Source code for pennylane.devices.default_gaussian
# Copyright 2018-2021 Xanadu Quantum Technologies Inc.
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# pylint: disable=inconsistent-return-statements
"""
The :code:`default.gaussian` device is a simulator for Gaussian continuous-variable
quantum computations, and can be used as a template for writing PennyLane
devices for new CV backends.
It implements the necessary :class:`~pennylane._device.Device` methods as well as all built-in
:mod:`continuous-variable Gaussian operations <pennylane.ops.cv>`, and provides a very simple simulation of a
Gaussian-based quantum circuit architecture.
"""
# pylint: disable=attribute-defined-outside-init,too-many-arguments
import math
import cmath
import numpy as np
from scipy.special import factorial as fac
import pennylane as qml
from pennylane.ops import Identity
from pennylane import Device
from .._version import __version__
# tolerance for numerical errors
tolerance = 1e-10
# ========================================================
# auxillary functions
# ========================================================
[docs]def partitions(s, include_singles=True):
"""Partitions a sequence into all groupings of pairs and singles of elements.
Args:
s (sequence): the sequence to partition
include_singles (bool): if False, only partitions into pairs
is returned.
Returns:
tuple: returns a nested tuple, containing all partitions of the sequence.
"""
# pylint: disable=too-many-branches
if len(s) == 2:
if include_singles:
yield (s[0],), (s[1],)
yield (tuple(s),)
else:
# pull off a single item and partition the rest
if include_singles:
if len(s) > 1:
item_partition = (s[0],)
rest = s[1:]
rest_partitions = partitions(rest, include_singles)
for p in rest_partitions:
yield ((item_partition),) + p
else:
yield (tuple(s),)
# pull off a pair of items and partition the rest
for idx1 in range(1, len(s)):
item_partition = (s[0], s[idx1])
rest = s[1:idx1] + s[idx1 + 1 :]
rest_partitions = partitions(rest, include_singles)
for p in rest_partitions:
yield ((item_partition),) + p
[docs]def fock_prob(cov, mu, event, hbar=2.0):
r"""Returns the probability of detection of a particular PNR detection event.
For more details, see:
* Kruse, R., Hamilton, C. S., Sansoni, L., Barkhofen, S., Silberhorn, C., & Jex, I.
"A detailed study of Gaussian Boson Sampling." `arXiv:1801.07488. (2018).
<https://arxiv.org/abs/1801.07488>`_
* Hamilton, C. S., Kruse, R., Sansoni, L., Barkhofen, S., Silberhorn, C., & Jex, I.
"Gaussian boson sampling." `Physical review letters, 119(17), 170501. (2017).
<https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.170501>`_
Args:
cov (array): :math:`2N\times 2N` covariance matrix
mu (array): length-:math:`2N` means vector
event (array): length-:math:`N` array of non-negative integers representing the
PNR detection event of the multi-mode system.
hbar (float): (default 2) the value of :math:`\hbar` in the commutation
relation :math:`[\x,\p]=i\hbar`.
Returns:
float: probability of detecting the event
"""
# number of modes
N = len(mu) // 2
I = np.identity(N)
# mean displacement of each mode
alpha = (mu[:N] + 1j * mu[N:]) / math.sqrt(2 * hbar)
# the expectation values (<a_1>, <a_2>,...,<a_N>, <a^\dagger_1>, ..., <a^\dagger_N>)
beta = np.concatenate([alpha, alpha.conj()])
x = cov[:N, :N] * 2 / hbar
xp = cov[:N, N:] * 2 / hbar
p = cov[N:, N:] * 2 / hbar
# the (Hermitian) matrix elements <a_i^\dagger a_j>
aidaj = (x + p + 1j * (xp - xp.T) - 2 * I) / 4
# the (symmetric) matrix elements <a_i a_j>
aiaj = (x - p + 1j * (xp + xp.T)) / 4
# calculate the covariance matrix sigma_Q appearing in the Q function:
# Q(alpha) = exp[-(alpha-beta).sigma_Q^{-1}.(alpha-beta)/2]/|sigma_Q|
Q = np.block([[aidaj, aiaj.conj()], [aiaj, aidaj.conj()]]) + np.identity(2 * N)
# inverse Q matrix
Qinv = np.linalg.inv(Q)
# 1/sqrt(|Q|)
sqrt_Qdet = 1 / math.sqrt(np.linalg.det(Q).real)
prefactor = cmath.exp(-beta @ Qinv @ beta.conj() / 2)
if np.all(np.array(event) == 0):
# all PNRs detect the vacuum state
return (prefactor * sqrt_Qdet).real / np.prod(fac(event))
# the matrix X_n = [[0, I_n], [I_n, 0]]
O = np.zeros_like(I)
X = np.block([[O, I], [I, O]])
gamma = X @ Qinv.conj() @ beta
# For each mode, repeat the mode number event[i] times
ind = [i for sublist in [[idx] * j for idx, j in enumerate(event)] for i in sublist]
# extend the indices for xp-ordering of the Gaussian state
ind += [i + N for i in ind]
if np.linalg.norm(beta) < tolerance:
# state has no displacement
part = partitions(ind, include_singles=False)
else:
part = partitions(ind, include_singles=True)
# calculate Hamilton's A matrix: A = X.(I-Q^{-1})*
A = X @ (np.identity(2 * N) - Qinv).conj()
summation = np.sum([np.prod([gamma[i[0]] if len(i) == 1 else A[i] for i in p]) for p in part])
return (prefactor * sqrt_Qdet * summation).real / np.prod(fac(event))
# ========================================================
# parametrized gates
# ========================================================
[docs]def rotation(phi):
"""Rotation in the phase space.
Args:
phi (float): rotation parameter
Returns:
array: symplectic transformation matrix
"""
return np.array([[math.cos(phi), -math.sin(phi)], [math.sin(phi), math.cos(phi)]])
[docs]def displacement(state, wire, alpha, hbar=2):
"""Displacement in the phase space.
Args:
state (tuple): contains covariance matrix and means vector
wire (int): wire that the displacement acts on
alpha (float): complex displacement
Returns:
tuple: contains the covariance matrix and the vector of means
"""
mu = state[1]
mu[wire] += alpha.real * math.sqrt(2 * hbar)
mu[wire + len(mu) // 2] += alpha.imag * math.sqrt(2 * hbar)
return state[0], mu
[docs]def squeezing(r, phi):
"""Squeezing in the phase space.
Args:
r (float): squeezing magnitude
phi (float): rotation parameter
Returns:
array: symplectic transformation matrix
"""
cp = math.cos(phi)
sp = math.sin(phi)
ch = math.cosh(r)
sh = math.sinh(r)
return np.array([[ch - cp * sh, -sp * sh], [-sp * sh, ch + cp * sh]])
[docs]def quadratic_phase(s):
"""Quadratic phase shift.
Args:
s (float): gate parameter
Returns:
array: symplectic transformation matrix
"""
return np.array([[1, 0], [s, 1]])
[docs]def beamsplitter(theta, phi):
r"""Beamsplitter.
Args:
theta (float): transmittivity angle (:math:`t=\cos\theta`)
phi (float): phase angle (:math:`r=e^{i\phi}\sin\theta`)
Returns:
array: symplectic transformation matrix
"""
cp = math.cos(phi)
sp = math.sin(phi)
ct = math.cos(theta)
st = math.sin(theta)
S = np.array(
[
[ct, -cp * st, 0, -st * sp],
[cp * st, ct, -st * sp, 0],
[0, st * sp, ct, -cp * st],
[st * sp, 0, cp * st, ct],
]
)
return S
[docs]def two_mode_squeezing(r, phi):
"""Two-mode squeezing.
Args:
r (float): squeezing magnitude
phi (float): rotation parameter
Returns:
array: symplectic transformation matrix
"""
cp = math.cos(phi)
sp = math.sin(phi)
ch = math.cosh(r)
sh = math.sinh(r)
S = np.array(
[
[ch, cp * sh, 0, sp * sh],
[cp * sh, ch, sp * sh, 0],
[0, sp * sh, ch, -cp * sh],
[sp * sh, 0, -cp * sh, ch],
]
)
return S
[docs]def controlled_addition(s):
"""CX gate.
Args:
s (float): gate parameter
Returns:
array: symplectic transformation matrix
"""
S = np.array([[1, 0, 0, 0], [s, 1, 0, 0], [0, 0, 1, -s], [0, 0, 0, 1]])
return S
[docs]def controlled_phase(s):
"""CZ gate.
Args:
s (float): gate parameter
Returns:
array: symplectic transformation matrix
"""
S = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, s, 1, 0], [s, 0, 0, 1]])
return S
[docs]def interferometer_unitary(U):
"""InterferometerUnitary
Args:
U (array): unitary matrix
Returns:
array: symplectic transformation matrix
"""
N = 2 * len(U)
X = U.real
Y = U.imag
rows = np.arange(N).reshape(2, -1).T.flatten()
S = np.vstack([np.hstack([X, -Y]), np.hstack([Y, X])])[:, rows][rows]
return S
# ========================================================
# Arbitrary states and operators
# ========================================================
[docs]def squeezed_cov(r, phi, hbar=2):
r"""Returns the squeezed covariance matrix of a squeezed state.
Args:
r (float): the squeezing magnitude
p (float): the squeezing phase :math:`\phi`
hbar (float): (default 2) the value of :math:`\hbar` in the commutation
relation :math:`[\x,\p]=i\hbar`
Returns:
array: the squeezed state
"""
cov = np.array([[math.exp(-2 * r), 0], [0, math.exp(2 * r)]]) * hbar / 2
R = rotation(phi / 2)
return R @ cov @ R.T
[docs]def vacuum_state(wires, hbar=2.0):
r"""Returns the vacuum state.
Args:
wires (int): the number of wires to initialize in the vacuum state
hbar (float): (default 2) the value of :math:`\hbar` in the commutation
relation :math:`[\x,\p]=i\hbar`
Returns:
array: the vacuum state
"""
means = np.zeros((2 * wires))
cov = np.identity(2 * wires) * hbar / 2
state = [cov, means]
return state
[docs]def coherent_state(a, phi=0, hbar=2.0):
r"""Returns a coherent state.
Args:
a (complex) : the displacement
phi (float): the phase
hbar (float): (default 2) the value of :math:`\hbar` in the commutation
relation :math:`[\x,\p]=i\hbar`
Returns:
array: the coherent state
"""
alpha = a * cmath.exp(1j * phi)
means = np.array([alpha.real, alpha.imag]) * math.sqrt(2 * hbar)
cov = np.identity(2) * hbar / 2
state = [cov, means]
return state
[docs]def squeezed_state(r, phi, hbar=2.0):
r"""Returns a squeezed state.
Args:
r (float): the squeezing magnitude
phi (float): the squeezing phase :math:`\phi`
hbar (float): (default 2) the value of :math:`\hbar` in the commutation
relation :math:`[\x,\p]=i\hbar`
Returns:
array: the squeezed state
"""
means = np.zeros((2))
state = [squeezed_cov(r, phi, hbar), means]
return state
[docs]def displaced_squeezed_state(a, phi_a, r, phi_r, hbar=2.0):
r"""Returns a squeezed coherent state
Args:
a (real): the displacement magnitude
phi_a (real): the displacement phase
r (float): the squeezing magnitude
phi_r (float): the squeezing phase :math:`\phi_r`
hbar (float): (default 2) the value of :math:`\hbar` in the commutation
relation :math:`[\x,\p]=i\hbar`
Returns:
array: the squeezed coherent state
"""
alpha = a * cmath.exp(1j * phi_a)
means = np.array([alpha.real, alpha.imag]) * math.sqrt(2 * hbar)
state = [squeezed_cov(r, phi_r, hbar), means]
return state
[docs]def thermal_state(nbar, hbar=2.0):
r"""Returns a thermal state.
Args:
nbar (float): the mean photon number
hbar (float): (default 2) the value of :math:`\hbar` in the commutation
relation :math:`[\x,\p]=i\hbar`
Returns:
array: the thermal state
"""
means = np.zeros([2])
state = [(2 * nbar + 1) * np.identity(2) * hbar / 2, means]
return state
[docs]def gaussian_state(cov, mu, hbar=2.0):
r"""Returns a Gaussian state.
This is simply a bare wrapper function,
since the covariance matrix and means vector
can be passed via the parameters unchanged.
Note that both the covariance and means vector
matrix should be in :math:`(\x_1,\dots, \x_N, \p_1, \dots, \p_N)`
ordering.
Args:
cov (array): covariance matrix. Must be dimension :math:`2N\times 2N`,
where N is the number of modes
mu (array): vector means. Must be length-:math:`2N`,
where N is the number of modes
hbar (float): (default 2) the value of :math:`\hbar` in the commutation
relation :math:`[\x,\p]=i\hbar`
Returns:
tuple: the mean and the covariance matrix of the Gaussian state
"""
# pylint: disable=unused-argument
# Note: the internal order of mu and cov is different to the one used in Strawberry Fields
return cov, mu
[docs]def set_state(state, wire, cov, mu):
r"""Inserts a single mode Gaussian into the
state representation of the complete system.
Args:
state (tuple): contains covariance matrix
and means vector of existing state
wire (Wires): wire corresponding to the new Gaussian state
cov (array): covariance matrix to insert
mu (array): vector of means to insert
Returns:
tuple: contains the vector of means and covariance matrix.
"""
cov0 = state[0]
mu0 = state[1]
N = len(mu0) // 2
# insert the new state into the means vector
mu0[[wire[0], wire[0] + N]] = mu
# insert the new state into the covariance matrix
ind = np.concatenate([wire.toarray(), wire.toarray() + N])
rows = ind.reshape(-1, 1)
cols = ind.reshape(1, -1)
cov0[rows, cols] = cov
return cov0, mu0
# ========================================================
# expectations
# ========================================================
[docs]def photon_number(cov, mu, params, hbar=2.0):
r"""Calculates the mean photon number for a given one-mode state.
Args:
cov (array): :math:`2\times 2` covariance matrix
mu (array): length-2 vector of means
params (None): no parameters are used for this expectation value
hbar (float): (default 2) the value of :math:`\hbar` in the commutation
relation :math:`[\x,\p]=i\hbar`
Returns:
tuple: contains the photon number expectation and variance
"""
# pylint: disable=unused-argument
ex = (np.trace(cov) + mu.T @ mu) / (2 * hbar) - 1 / 2
var = (np.trace(cov @ cov) + 2 * mu.T @ cov @ mu) / (2 * hbar**2) - 1 / 4
return ex, var
[docs]def homodyne(phi=None):
"""Function factory that returns the Homodyne expectation of a one mode state.
Args:
phi (float): the default phase space axis to perform the Homodyne measurement
Returns:
function: A function that accepts a single mode means vector, covariance matrix,
and phase space angle phi, and returns the quadrature expectation
value and variance.
"""
if phi is not None:
def _homodyne(cov, mu, params, hbar=2.0):
"""Arbitrary angle homodyne expectation."""
# pylint: disable=unused-argument
rot = rotation(phi)
muphi = rot.T @ mu
covphi = rot.T @ cov @ rot
return muphi[0], covphi[0, 0]
return _homodyne
def _homodyne(cov, mu, params, hbar=2.0):
"""Arbitrary angle homodyne expectation."""
# pylint: disable=unused-argument
rot = rotation(params[0])
muphi = rot.T @ mu
covphi = rot.T @ cov @ rot
return muphi[0], covphi[0, 0]
return _homodyne
[docs]def poly_quad_expectations(cov, mu, wires, device_wires, params, hbar=2.0):
r"""Calculates the expectation and variance for an arbitrary
polynomial of quadrature operators.
Args:
cov (array): covariance matrix
mu (array): vector of means
wires (Wires): wires to calculate the expectation for
device_wires (Wires): corresponding wires on the device
params (array): a :math:`(2N+1)\times (2N+1)` array containing the linear
and quadratic coefficients of the quadrature operators
:math:`(\I, \x_0, \p_0, \x_1, \p_1,\dots)`
hbar (float): (default 2) the value of :math:`\hbar` in the commutation
relation :math:`[\x,\p]=i\hbar`
Returns:
tuple: the mean and variance of the quadrature-polynomial observable
"""
Q = params[0]
# HACK, we need access to the Poly instance in order to expand the matrix!
# TODO: maybe we should make heisenberg_obs a class method or a static method to avoid this being a 'hack'?
op = qml.PolyXP(Q, wires=wires)
Q = op.heisenberg_obs(device_wires)
if Q.ndim == 1:
d = np.r_[Q[1::2], Q[2::2]]
return d.T @ mu + Q[0], d.T @ cov @ d
# convert to the (I, x1,x2,..., p1,p2...) ordering
M = np.vstack((Q[0:1, :], Q[1::2, :], Q[2::2, :]))
M = np.hstack((M[:, 0:1], M[:, 1::2], M[:, 2::2]))
d1 = M[1:, 0]
d2 = M[0, 1:]
A = M[1:, 1:]
d = d1 + d2
k = M[0, 0]
d2 = 2 * A @ mu + d
k2 = mu.T @ A @ mu + mu.T @ d + k
ex = np.trace(A @ cov) + k2
var = 2 * np.trace(A @ cov @ A @ cov) + d2.T @ cov @ d2
modes = np.arange(2 * len(device_wires)).reshape(2, -1).T
groenewald_correction = np.sum([np.linalg.det(hbar * A[:, m][n]) for m in modes for n in modes])
var -= groenewald_correction
return ex, var
[docs]def fock_expectation(cov, mu, params, hbar=2.0):
r"""Calculates the expectation and variance of a Fock state probability.
Args:
cov (array): :math:`2N\times 2N` covariance matrix
mu (array): length-:math:`2N` vector of means
params (Sequence[int]): the Fock state to return the expectation value for
hbar (float): (default 2) the value of :math:`\hbar` in the commutation
relation :math:`[\x,\p]=i\hbar`
Returns:
tuple: the Fock state expectation and variance
"""
# pylint: disable=unused-argument
ex = fock_prob(cov, mu, params[0], hbar=hbar)
# var[|n><n|] = E[|n><n|^2] - E[|n><n|]^2 = E[|n><n|] - E[|n><n|]^2
var = ex - ex**2
return ex, var
[docs]def identity(*_, **__):
r"""Returns 1.
Returns:
tuple: the Fock state expectation and variance
"""
return 1, 0
# ========================================================
# device
# ========================================================
[docs]class DefaultGaussian(Device):
r"""Default Gaussian device for PennyLane.
Args:
wires (int, Iterable[Number, str]): Number of subsystems represented by the device,
or iterable that contains unique labels for the subsystems as numbers (i.e., ``[-1, 0, 2]``)
or strings (``['ancilla', 'q1', 'q2']``). Default 1 if not specified.
shots (None, int): How many times the circuit should be evaluated (or sampled) to estimate
the expectation values. If ``None``, the results are analytically computed and hence deterministic.
hbar (float): (default 2) the value of :math:`\hbar` in the commutation
relation :math:`[\x,\p]=i\hbar`
"""
name = "Default Gaussian PennyLane plugin"
short_name = "default.gaussian"
pennylane_requires = __version__
version = __version__
author = "Xanadu Inc."
_operation_map = {
"Identity": Identity.identity_op,
"Snapshot": None,
"Beamsplitter": beamsplitter,
"ControlledAddition": controlled_addition,
"ControlledPhase": controlled_phase,
"Displacement": displacement,
"QuadraticPhase": quadratic_phase,
"Rotation": rotation,
"Squeezing": squeezing,
"TwoModeSqueezing": two_mode_squeezing,
"CoherentState": coherent_state,
"DisplacedSqueezedState": displaced_squeezed_state,
"SqueezedState": squeezed_state,
"ThermalState": thermal_state,
"GaussianState": gaussian_state,
"InterferometerUnitary": interferometer_unitary,
}
_observable_map = {
"NumberOperator": photon_number,
"QuadX": homodyne(0),
"QuadP": homodyne(np.pi / 2),
"QuadOperator": homodyne(None),
"PolyXP": poly_quad_expectations,
"FockStateProjector": fock_expectation,
"Identity": identity,
}
_circuits = {}
def __init__(self, wires, *, shots=None, hbar=2, analytic=None):
super().__init__(wires, shots, analytic=analytic)
self.eng = None
self.hbar = hbar
self._debugger = None
self.reset()
[docs] @classmethod
def capabilities(cls):
capabilities = super().capabilities().copy()
capabilities.update(
model="cv",
supports_analytic_computation=True,
supports_finite_shots=True,
returns_probs=False,
returns_state=False,
)
return capabilities
[docs] def apply(self, operation, wires, par):
# translate to wire labels used by device
device_wires = self.map_wires(wires)
if operation == "Displacement":
self._state = displacement(
self._state, device_wires.labels[0], par[0] * cmath.exp(1j * par[1])
)
return # we are done here
if operation == "GaussianState":
if len(device_wires) != self.num_wires:
raise ValueError(
"GaussianState covariance matrix or means vector is "
"the incorrect size for the number of subsystems."
)
self._state = self._operation_map[operation](*par, hbar=self.hbar)
return # we are done here
if operation == "Snapshot":
if self._debugger and self._debugger.active:
gaussian = {"cov_matrix": self._state[0].copy(), "means": self._state[1].copy()}
self._debugger.snapshots[len(self._debugger.snapshots)] = gaussian
return # we are done here
if "State" in operation:
# set the new device state
cov, mu = self._operation_map[operation](*par, hbar=self.hbar)
# state preparations only act on at most 1 subsystem
self._state = set_state(self._state, device_wires[:1], cov, mu)
return # we are done here
# get the symplectic matrix
S = self._operation_map[operation](*par)
# expand the symplectic to act on the proper subsystem
S = self.expand(S, device_wires)
# apply symplectic matrix to the means vector
means = S @ self._state[1]
# apply symplectic matrix to the covariance matrix
cov = S @ self._state[0] @ S.T
self._state = [cov, means]
[docs] def expand(self, S, wires):
r"""Expands a Symplectic matrix S to act on the entire subsystem.
Args:
S (array): a :math:`2M\times 2M` Symplectic matrix
wires (Wires): wires of the modes that S acts on
Returns:
array: the resulting :math:`2N\times 2N` Symplectic matrix
"""
if self.num_wires == 1:
# total number of wires is 1, simply return the matrix
return S
N = self.num_wires
w = wires.toarray()
M = len(S) // 2
S2 = np.identity(2 * N)
if M != len(wires):
raise ValueError("Incorrect number of subsystems for provided operation.")
S2[w.reshape(-1, 1), w.reshape(1, -1)] = S[:M, :M].copy() # XX
S2[(w + N).reshape(-1, 1), (w + N).reshape(1, -1)] = S[M:, M:].copy() # PP
S2[w.reshape(-1, 1), (w + N).reshape(1, -1)] = S[:M, M:].copy() # XP
S2[(w + N).reshape(-1, 1), w.reshape(1, -1)] = S[M:, :M].copy() # PX
return S2
[docs] def expval(self, observable, wires, par):
if observable == "PolyXP":
cov, mu = self._state
ev, var = self._observable_map[observable](
cov, mu, wires, self.wires, par, hbar=self.hbar
)
else:
cov, mu = self.reduced_state(wires)
ev, var = self._observable_map[observable](cov, mu, par, hbar=self.hbar)
if self.shots is not None:
# estimate the ev
# use central limit theorem, sample normal distribution once, only ok if n_eval is large
# (see https://en.wikipedia.org/wiki/Berry%E2%80%93Esseen_theorem)
ev = np.random.normal(ev, math.sqrt(var / self.shots))
return ev
[docs] def var(self, observable, wires, par):
if observable == "PolyXP":
cov, mu = self._state
_, var = self._observable_map[observable](
cov, mu, wires, self.wires, par, hbar=self.hbar
)
else:
cov, mu = self.reduced_state(wires)
_, var = self._observable_map[observable](cov, mu, par, hbar=self.hbar)
return var
[docs] def sample(self, observable, wires, par):
"""Return a sample of an observable.
.. note::
The ``default.gaussian`` plugin only supports sampling
from :class:`~.X`, :class:`~.P`, and :class:`~.QuadOperator`
observables.
Args:
observable (str): name of the observable
wires (Wires): wires the observable is to be measured on
par (tuple): parameters for the observable
Returns:
array[float]: samples in an array of dimension ``(n, num_wires)``
"""
if len(wires) != 1:
raise ValueError("Only one mode can be measured in homodyne.")
if observable == "QuadX":
phi = 0.0
elif observable == "QuadP":
phi = np.pi / 2
elif observable == "QuadOperator":
phi = par[0]
else:
raise NotImplementedError(f"default.gaussian does not support sampling {observable}")
cov, mu = self.reduced_state(wires)
rot = rotation(phi)
muphi = rot.T @ mu
covphi = rot.T @ cov @ rot
stdphi = math.sqrt(covphi[0, 0])
meanphi = muphi[0]
return np.random.normal(meanphi, stdphi, self.shots)
[docs] def reset(self):
"""Reset the device"""
# init the state vector to |00..0>
self._state = vacuum_state(self.num_wires, self.hbar)
[docs] def reduced_state(self, wires):
r"""Returns the covariance matrix and the vector of means of the specified wires.
Args:
wires (Wires): requested wires
Returns:
tuple (cov, means): cov is a square array containing the covariance matrix,
and means is an array containing the vector of means
"""
if len(wires) == self.num_wires:
# reduced state is full state
return self._state
# translate to wire labels used by device
device_wires = self.map_wires(wires)
# reduce rho down to specified subsystems
ind = np.concatenate([device_wires.toarray(), device_wires.toarray() + self.num_wires])
rows = ind.reshape(-1, 1)
cols = ind.reshape(1, -1)
return self._state[0][rows, cols], self._state[1][ind]
@property
def operations(self):
return set(self._operation_map.keys())
@property
def observables(self):
return set(self._observable_map.keys())
# pylint: disable=arguments-differ
[docs] def execute(self, operations, observables):
if len(observables) > 1:
raise qml.QuantumFunctionError("Default gaussian only support single measurements.")
return super().execute(operations, observables)
[docs] def batch_execute(self, circuits):
results = super().batch_execute(circuits)
results = [qml.math.squeeze(res) for res in results]
return results
_modules/pennylane/devices/default_gaussian
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