Source code for strawberryfields.backends.fockbackend.backend
# Copyright 2019 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.
"""Fock backend simulator"""
# pylint: disable=protected-access,too-many-public-methods
import string
from cmath import phase
import numpy as np
from strawberryfields.backends import BaseFock, ModeMap
from strawberryfields.backends.states import BaseFockState
from .circuit import Circuit
indices = string.ascii_lowercase
[docs]class FockBackend(BaseFock):
r"""Implements a simulation of quantum optical circuits in a truncated
Fock basis using NumPy, returning a :class:`~.BaseFock`
state object.
The primary component of the FockBackend is a
:attr:`~.FockBackend.circuit` object which is used to simulate a multi-mode quantum optical system. The
:class:`FockBackend` provides the basic API-compatible interface to the simulator, while the
:attr:`~.FockBackend.circuit` object actually carries out the mathematical simulation.
The :attr:`~.FockBackend.circuit` simulator maintains an internal tensor representation of the quantum state of a multi-mode quantum optical system
using a (truncated) Fock basis representation. As its various state manipulation methods are called, the quantum state is updated
to reflect these changes. The simulator will try to keep the internal state in a pure (vector) representation
for as long as possible. Unitary gates will not change the type of representation, while state preparations and measurements will.
A number of factors determine the shape and dimensionality of the state tensor:
* the underlying state representation being used (either a ket vector or a density matrix)
* the number of modes :math:`n` actively being simulated
* the cutoff dimension :math:`D` for the Fock basis
The state tensor corresponds to a multimode quantum system. If the
representation is a pure state, the state tensor has shape
:math:`(\underbrace{D,...,D}_{n~\text{times}})`.
In a mixed state representation, the state tensor has shape
:math:`(\underbrace{D,D,...,D,D}_{2n~\text{times}})`.
Indices for the same mode appear consecutively. Hence, for a mixed state, the first two indices
are for the first mode, the second are for the second mode, etc.
..
.. currentmodule:: strawberryfields.backends.fockbackend
.. autosummary::
:toctree:
~circuit.Circuit
~ops
"""
short_name = "fock"
circuit_spec = "fock"
def __init__(self):
"""Instantiate a FockBackend object."""
super().__init__()
self._supported["mixed_states"] = True
self._init_modes = None #: int: initial number of modes in the circuit
self._modemap = None #: Modemap: maps external mode indices to internal ones
self.circuit = (
None #: ~.fockbackend.circuit.Circuit: representation of the simulated quantum state
)
def _remap_modes(self, modes):
if isinstance(modes, int):
modes = [modes]
was_int = True
else:
was_int = False
map_ = self._modemap.show()
submap = [map_[m] for m in modes]
if not self._modemap.valid(modes) or None in submap:
raise ValueError("The specified modes are not valid.")
remapped_modes = self._modemap.remap(modes)
if was_int:
remapped_modes = remapped_modes[0]
return remapped_modes
[docs] def begin_circuit(self, num_subsystems, **kwargs):
r"""Instantiate a quantum circuit.
Instantiates a representation of a quantum optical state with ``num_subsystems`` modes.
The state is initialized to vacuum.
The modes in the circuit are indexed sequentially using integers, starting from zero.
Once an index is assigned to a mode, it can never be re-assigned to another mode.
If the mode is deleted its index becomes invalid.
An operation acting on an invalid or unassigned mode index raises an ``IndexError`` exception.
Args:
num_subsystems (int): number of modes in the circuit
Keyword Args:
cutoff_dim (int): Numerical Hilbert space cutoff dimension for the modes.
For each mode, the simulator can represent the Fock states :math:`\ket{0}, \ket{1}, \ldots, \ket{\text{cutoff_dim}-1}`.
pure (bool): If True (default), use a pure state representation (otherwise will use a mixed state representation).
"""
cutoff_dim = kwargs.get("cutoff_dim", None)
pure = kwargs.get("pure", True)
if cutoff_dim is None:
raise ValueError("Argument 'cutoff_dim' must be passed to the Fock backend")
if not isinstance(cutoff_dim, int):
raise ValueError("Argument 'cutoff_dim' must be a positive integer")
if not isinstance(num_subsystems, int):
raise ValueError("Argument 'num_subsystems' must be a positive integer")
if not isinstance(pure, bool):
raise ValueError("Argument 'pure' must be either True or False")
self._init_modes = num_subsystems
self.circuit = Circuit(num_subsystems, cutoff_dim, pure)
self._modemap = ModeMap(num_subsystems)
[docs] def del_mode(self, modes):
remapped_modes = self._remap_modes(modes)
if isinstance(remapped_modes, int):
remapped_modes = [remapped_modes]
self.circuit.dealloc(remapped_modes)
self._modemap.delete(modes)
[docs] def reset(self, pure=True, **kwargs):
cutoff = kwargs.get("cutoff_dim", self.circuit._trunc)
self._modemap.reset()
self.circuit.reset(pure, num_subsystems=self._init_modes, cutoff_dim=cutoff)
[docs] def prepare_vacuum_state(self, mode):
self.circuit.prepare_mode_fock(0, self._remap_modes(mode))
[docs] def prepare_coherent_state(self, r, phi, mode):
self.circuit.prepare_mode_coherent(r, phi, self._remap_modes(mode))
[docs] def prepare_squeezed_state(self, r, phi, mode):
self.circuit.prepare_mode_squeezed(r, phi, self._remap_modes(mode))
[docs] def prepare_displaced_squeezed_state(self, r_d, phi_d, r_s, phi_s, mode):
self.circuit.prepare_mode_displaced_squeezed(
r_d, phi_d, r_s, phi_s, self._remap_modes(mode)
)
[docs] def prepare_thermal_state(self, nbar, mode):
self.circuit.prepare_mode_thermal(nbar, self._remap_modes(mode))
[docs] def displacement(self, r, phi, mode):
self.circuit.displacement(r, phi, self._remap_modes(mode))
[docs] def two_mode_squeeze(self, r, phi, mode1, mode2):
self.circuit.two_mode_squeeze(r, phi, self._remap_modes(mode1), self._remap_modes(mode2))
[docs] def beamsplitter(self, theta, phi, mode1, mode2):
self.circuit.beamsplitter(theta, phi, self._remap_modes(mode1), self._remap_modes(mode2))
[docs] def mzgate(self, phi_in, phi_ex, mode1, mode2):
self.circuit.mzgate(phi_in, phi_ex, self._remap_modes(mode1), self._remap_modes(mode2))
[docs] def measure_homodyne(self, phi, mode, shots=1, select=None, **kwargs):
"""Perform a homodyne measurement on the specified mode.
See :meth:`.BaseBackend.measure_homodyne`.
Keyword Args:
num_bins (int): Number of equally spaced bins for the probability distribution function
(pdf) simulating the homodyne measurement (default: 100000).
max (float): The pdf is discretized onto the 1D grid [-max,max] (default: 10).
"""
if shots != 1:
raise NotImplementedError(
"fock backend currently does not support " "shots != 1 for homodyne measurement"
)
return self.circuit.measure_homodyne(phi, self._remap_modes(mode), select=select, **kwargs)
[docs] def state(self, modes=None, **kwargs):
s, pure = self.circuit.get_state()
if modes is None:
# reduced state is full state
red_state = s
num_modes = len(s.shape) if pure else len(s.shape) // 2
modes = [m for m in range(num_modes)]
else:
# convert to mixed state representation
if pure:
num_modes = len(s.shape)
left_str = [indices[i] for i in range(0, 2 * num_modes, 2)]
right_str = [indices[i] for i in range(1, 2 * num_modes, 2)]
out_str = [indices[: 2 * num_modes]]
einstr = "".join(left_str + [","] + right_str + ["->"] + out_str)
rho = np.einsum(einstr, s, s.conj())
else:
rho = s
# reduce rho down to specified subsystems
if isinstance(modes, int):
modes = [modes]
if len(modes) != len(set(modes)):
raise ValueError("The specified modes cannot be duplicated.")
num_modes = len(rho.shape) // 2
if len(modes) > num_modes:
raise ValueError(
"The number of specified modes cannot be larger than the number of subsystems."
)
keep_indices = indices[: 2 * len(modes)]
trace_indices = indices[2 * len(modes) : len(modes) + num_modes]
ind = [i * 2 for i in trace_indices]
ctr = 0
for m in range(num_modes):
if m in modes:
ind.insert(m, keep_indices[2 * ctr : 2 * (ctr + 1)])
ctr += 1
indStr = "".join(ind) + "->" + keep_indices
red_state = np.einsum(indStr, rho)
# permute indices of returned state to reflect the ordering of modes (we know and hence can assume that red_state is a mixed state)
if modes != sorted(modes):
mode_permutation = np.argsort(modes)
index_permutation = [2 * x + i for x in mode_permutation for i in (0, 1)]
red_state = np.transpose(red_state, np.argsort(index_permutation))
cutoff = self.circuit._trunc
mode_names = ["q[{}]".format(i) for i in np.array(self.get_modes())[modes]]
state = BaseFockState(red_state, len(modes), pure, cutoff, mode_names)
return state
# ==============================================
# Fock state specific
# ==============================================
[docs] def prepare_fock_state(self, n, mode):
self.circuit.prepare_mode_fock(n, self._remap_modes(mode))
[docs] def prepare_ket_state(self, state, modes):
self.circuit.prepare_multimode(state, self._remap_modes(modes))
[docs] def prepare_dm_state(self, state, modes):
self.circuit.prepare_multimode(state, self._remap_modes(modes))
[docs] def cubic_phase(self, gamma, mode):
self.circuit.cubic_phase_shift(gamma, self._remap_modes(mode))
[docs] def kerr_interaction(self, kappa, mode):
self.circuit.kerr_interaction(kappa, self._remap_modes(mode))
[docs] def cross_kerr_interaction(self, kappa, mode1, mode2):
self.circuit.cross_kerr_interaction(
kappa, self._remap_modes(mode1), self._remap_modes(mode2)
)
[docs] def measure_fock(self, modes, shots=1, select=None, **kwargs):
if shots != 1:
raise NotImplementedError(
"fock backend currently does not support " "shots != 1 for Fock measurement"
)
return self.circuit.measure_fock(self._remap_modes(modes), select=select)
[docs] def prepare_gkp(
self, state, epsilon, ampl_cutoff, representation="real", shape="square", mode=None
):
r"""Prepares the Fock representation of a finite energy GKP state.
GKP states are qubits, with the qubit state defined by:
:math:`\ket{\psi}_{gkp} = \cos\frac{\theta}{2}\ket{0}_{gkp} + e^{-i\phi}\sin\frac{\theta}{2}\ket{1}_{gkp}`
where the computational basis states are :math:`\ket{\mu}_{gkp} = \sum_{n} \ket{(2n+\mu)\sqrt{\pi\hbar}}_{q}`.
Args:
state (list): ``[theta,phi]`` for qubit definition above
epsilon (float): finite energy parameter of the state
amplcutoff (float): this determines how many terms to keep
representation (str): ``'real'`` or ``'complex'`` reprsentation
shape (str): shape of the lattice; default 'square'
Returns:
tuple: arrays of the weights, means and covariances for the state
Raises:
NotImplementedError: if the complex representation or a non-square lattice is attempted
"""
if representation == "complex":
raise NotImplementedError("The complex description of GKP is not implemented")
if shape != "square":
raise NotImplementedError("Only square GKP are implemented for now")
theta, phi = state[0], state[1]
self.circuit.prepare_gkp(theta, phi, epsilon, ampl_cutoff, self._remap_modes(mode))
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