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_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 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