def glue_pairs(H1, H2, pairs):
m1, n1 = H1.shape
m2, n2 = H2.shape
k = len(pairs)
A1 = Chain([H1])
A2 = Chain([H2])
C = Chain([identity2(k)])
C1n = zeros2(n1, k)
for idx, pair in enumerate(pairs):
i, j = pair
C1n[i, idx] = 1
C1m = dot2(H1, C1n)
C1 = Morphism(C, A1, [C1m, C1n])
C2n = zeros2(n2, k)
for idx, pair in enumerate(pairs):
i, j = pair
C2n[j, idx] = 1
C2m = dot2(H2, C2n)
C2 = Morphism(C, A2, [C2m, C2n])
AD, BD, D, _ = chain.pushout(C1, C2)
H = D[0]
#print(H.shape)
#print(H)
return H
def glue_self(Hx, Hz, pairs):
mx, n = Hx.shape
mz, _ = Hz.shape
k = len(pairs)
A = Chain([Hz, Hx.transpose()])
C = Chain([identity2(k), zeros2(k, 0)])
fn = zeros2(n, k)
for idx, pair in enumerate(pairs):
i1, i2 = pair
fn[i1, idx] = 1
fm = dot2(Hz, fn)
f = Morphism(C, A, [fm, fn, zeros2(mx, 0)])
gn = zeros2(n, k)
for idx, pair in enumerate(pairs):
i1, i2 = pair
gn[i2, idx] = 1
gm = dot2(Hz, gn)
g = Morphism(C, A, [gm, gn, zeros2(mx, 0)])
_, _, D = chain.equalizer(f, g)
Hz, Hxt = D[0], D[1]
return Hxt.transpose(), Hz
def glue_quantum(Hx1, Hz1, Hx2, Hz2, pairs):
mx1, n1 = Hx1.shape
mx2, n2 = Hx2.shape
mz1, _ = Hz1.shape
mz2, _ = Hz2.shape
k = len(pairs)
A1 = Chain([Hz1, Hx1.transpose()])
A2 = Chain([Hz2, Hx2.transpose()])
C = Chain([identity2(k), zeros2(k, 0)])
C1n = zeros2(n1, k)
for idx, pair in enumerate(pairs):
i, j = pair
C1n[i, idx] = 1
C1m = dot2(Hz1, C1n)
C1 = Morphism(C, A1, [C1m, C1n, zeros2(mx1, 0)])
C2n = zeros2(n2, k)
for idx, pair in enumerate(pairs):
i, j = pair
C2n[j, idx] = 1
C2m = dot2(Hz2, C2n)
C2 = Morphism(C, A2, [C2m, C2n, zeros2(mx2, 0)])
AD, BD, D, _ = chain.pushout(C1, C2)
Hz, Hxt = D[0], D[1]
#print(H.shape)
#print(H)
return Hz, Hxt.transpose()
def test_selfdual():
HxA = array2([[1, 1, 1, 1]])
HzA = array2([[1, 1, 1, 1]])
A = Chain([HxA, HzA.transpose()])
HxB = array2([[1, 1, 1, 1]])
HzB = array2([[1, 1, 1, 1]])
B = Chain([HxB, HzB.transpose()])
HzC = zeros2(0, 2)
HxC = array2([[1, 1]])
C = Chain([HxC, HzC.transpose()])
#HzC = zeros2(0, 2)
#HxC = zeros2(0, 2)
#C = Chain([HxC, HzC.transpose()])
# Chain map from C -> A
CAz = zeros2(1, 0)
CAn = zeros2(4, 2)
CAn[0, 0] = 1
CAn[1, 1] = 1
CAx = array2([[1]])
CA = Morphism(C, A, [CAx, CAn, CAz])
# Chain map from C -> B
CBz = CAz
CBn = CAn
CBx = CAx
CB = Morphism(C, B, [CBx, CBn, CBz])
AD, BD, D, _ = chain.pushout(CA, CB)
code = D.get_code()
def test_glue():
m = argv.get("m", 9)
n = argv.get("n", 10)
d = argv.get("d", 0)
p = argv.get("p", 0.5)
weight = argv.weight
H1 = rand2(m, n, p, weight)
G1 = find_kernel(H1)
G1t = G1.transpose()
H1t = H1.transpose()
A1 = Chain([G1, H1t])
k1 = len(G1)
print("H1")
print(fstr(H1))
print()
print(fstr(G1))
w = wenum(H1)
print("wenum:", [len(wi) for wi in w])
H2 = rand2(m, n, p, weight)
H2t = H2.transpose()
G2 = find_kernel(H2)
G2t = G2.transpose()
A2 = Chain([G2, H2t])
k2 = len(G2)
print("H2")
print(fstr(H2))
print()
print(fstr(G2))
w = wenum(H2)
print("wenum:", [len(wi) for wi in w])
if k1 != k2:
return
k = k1
I = identity2(k)
B = Chain([I, zeros2(k, 0)])
a = zeros2(n, k)
for i in range(k):
a[i, i] = 1
f1 = Morphism(B, A1, [dot2(G1, a), a, zeros2(m, 0)])
f2 = Morphism(B, A2, [dot2(G2, a), a, zeros2(m, 0)])
a, b, C, _ = chain.pushout(f1, f2)
H = C[1].transpose()
print("H:")
print(fstr(H))
w = wenum(H)
print("wenum:", [len(wi) for wi in w])
def glue2(H1, H2, i1, i2):
m1, n1 = H1.shape
m2, n2 = H2.shape
A1 = Chain([H1])
A2 = Chain([H2])
C = Chain([array2([[1]])])
C1n = zeros2(n1, 1)
C1n[i1, 0] = 1
C1m = dot2(H1, C1n)
C1 = Morphism(C, A1, [C1m, C1n])
C2n = zeros2(n2, 1)
C2n[i2, 0] = 1
C2m = dot2(H2, C2n)
C2 = Morphism(C, A2, [C2m, C2n])
AD, BD, D, _ = chain.pushout(C1, C2)
H = D[0]
#print(H.shape)
#print(H)
return H
def glue_self_classical(Hz, pairs):
mz, n = Hz.shape
k = len(pairs)
A = Chain([Hz])
C = Chain([identity2(k)])
fn = zeros2(n, k)
for idx, pair in enumerate(pairs):
i1, i2 = pair
fn[i1, idx] = 1
fm = dot2(Hz, fn)
f = Morphism(C, A, [fm, fn])
gn = zeros2(n, k)
for idx, pair in enumerate(pairs):
i1, i2 = pair
gn[i2, idx] = 1
gm = dot2(Hz, gn)
g = Morphism(C, A, [gm, gn])
_, _, D = chain.equalizer(f, g)
Hz = D[0]
return Hz
def glue(self, i1, i2):
assert i1!=i2
Hx = self.Hx
Hz = self.Hz
mx, n = Hx.shape
mz, _ = Hz.shape
k = 1
A = Chain([Hz, Hx.transpose()])
C = Chain([identity2(k), zeros2(k, 0)])
fn = zeros2(n, 1)
fn[i1, 0] = 1
fm = dot2(Hz, fn)
f = Morphism(C, A, [fm, fn, zeros2(mx, 0)])
gn = zeros2(n, 1)
gn[i2, 0] = 1
gm = dot2(Hz, gn)
g = Morphism(C, A, [gm, gn, zeros2(mx, 0)])
_, _, D = equalizer(f, g)
Hz, Hxt = D[0], D[1]
Hx = Hxt.transpose()
code = CSSCode(Hx=Hx, Hz=Hz)
return code
def test_equalizer():
n = 4
m = n - 1
H = zeros2(m, n)
for i in range(m):
H[i, i] = 1
H[i, i + 1] = 1
A = Chain([H])
C = Chain([array2([[1]])])
fm = zeros2(m, 1)
fm[m - 1, 0] = 1
fn = zeros2(n, 1)
fn[n - 1, 0] = 1
f = Morphism(C, A, [fm, fn])
gm = zeros2(m, 1)
gm[0, 0] = 1
gn = zeros2(n, 1)
gn[0, 0] = 1
g = Morphism(C, A, [gm, gn])
AD, BD, D = chain.equalizer(f, g)
assert eq2(D[0], array2([[1, 1, 1], [0, 1,
1]])) # glue two checks at a bit
# --------------------------
A = Chain([H.transpose()])
C = Chain([zeros2(1, 0)])
fn = zeros2(n, 1)
fn[0, 0] = 1
fm = zeros2(m, 0)
f = Morphism(C, A, [fn, fm])
gn = zeros2(n, 1)
gn[n - 1, 0] = 1
gm = zeros2(m, 0)
g = Morphism(C, A, [gn, gm])
AD, BD, D = chain.equalizer(f, g)
D = D[0]
#print(D)
assert eq2(D, array2([[1, 0, 1], [1, 1, 0], [0, 1, 1]])) # glue two bits
def get_chain(self):
if self.mx and self.mz:
chain = Chain([self.Hx, self.Hz.transpose()])
elif self.mx:
chain = Chain([self.Hx])
else:
chain = Chain([self.Hz])
chain.check()
return chain
def test_universal():
for trial in range(100):
m, n = 3, 4
J = rand2(m, n)
K = rand2(m, n)
a = Chain([J])
b = Chain([K])
amorph = a.from_zero()
bmorph = b.from_zero()
am, bm, c, u = chain.pushout(amorph, bmorph)
assert u is None
C = c[0]
mm, nn = C.shape
f = rand_full_rank(nn - 2, nn)
g, H, _ = solve.pushout(C, f)
_c = Chain([H])
m = Morphism(c, _c, [g, f])
assert m * am is not None
assert m * bm is not None
_, _, _, u = chain.pushout(amorph, bmorph, m * am, m * bm, _c)
assert u is not None
assert u == m
def test_color():
HxA = array2([[1, 1, 0, 0], [1, 0, 1, 0], [1, 1, 1, 1]])
HzA = array2([[1, 1, 1, 1]])
A = Chain([HxA, HzA.transpose()])
HxB = HxA
HzB = HzA
B = Chain([HxB, HzB.transpose()])
HzC = zeros2(0, 2)
HxC = array2([[1, 0], [0, 1]])
C = Chain([HxC, HzC.transpose()])
# Chain map from C -> A
CAz = zeros2(1, 0)
CAn = zeros2(4, 2)
CAn[0, 0] = 1
CAn[1, 1] = 1
CAx = dot2(HxA, CAn)
#print(CAx)
CA = Morphism(C, A, [CAx, CAn, CAz])
# Chain map from C -> B
CBz = CAz
CBn = CAn
CBx = CAx
CB = Morphism(C, B, [CBx, CBn, CBz])
AD, BD, D, _ = chain.pushout(CA, CB)
code = D.get_code()
print(code)
print("A --> D")
print(fstr(AD[0]))
print("-----------")
print(fstr(AD[1]))
print("B --> D")
print(fstr(BD[0]))
print("-----------")
print(fstr(BD[1]))
print("Hx:")
print(fstr(code.Hx))
def glue1(H, i1, i2):
m, n = H.shape
A = Chain([H])
C = Chain([array2([[1]])])
fn = zeros2(n, 1)
fn[i1, 0] = 1
fm = dot2(H, fn)
f = Morphism(C, A, [fm, fn])
gn = zeros2(n, 1)
gn[i2, 0] = 1
gm = dot2(H, gn)
g = Morphism(C, A, [gm, gn])
_, _, D = chain.equalizer(f, g)
H = D[0]
#print(H.shape)
#print(H)
return H
def glue1_quantum(Hx, Hz, i1, i2):
assert i1 != i2
mx, n = Hx.shape
mz, _ = Hz.shape
k = 1
A = Chain([Hz, Hx.transpose()])
C = Chain([identity2(k), zeros2(k, 0)])
fn = zeros2(n, 1)
fn[i1, 0] = 1
fm = dot2(Hz, fn)
f = Morphism(C, A, [fm, fn, zeros2(mx, 0)])
gn = zeros2(n, 1)
gn[i2, 0] = 1
gm = dot2(Hz, gn)
g = Morphism(C, A, [gm, gn, zeros2(mx, 0)])
_, _, D = chain.equalizer(f, g)
Hz, Hxt = D[0], D[1]
return Hxt.transpose(), Hz
def test_colimit():
n = 4
m = n - 1
H = zeros2(m, n)
for i in range(m):
H[i, i] = 1
H[i, i + 1] = 1
A = Chain([H])
B = Chain([zeros2(0, 0)])
C = Chain([array2([[1]])])
CAm = zeros2(m, 1)
CAm[0, 0] = 1
CAm[m - 1, 0] = 1
CAn = zeros2(n, 1)
CAn[0, 0] = 1
CAn[n - 1, 0] = 1
CA = Morphism(C, A, [CAm, CAn])
CBm = zeros2(0, 1)
CBn = zeros2(0, 1)
CB = Morphism(C, B, [CBm, CBn])
AD, BD, D, _ = chain.pushout(CA, CB)
assert eq2(D[0], array2([[1, 1, 1], [0, 1,
1]])) # glue two checks at a bit
# --------------------------
A = Chain([H.transpose()])
B = Chain([zeros2(0, 0)])
C = Chain([zeros2(1, 0)])
CAn = zeros2(n, 1)
CAn[0, 0] = 1
CAn[n - 1, 0] = 1
CAm = zeros2(m, 0)
CA = Morphism(C, A, [CAn, CAm])
CBn = zeros2(0, 1)
CBm = zeros2(0, 0)
CB = Morphism(C, B, [CBn, CBm])
AD, BD, D, _ = chain.pushout(CA, CB)
D = D[0]
#print(D)
assert eq2(D, array2([[1, 0, 1], [1, 1, 0], [0, 1, 1]])) # glue two bits
def test():
HxA = array2([[1, 1, 1, 0, 0], [0, 0, 1, 1, 1]])
HzA = array2([[1, 0, 1, 1, 0], [0, 1, 1, 0, 1]])
A = Chain([HxA, HzA.transpose()])
HxB = array2([[1, 1, 1, 0, 0], [0, 0, 1, 1, 1]])
HzB = array2([[1, 0, 1, 1, 0], [0, 1, 1, 0, 1]])
B = Chain([HxB, HzB.transpose()])
HzC = zeros2(0, 2)
HxC = array2([[1, 1]])
C = Chain([HxC, HzC.transpose()])
# Chain map from C -> A
CAz = array2(shape=(2, 0))
CAn = array2([[0, 0], [0, 0], [0, 0], [1, 0], [0, 1]])
CAx = array2([[0], [1]])
CA = Morphism(C, A, [CAx, CAn, CAz])
# Chain map from C -> B
CBz = CAz
CBn = CAn
CBx = CAx
CB = Morphism(C, B, [CBx, CBn, CBz])
AD, BD, D, _ = chain.pushout(CA, CB)
code = D.get_code()
assert code.mx == 3
assert code.mz == 4
assert code.k == 1
#print(code.longstr())
# Chain map from C -> D
CDz = zeros2(4, 0)
CDn = zeros2(8, 2)
CDn[4, 0] = 1
CDn[3, 1] = 1
CDx = zeros2(3, 1)
CDx[1, 0] = 1
CD = Morphism(C, D, [CDx, CDn, CDz])
_, _, E, _ = chain.pushout(CA, CD)
code = E.get_code()
#print(code.longstr())
return
#dual = code.dual()
#print(css.lookup_distance(code))
print("Hz:")
print(code.Hz)
print("Hx:")
print(code.Hx)
print("Lx:")
print(code.Lx)
print()
#H = numpy.concatenate((code.Lx, code.Hx))
u = code.Lx
H = code.Hx
#print(H)
d = H.shape[1]
for v in image(H.transpose()):
v = (u + v) % 2
d = min(d, v.sum()) or d
if v.sum() == 4:
print(v)
print("distance:", d)