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.
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"""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_ = 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 add_mode(self, n=1, **kwargs): self.circuit.alloc(n) self._modemap.add(n)
[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 get_modes(self): return [i for i, j in enumerate(self._modemap._map) if j is not None]
[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 rotation(self, phi, mode): self.circuit.phase_shift(phi, self._remap_modes(mode))
[docs] def displacement(self, r, phi, mode): self.circuit.displacement(r, phi, self._remap_modes(mode))
[docs] def squeeze(self, r, phi, mode): self.circuit.squeeze(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 loss(self, T, mode): self.circuit.loss(T, self._remap_modes(mode))
[docs] def is_vacuum(self, tol=0.0, **kwargs): return self.circuit.is_vacuum(tol)
[docs] def get_cutoff_dim(self): return self.circuit._trunc
[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))