def measure_homodyne(self, phi, mode, select=None, **kwargs):
"""
Performs a homodyne measurement on a mode.
"""
m_omega_over_hbar = 1 / self._hbar
# Make sure the state is mixed for reduced density matrix
if self._pure:
state = ops.mix(self._state, self._num_modes)
else:
state = self._state
if select is not None:
meas_result = select
if isinstance(meas_result, numbers.Number):
homodyne_sample = float(meas_result)
else:
raise TypeError(
"Selected measurement result must be of numeric type.")
else:
# Compute reduced density matrix
unmeasured = [i for i in range(self._num_modes) if not i == mode]
reduced = ops.partial_trace(state, self._num_modes, unmeasured)
# Rotate to measurement basis
args = [
ops.phase(-phi, self._trunc), reduced, False, [0], 1,
self._trunc
]
if self._mode == 'blas':
reduced = ops.apply_gate_BLAS(*args)
elif self._mode == 'einsum':
reduced = ops.apply_gate_einsum(*args)
# Create pdf. Same as tf implementation, but using
# the recursive relation H_0(x) = 1, H_1(x) = 2x, H_{n+1}(x) = 2xH_n(x) - 2nH_{n-1}(x)
q_mag = kwargs.get('max', 10)
num_bins = kwargs.get('num_bins', 100000)
q_tensor, Hvals = ops.hermiteVals(q_mag, num_bins,
m_omega_over_hbar, self._trunc)
H_matrix = np.zeros((self._trunc, self._trunc, num_bins))
for n, m in product(range(self._trunc), repeat=2):
H_matrix[n][m] = 1 / sqrt(
2**n * bang(n) * 2**m * bang(m)) * Hvals[n] * Hvals[m]
H_terms = np.expand_dims(reduced, -1) * np.expand_dims(H_matrix, 0)
rho_dist = np.sum(H_terms, axis=(1, 2)) \
* (m_omega_over_hbar/pi)**0.5 \
* np.exp(-m_omega_over_hbar * q_tensor**2) \
* (q_tensor[1] - q_tensor[0]) # Delta_q for normalization (only works if the bins are equally spaced)
# Sample from rho_dist. This is a bit different from tensorflow due to how
# numpy treats multinomial sampling. In particular, numpy returns a
# histogram of the samples whereas tensorflow gives the list of samples.
# Numpy also does not use the log probabilities
probs = rho_dist.flatten().real
probs /= np.sum(probs)
sample_hist = np.random.multinomial(1, probs)
sample_idx = list(sample_hist).index(1)
homodyne_sample = q_tensor[sample_idx]
# Project remaining modes into the conditional state
inf_squeezed_vac = \
np.array([(-0.5)**(n//2) * sqrt(bang(n)) / bang(n//2) if n%2 == 0 else 0.0 + 0.0j \
for n in range(self._trunc)], dtype=ops.def_type)
alpha = homodyne_sample * sqrt(m_omega_over_hbar / 2)
composed = np.dot(ops.phase(phi, self._trunc),
ops.displacement(alpha, self._trunc))
args = [composed, inf_squeezed_vac, True, [0], 1, self._trunc]
if self._mode == 'blas':
eigenstate = ops.apply_gate_BLAS(*args)
elif self._mode == 'einsum':
eigenstate = ops.apply_gate_einsum(*args)
vac_state = np.array(
[1.0 + 0.0j if i == 0 else 0.0 + 0.0j for i in range(self._trunc)],
dtype=ops.def_type)
projector = np.outer(vac_state, eigenstate.conj())
self._apply_gate(projector, [mode])
# Normalize
self._state = self._state / self.norm()
return homodyne_sample
def measure_homodyne(self, phi, mode, select=None, **kwargs):
"""
Performs a homodyne measurement on a mode.
"""
m_omega_over_hbar = 1 / self._hbar
# Make sure the state is mixed for reduced density matrix
if self._pure:
state = ops.mix(self._state, self._num_modes)
else:
state = self._state
if select is not None:
meas_result = select
if isinstance(meas_result, numbers.Number):
homodyne_sample = float(meas_result)
else:
raise TypeError(
"Selected measurement result must be of numeric type.")
else:
# Compute reduced density matrix
unmeasured = [i for i in range(self._num_modes) if not i == mode]
reduced = ops.partial_trace(state, self._num_modes, unmeasured)
# Rotate to measurement basis
reduced = self.apply_gate_BLAS(ops.phase(-phi, self._trunc), [0],
state=reduced,
pure=False,
n=1)
# Create pdf. Same as tf implementation, but using
# the recursive relation H_0(x) = 1, H_1(x) = 2x, H_{n+1}(x) = 2xH_n(x) - 2nH_{n-1}(x)
q_mag = kwargs.get("max", 10)
num_bins = kwargs.get("num_bins", 100000)
q_tensor, Hvals = ops.hermiteVals(q_mag, num_bins,
m_omega_over_hbar, self._trunc)
H_matrix = np.zeros((self._trunc, self._trunc, num_bins))
for n, m in product(range(self._trunc), repeat=2):
H_matrix[n][m] = 1 / sqrt(
2**n * bang(n) * 2**m * bang(m)) * Hvals[n] * Hvals[m]
H_terms = np.expand_dims(reduced, -1) * np.expand_dims(H_matrix, 0)
rho_dist = (
np.sum(H_terms, axis=(1, 2)) * (m_omega_over_hbar / pi)**0.5 *
np.exp(-m_omega_over_hbar * q_tensor**2) *
(q_tensor[1] - q_tensor[0])
) # Delta_q for normalization (only works if the bins are equally spaced)
# Sample from rho_dist. This is a bit different from tensorflow due to how
# numpy treats multinomial sampling. In particular, numpy returns a
# histogram of the samples whereas tensorflow gives the list of samples.
# Numpy also does not use the log probabilities
probs = rho_dist.flatten().real
probs /= np.sum(probs)
# Due to floating point precision error, values in the calculated probability distribution
# may have a very small negative value of -epsilon. The following sets
# these small negative values to 0.
probs[np.abs(probs) < 1e-10] = 0
sample_hist = np.random.multinomial(1, probs)
sample_idx = list(sample_hist).index(1)
homodyne_sample = q_tensor[sample_idx]
# Project remaining modes into the conditional state
inf_squeezed_vac = np.array(
[(-0.5)**(n // 2) * sqrt(bang(n)) / bang(n // 2) if n %
2 == 0 else 0.0 + 0.0j for n in range(self._trunc)],
dtype=ops.def_type,
)
alpha = homodyne_sample * sqrt(m_omega_over_hbar / 2)
composed = np.dot(
ops.phase(phi, self._trunc),
ops.displacement(np.abs(alpha), np.angle(alpha), self._trunc),
)
eigenstate = self.apply_gate_BLAS(composed, [0],
state=inf_squeezed_vac,
pure=True,
n=1)
vac_state = np.array(
[1.0 + 0.0j if i == 0 else 0.0 + 0.0j for i in range(self._trunc)],
dtype=ops.def_type)
projector = np.outer(vac_state, eigenstate.conj())
self._state = self.apply_gate_BLAS(projector, [mode])
# Normalize
self._state = self._state / self.norm()
# `homodyne_sample` will always be a single value since multiple shots is not supported
return np.array([[homodyne_sample]])