 0
found.add(str(A))
#print(len(A))
#return
n = 4
I = Matrix.identity(n)
H = Matrix.hadamard(n, 0)
assert H * H == I
CN_01 = Matrix.cnot(n, 0, 1)
assert CN_01 * CN_01 == I
n = 3
trivial = CSSCode(Lx=parse("1.."),
Lz=parse("1.."),
Hx=zeros2(0, n),
Hz=parse(".1. ..1"))
assert trivial.row_equal(CSSCode.get_trivial(3, 0))
repitition = CSSCode(Lx=parse("111"),
Lz=parse("1.."),
Hx=zeros2(0, n),
Hz=parse("11. .11"))
assert not trivial.row_equal(repitition)
CN_01 = Matrix.cnot(n, 0, 1)
CN_12 = Matrix.cnot(n, 1, 2)
CN_21 = Matrix.cnot(n, 2, 1)
CN_10 = Matrix.cnot(n, 1, 0)
encode = CN_12 * CN_01
code = CN_01(trivial)
assert not code.row_equal(repitition)
code = CN_12(code)
assert code.row_equal(repitition)
A = get_encoder(trivial, repitition)
gen, names = get_gen(3)
word = mulclose_find(gen, names, A)
if 1:
assert type(word) is tuple
#print("word:")
#print(repr(word))
items = [gen[names.index(op)] for op in word]
op = reduce(mul, items)
#print(op)
#assert op*(src) == (tgt)
#print(op(trivial).longstr())
assert op(trivial).row_equal(repitition)
def make_surface_54_oriented(G0):
" find integer chain complex "
from bruhat.solve import shortstr, zeros2, dot2
from numpy import alltrue, zeros, dot
print()
print("|G0| =", len(G0))
a, ai, b, bi, c, ci, d, di = G0.gens
# 5,5 coxeter subgroup
G_55 = Group.generate([a, b, c])
assert G0.is_subgroup(G_55)
# orientation subgroup
L = Group.generate([a * b, a * d])
#assert len(L) == 60, len(L)
print("L:", len(L))
orients = G0.left_cosets(L)
assert len(orients) == 2
orients = list(orients)
H = Group.generate([a, b])
faces = G_55.left_cosets(H)
fold_faces = G0.left_cosets(H)
print("faces:", len(faces))
print("fold_faces:", len(fold_faces))
#hom = G.left_action(faces)
o_faces = [face.intersect(orients[0]) for face in faces] # oriented faces
r_faces = [face.intersect(orients[1])
for face in faces] # reverse oriented faces
K = Group.generate([b, c])
vertices = G_55.left_cosets(K)
#assert len(vertices) == 12 # unoriented vertices
o_vertices = [vertex.intersect(orients[0])
for vertex in vertices] # oriented vertices
print("o_vertices:", len(o_vertices))
J0 = Group.generate([a, d])
assert len(J0) == 8
assert G0.is_subgroup(J0)
act_edges = G0.action_subgroup(J0)
act_fold_faces = G0.action_subgroup(H)
#print("stab:", len(act_edges.get_stabilizer()))
print("|G0| =", len(G0))
print("edges:", len(G0) // len(J0))
edges = G0.left_cosets(J0)
#for e in edges:
# k = choice(e.perms)
# e1 = e.left_mul(~k)
# assert set(e1.perms) == set(J0.perms)
fold_perms = []
for i, g in enumerate(G0):
assert g in G0
#h_edge = act_edges.tgt[act_edges.send_perms[i]]
#h_fold_faces = act_fold_faces.tgt[act_fold_faces.send_perms[i]]
h_edge = act_edges[g]
h_fold_faces = act_fold_faces[g]
n_edge = len(h_edge.fixed())
n_fold_faces = len(h_fold_faces.fixed())
count = 0
#perms = [] # extract action on the fixed edges
#for e0 in edges:
# #e1 = e0.left_mul(g)
# e1 = g*e0
# if e0 != e1:
# continue
# perm = e0.left_mul_perm(g)
# #print(perm, end=" ")
# perms.append(perm)
# count += 1
#assert count == n_edge
if g.order() == 2 and g not in G_55 and g not in L:
fold_perms.append(g)
else:
continue
#print([p.order() for p in perms] or '', end="")
print(
"[|g|=%s,%s.%s.%s.%s]" % (
g.order(),
n_edge or ' ', # num fixed edges
n_fold_faces or ' ', # num fixed faces+vertexes
[" ", "pres"
][int(g in G_55)], # preserves face/vertex distinction
["refl", "rot "][int(g in L)], # oriented or un-oriented
),
end=" ",
flush=True)
print()
print()
J = Group.generate([a, c])
u_edges = G_55.left_cosets(J)
print("u_edges:", len(u_edges))
J = Group.generate([c])
edges = G_55.left_cosets(J)
print("edges:", len(edges))
# Here we choose an orientation on each edge:
pairs = {}
for e in u_edges:
pairs[e] = []
for e1 in edges:
if e.intersect(e1):
pairs[e].append(e1)
assert len(pairs[e]) == 2, len(pairs[e])
def shortstr(A):
s = str(A)
s = s.replace("0", '.')
return s
Hz = zeros((len(o_faces), len(u_edges)), dtype=int)
for i, l in enumerate(o_faces):
for j, e in enumerate(u_edges):
le = l.intersect(e)
if not le:
continue
e1, e2 = pairs[e]
if e1.intersect(le):
Hz[i, j] = 1
elif e2.intersect(le):
Hz[i, j] = -1
else:
assert 0
Hxt = zeros((len(u_edges), len(o_vertices)), dtype=int)
for i, e in enumerate(u_edges):
for j, v in enumerate(o_vertices):
ev = e.intersect(v)
if not ev:
continue
e1, e2 = pairs[e]
if e1.intersect(ev):
Hxt[i, j] = 1
elif e2.intersect(ev):
Hxt[i, j] = -1
else:
assert 0
#print(shortstr(Hz))
#print()
#print(shortstr(Hxt))
#print()
assert alltrue(dot(Hz, Hxt) == 0)
for perm in fold_perms:
pass
import qupy.ldpc.solve
import bruhat.solve
qupy.ldpc.solve.int_scalar = bruhat.solve.int_scalar
from qupy.ldpc.css import CSSCode
Hz = Hz % 2
Hx = Hxt.transpose() % 2
code = CSSCode(Hz=Hz, Hx=Hx)
print(code)
def get_code(self, grade=1):
Hz, Hx = self.get_parity_checks(grade)
code = CSSCode(Hx=Hx, Hz=Hz)
return code
def test_code(Hxi, Hzi, Hx, Lx, Lz, Lx0, Lx1, LxiHx, **kw):
code = CSSCode(Hx=Hxi, Hz=Hzi)
print(code)
assert rank(intersect(Lx, code.Lx)) == code.k
assert rank(intersect(Lz, code.Lz)) == code.k
verbose = argv.verbose
decoder = get_decoder(argv, argv.decode, code)
if decoder is None:
return
p = argv.get("p", 0.01)
N = argv.get("N", 0)
distance = code.n
count = 0
failcount = 0
nonuniq = 0
logops = []
for i in range(N):
err_op = ra.binomial(1, p, (code.n, ))
err_op = err_op.astype(numpy.int32)
op = decoder.decode(p, err_op, verbose=verbose, argv=argv)
c = 'F'
success = False
if op is not None:
op = (op + err_op) % 2
# Should be a codeword of Hz (kernel of Hz)
assert dot2(code.Hz, op).sum() == 0
write("%d:" % op.sum())
# Are we in the image of Hx ? If so, then success.
success = dot2(code.Lz, op).sum() == 0
if success and op.sum():
nonuniq += 1
c = '.' if success else 'x'
if op.sum() and not success:
distance = min(distance, op.sum())
write("L")
logops.append(op.copy())
else:
failcount += 1
write(c + ' ')
count += success
if N:
print()
print(argv)
print("error rate = %.8f" % (1. - 1. * count / (i + 1)))
print("fail rate = %.8f" % (1. * failcount / (i + 1)))
print("nonuniq = %d" % nonuniq)
print("distance <= %d" % distance)
mx0, mx1 = len(Lx0), len(Lx1)
LxHx = numpy.concatenate((Lx0, Lx1, Hx))
for op in logops:
print(op.sum())
#print(shortstr(op))
#print(op.shape)
#print(op)
K = solve(LxHx.transpose(), op)
K.shape = (1, len(K))
print(shortstrx(K[:, :mx0], K[:, mx0:mx0 + mx1], K[:, mx0 + mx1:]))
def main():
l = argv.get('l', 8)
li = argv.get('li', l)
lj = argv.get('lj', l)
si = argv.get('si', 0)
sj = argv.get('sj', 0)
toric = Toric2D(li, lj, si, sj)
Hx, Hz = toric.Hx, toric.Hz
strop = toric.strop
#print("Hx:")
#print(shortstr(Hx))
#print("Lx:")
#print(shortstr(toric.Lx))
code = CSSCode(Hx=Hx, Hz=Hz, Lx=toric.Lx, Lz=toric.Lz)
print(code)
print(code.Lx)
decoder = ClusterCSSDecoder(2, code.Hx, code.Hz)
N = argv.get("N", 0)
p = argv.get("p", 0.05)
verbose = argv.verbose
distance = code.n
count = 0
failcount = 0
nonuniq = 0
total = numpy.array([0.] * code.k)
for trial in range(N):
err_op = ra.binomial(1, p, (code.n, ))
err_op = err_op.astype(numpy.int32)
write(str(err_op.sum()))
#print err_op.shape
s = dot2(code.Hz, err_op)
write(":s%d:" % s.sum())
op = decoder.decode(p, err_op, verbose=verbose, argv=argv)
c = 'F'
success = False
result = numpy.array([1] * code.k)
if op is not None:
op = (op + err_op) % 2
# Should be a codeword of Hz (kernel of Hz)
if dot2(code.Hz, op).sum() != 0:
print(dot2(code.Hz, op))
print("\n!!!!! BUGBUG !!!!!", sparsestr(err_op))
continue
write("%d:" % op.sum())
# Are we in the image of Hx ? If so, then success.
result = dot2(code.Lz, op)
success = result.sum() == 0
#print(result, end=" ")
if success and op.sum():
nonuniq += 1
# print "\n", shortstr(err_op)
# return
c = '.' if success else 'x'
if op.sum() and not success:
distance = min(distance, op.sum())
else:
failcount += 1
if failures:
print(shortstr(err_op), file=failures)
failures.flush()
total += result
write(c + ' ')
count += success
if N:
print()
print(datestr)
print(argv)
print("error rate = %.8f" % (1. - 1. * count / (trial + 1)))
print("fail rate = %.8f" % (1. * failcount / (trial + 1)))
print("nonuniq = %d" % nonuniq)
print("distance <= %d" % distance)
total = total / (trial + 1)
print("logop errors = [%s]" % ', '.join(str(x) for x in total))
def main():
n = 5
Tx = parse("""
1....
1.1..
1.1.1
""")
Tz = parse("""
.1...
...1.
""")
code = CSSCode(Hx=Tx, Hz=Tz)
#print(code)
#print(code.longstr())
S = parse("""
1.1..1
11.1..
.11.1.
...111
""")
I = parse("""
1...
.1..
..1.
...1
""")
A = parse("""
1...
11..
..1.
...1
""")
B = parse("""
1...
.1..
.11.
...1
""")
C = parse("""
1...
.1..
..1.
..11
""")
#print(I)
#print(dot2(A))
#print(dot2(B, A))
L = dot2(C, B, A)
#print(dot2(L, S)) # row reduced S
L = L[:3, :3]
S = S[:3, :]
print("S =")
print(S)
print("LS =")
print(dot2(L, S))
J = parse("""
1..
11.
...
...
111
...
""")
U = parse("""
1..
.11
..1
""")
print(dot2(U, L, S))
def get_code(self, **kw):
from qupy.ldpc.css import CSSCode
code = CSSCode(Hx=self.Hx, Hz=self.Hz, **kw)
code.__dict__.update(self.__dict__)
return code
def check_dualities(Hz, Hxt, dualities):
from bruhat.solve import shortstr, zeros2, dot2, array2, solve, span
from numpy import alltrue, zeros, dot
import qupy.ldpc.solve
import bruhat.solve
qupy.ldpc.solve.int_scalar = bruhat.solve.int_scalar
from qupy.ldpc.css import CSSCode
Hz = Hz % 2
Hx = Hxt.transpose() % 2
code = CSSCode(Hz=Hz, Hx=Hx)
print(code)
n = code.n
Lx, Lz = code.Lx, code.Lz
# check we really do have weak dualities here:
for perm in dualities:
Hz1 = Hz[:, perm]
Hxt1 = Hxt[perm, :]
assert solve(Hxt, Hz1.transpose()) is not None
assert solve(Hz1.transpose(), Hxt) is not None
Lz1 = Lz[:, perm]
Lx1 = Lx[:, perm]
find_xz = solve(concatenate((Lx, Hx)).transpose(),
Lz1.transpose()) is not None
find_zx = solve(concatenate((Lz1, Hz1)).transpose(),
Lx.transpose()) is not None
#print(find_xz, find_zx)
assert find_xz
assert find_zx
# the fixed points live simultaneously in the homology & the cohomology
fixed = [i for i in range(n) if perm[i] == i]
if len(fixed) == 0:
continue
v = array2([0] * n)
v[fixed] = 1
v.shape = (n, 1)
find_xz = solve(concatenate((Lx, Hx)).transpose(), v) is not None
find_zx = solve(concatenate((Lz, Hz)).transpose(), v) is not None
#print(find_xz, find_zx)
assert find_xz
assert find_zx
from qupy.ldpc.asymplectic import Stim as Clifford
s_gates = []
h_gates = []
s_names = []
for idx, swap in enumerate(dualities):
fixed = [i for i in range(n) if swap[i] == i]
print(idx, fixed)
for signs in cross([(-1, 1)] *
len(fixed)): # <------- does not scale !!! XXX
v = [0] * n
for i, sign in enumerate(signs):
v[fixed[i]] = sign
ux = numpy.dot(Hx, v)
uz = numpy.dot(Hz, v)
if numpy.alltrue(ux == 0) and numpy.alltrue(uz == 0):
#print("*", end=" ")
break
#else:
# assert 0
#print(v)
#print()
# transversal S/CZ
g = Clifford.identity(n)
name = []
for i in range(n):
j = swap[i]
if j < i:
continue
if j == i:
assert v[i] in [1, -1]
if v[i] == 1:
op = Clifford.s_gate(n, i)
name.append("S_%d" % (i, ))
else:
op = Clifford.s_gate(n, i).inverse()
name.append("Si_%d" % (i, ))
else:
op = Clifford.cz_gate(n, i, j)
name.append("CZ_%d_%d" % (i, j))
g = op * g
name = "*".join(reversed(name))
s_names.append(name)
#print(g)
#print()
#assert g.is_transversal(code)
s_gates.append(g)
h = Clifford.identity(n)
for i in range(n):
h = h * Clifford.h_gate(n, i)
for i in range(n):
j = swap[i]
if j <= i:
continue
h = h * Clifford.swap_gate(n, i, j)
#print(g)
#print()
#assert h.is_transversal(code)
h_gates.append(h)
if 0:
print()
print("CZ:")
CZ = Clifford.cz_gate(2, 0, 1)
op = (1., [0, 0], [1, 1])
for i in range(4):
print(op)
op = CZ(*op)
return
for idx, sop in enumerate(s_gates):
print("idx =", idx)
#for hx in Hx:
perm = dualities[idx]
#for hx in span(Hx):
for hx in Hx:
#print("hx =", hx)
#print(s_names[idx])
phase, zop, xop = sop(1., None, hx)
assert numpy.alltrue(xop == hx) # fixes x component
print(phase, zop, xop, dot2(zop, xop))
for (i, j) in enumerate(perm):
if xop[i] and xop[j] and i < j:
print("pair", (i, j))
if toric is None:
continue
print("xop =")
print(toric.strop(xop))
print("zop =")
print(toric.strop(zop))
print()