def test_mppovm_expectation(nr_sites, width, local_dim, rank, nopovm, rgen):
# Verify that :func:`povm.MPPovm.expectations()` produces
# correct results.
pmap = nopovm.probability_map
mpnopovm = povm.MPPovm.from_local_povm(nopovm, width)
# Use a random MPO rho for testing (instead of a positive MPO).
rho = factory.random_mpo(nr_sites, local_dim, rank, rgen)
reductions = mpsmpo.reductions_mpo(rho, width)
# Compute expectation values with mpnopovm.expectations(), which
# uses mpnopovm.probability_map.
expectations = list(mpnopovm.expectations(rho))
assert len(expectations) == nr_sites - width + 1
for evals_mp, rho_red in zip_longest(expectations, reductions):
# Compute expectation values by constructing each tensor
# product POVM element.
rho_red_matrix = rho_red.to_array_global().reshape(
(local_dim**width,) * 2)
evals = []
for factors in it.product(nopovm, repeat=width):
elem = utils.mkron(*factors)
evals.append(np.trace(np.dot(elem, rho_red_matrix)))
evals = np.array(evals).reshape((len(nopovm),) * width)
# Compute expectation with a different construction. In the
# end, this is (should be, we verify it here) equivalent to
# what `mpnopovm.expectations()` does.
evals_ten = rho_red.ravel().to_array()
for _ in range(width):
evals_ten = np.tensordot(evals_ten, pmap, axes=(0, 1))
assert_array_almost_equal(evals_ten, evals)
assert_array_almost_equal(evals_mp.to_array(), evals)
def test_reductions_mps(nr_sites, local_dim, rank, width, rgen):
mps = factory.random_mps(nr_sites, local_dim, rank, randstate=rgen)
mpo = mp.localouter(mps, mps.conj())
pmps_reds = mm.reductions_mps_as_mpo(mps, width)
mpo_reds = mm.reductions_mpo(mpo, width)
for red1, red2 in zip(pmps_reds, mpo_reds):
assert_array_almost_equal(red1.to_array(), red2.to_array())
def test_reductions_mps(nr_sites, local_dim, rank, width, rgen):
mps = factory.random_mps(nr_sites, local_dim, rank, randstate=rgen)
mpo = mp.localouter(mps, mps.conj())
pmps_reds = mm.reductions_mps_as_mpo(mps, width)
mpo_reds = mm.reductions_mpo(mpo, width)
for red1, red2 in zip(pmps_reds, mpo_reds):
assert_array_almost_equal(red1.to_array(), red2.to_array())
def test_reductions_mpo(nr_sites, local_dim, rank, max_red_width, rgen):
mpo = factory.random_mpo(nr_sites, local_dim, rank,
randstate=rgen)
op = mpo.to_array_global()
start, stop, red = _get_reductions(mm.reductions_mpo, mpo, max_red_width)
for start, stop, reduced_mpo in zip(start, stop, red):
# Check that startsites/stopsites and width produce the same result:
reduced_mpo2 = tuple(mm.reductions_mpo(mpo, stop - start))[start]
assert_array_almost_equal(reduced_mpo.to_array(),
reduced_mpo2.to_array())
traceout = tuple(range(start)) + tuple(range(stop, nr_sites))
red_from_op = utils.partial_trace(op, traceout)
assert_array_almost_equal(
reduced_mpo.to_array_global(), red_from_op,
err_msg="not equal at {}:{}".format(start, stop))
# check default argument for startsite
assert len(list(mm.reductions_mpo(mpo, max_red_width))) \
== nr_sites - max_red_width + 1
def test_reductions_mpo(nr_sites, local_dim, rank, max_red_width, rgen):
mpo = factory.random_mpo(nr_sites, local_dim, rank,
randstate=rgen)
op = mpo.to_array_global()
start, stop, red = _get_reductions(mm.reductions_mpo, mpo, max_red_width)
for start, stop, reduced_mpo in zip(start, stop, red):
# Check that startsites/stopsites and width produce the same result:
reduced_mpo2 = tuple(mm.reductions_mpo(mpo, stop - start))[start]
assert_array_almost_equal(reduced_mpo.to_array(),
reduced_mpo2.to_array())
traceout = tuple(range(start)) + tuple(range(stop, nr_sites))
red_from_op = utils.partial_trace(op, traceout)
assert_array_almost_equal(
reduced_mpo.to_array_global(), red_from_op,
err_msg="not equal at {}:{}".format(start, stop))
# check default argument for startsite
assert len(list(mm.reductions_mpo(mpo, max_red_width))) \
== nr_sites - max_red_width + 1