Update Clements decomposition for unitary matrices

[Hugh-888]

Update Clements decomposition for unitary matrices

• case1

nmode = 6
u = unitary_group.rvs(nmode, random_state=20)
method = 'cssr'

ud = dq.photonic.UnitaryDecomposer(u, method)
test = ud.decomp()

dic_mzi = test[2]
cir = dq.Clements(nmode=nmode, init_state=[0,1,0,1,0,0], cutoff=3, phi_first=True)
data_new = cir.dict2data(dic_mzi)
u_check = cir(data=data_new)
print('error:', abs(u_check- torch.tensor(u))) 

• case2

nmode = 6
u = unitary_group.rvs(nmode, random_state=20)
method = 'cssr'
batch = 2
u_ts = torch.tensor(u).repeat(batch, 1, 1)
ud = dq.photonic.UnitaryDecomposer(u_ts, method)
test1 = ud.decomp()

dic_mzi = test1[2]
cir = dq.Clements(nmode=nmode, init_state=[0]*nmode, cutoff=2)

data_new = cir.dict2data(dic_mzi).reshape(-1, batch).mT
u_check = cir(data=data_new)
print('error:', abs(u_check- torch.tensor(u)))

• case3

nmode = 8
u = unitary_group.rvs(nmode)
method = 'cssl'
batch = 2
u_ts = torch.tensor(u).repeat(batch, 1, 1)
ud = dq.photonic.UnitaryDecomposer(u_ts, method)
test1 = ud.decomp()

dic_mzi = test1[2]
cir = dq.Clements(nmode=nmode, init_state=[0]*nmode, cutoff=2, phi_first=False)

data_new = cir.dict2data(dic_mzi).reshape(-1, batch).mT
u_check = cir(data=data_new)
error = abs(u_check- torch.tensor(u))
print('error:', torch.sum(error, dim=[1,2]))
cir.draw()