def test_projected_entropy(self):
Y = 13
N = 21
L = aux.lfy(N)
k = L
number_of_qubits = k + L
proj_state = construct_modular_state(k, L, aux.nonzeros_decimal(
k, Y, N)).toarray().flatten()
state = np.zeros(2**(3 * L))
state[:2**(k + L)] = proj_state.flatten()
tries = 100
for i in range(tries):
chosen_qubits = random_bipartition(range(number_of_qubits),
number_of_qubits // 2)
proj_entr = entanglement_entropy_from_state(proj_state,
chosen_qubits,
sparse=False,
gpu=False)
entr = entanglement_entropy_from_state(state,
chosen_qubits,
sparse=False,
gpu=False)
np.testing.assert_almost_equal(proj_entr, entr)
def test_svd_eigvals(self):
Y = 13
numb = [21, 33, 66]
tries = 50
for N in numb:
eigval_entr = []
svd_entr = []
L = aux.lfy(N)
k = 2 * L
number_of_qubits = k + L
state = construct_modular_state(k, L, aux.nonzeros_decimal(
k, Y, N)).toarray().flatten()
chosens = [
random_bipartition(range(number_of_qubits),
number_of_qubits // 2) for i in range(tries)
]
for i in range(tries):
chosen = chosens[i]
notchosen = bip.notchosen(chosen, k + L)
W = W_from_state_numba(state, chosen, notchosen)
sv = numpysvd(W, compute_uv=False)
sv2 = sv**2
sv2[sv2 < 1e-15] = 1
svd_entr.append(np.sum(sv2 * np.log2(sv2)))
l = np.linalg.eigvalsh(W.dot(W.T))
l[l < 1e-15] = 1
eigval_entr.append(np.sum(l * np.log2(l)))
np.testing.assert_array_almost_equal(eigval_entr,
svd_entr,
decimal=12)
def test_sparse_entropy_equal_qiskit(self):
N = 33
Y = aux.coprime(N)
L = aux.lfy(N)
k = 2 * L
number_of_qubits = k + L
nonzeros_decimal = aux.nonzeros_decimal(k, N, Y)
state = construct_modular_state(k, L, nonzeros_decimal)
tries = 200
for i in range(tries):
chosen = random_bipartition(range(number_of_qubits),
number_of_qubits // 2)
notchosen = bip.notchosen(chosen, number_of_qubits)
state_entropy = entanglement_entropy_from_state(state,
chosen,
sparse=True)
qentropy = entropy(
partial_trace(Statevector(state.toarray().flatten()),
[k + L - 1 - i for i in notchosen]))
self.assertTrue(np.abs(qentropy - state_entropy) < 1e-12)
def test_IQFT_entropy_equals_qiskit(self):
Y = 13
N = 28
L = aux.lfy(N)
k = 2 * L
number_of_qubits = k + L
state = construct_modular_state(k, L, aux.nonzeros_decimal(k, Y, N))
state = apply_IQFT(L, state.toarray())
tries = 30
for i in range(tries):
chosen_qubits = random_bipartition(range(number_of_qubits),
number_of_qubits // 2)
notchosen_qubits = notchosen(chosen_qubits, number_of_qubits)
myentropy = entanglement_entropy_from_state(state,
chosen_qubits,
sparse=False,
gpu=False)
qentropy = entropy(
partial_trace(Statevector(state), notchosen_qubits))
self.assertTrue(np.abs(myentropy - qentropy) < 1e-5)
numb = [21, 33] #, 66, 129]
L_list = []
tries = 20
percentages = [5, 10, 15, 20, 25, 30, 100]
L_times = np.zeros((tries, len(percentages)))
means = np.zeros((len(numb), len(percentages)))
with open("jax_eigh_time_scaling.txt", "a+") as file:
for idx, N in enumerate(numb):
L = aux.lfy(N)
L_list.append(L)
k = 2 * L
number_of_qubits = k + L
state = construct_modular_state(k, L, aux.nonzeros_decimal(k, Y, N))
chosens = [
bip.random_bipartition(range(number_of_qubits),
number_of_qubits // 2) for i in range(tries)
]
for i, perc in enumerate(percentages):
number_total_eigvals = 2**(number_of_qubits // 2)
number_eigvals_computed = int(
ceil(perc * number_total_eigvals / 100))
for j in range(tries):
chosen = chosens[i]
notchosen = bip.notchosen(chosen, k + L)
W = matrix_from_sparse_modular_state(state, chosen, notchosen,
False)
start = time()
sl = jseigh(W.dot(W.T),
eigvals_only=True,
turbo=False,