plutoniumm/ranken

Finding entanglement rank

Ranken

Finding entanglement rank

Usage

After pip install ranken, you can use the package as follows:

Create a State

from ranken.core import State

Rn = 3
theta = np.pi/2

basis = np.eye(Rn)
def PSI(i):
  A = State.create(State.Ket_0, basis[i%Rn])
  B = State.create(State.Ket_1, basis[(i+1)%Rn])

  return State.combine([A, B], [np.cos(theta/2), np.sin(theta/2)])

Make Projectors

from ranken.core import Projector

subspace_basis = np.array([PSI(i) for i in range(2)])
proj, proj_perp = Projector(basis=subspace_basis)
# optionally pass gs=True to run Gram-Schmidt on basis

Find Rank

from ranken.utils import Loss, rand, minima
from ranken.core import Qdit

size = (2*D + 1)*(r - 1)
def phi_ik(X):
  lmda = X[0]
  qubit = Qdit(2, X[1:5].reshape(2, 2))
  qutrit = Qdit(3, X[5:11].reshape(3, 2))

  return lmda, qubit, qutrit

def f(X):
  L, qbit, qtrit = phi_ik(X)
  PHI_rx = normalise(L * np.kron(qbit, qtrit))
  # Multiple phis can be done with
  # PHI_rx = State.combine([phi_rx1, phi_rx2, phi_rx3], [1, 1, 1])

  return Loss(PHI_rx, proj_perp)

# minima accepts all the arguments of scipy.optimize.minimize
res = minima(f, rand(R_MAX, size), tries=2)
print(f'E_r(θ={THETA:.2f}) = {res:.4f}')

Dev

python3 test.py

License

MIT