sf.backends.FockBackend¶

class
FockBackend
[source]¶ Bases:
strawberryfields.backends.base.BaseFock
Implements a simulation of quantum optical circuits in a truncated Fock basis using NumPy, returning a
BaseFock
state object.The primary component of the FockBackend is a
circuit
object which is used to simulate a multimode quantum optical system. TheFockBackend
provides the basic APIcompatible interface to the simulator, while thecircuit
object actually carries out the mathematical simulation.The
circuit
simulator maintains an internal tensor representation of the quantum state of a multimode 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 \(n\) actively being simulated
the cutoff dimension \(D\) 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 \((\underbrace{D,...,D}_{n~\text{times}})\). In a mixed state representation, the state tensor has shape \((\underbrace{D,D,...,D,D}_{2n~\text{times}})\). 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.
Attributes
Methods
add_mode
([n])Add modes to the circuit.
beamsplitter
(theta, phi, mode1, mode2)Apply the beamsplitter operation to the specified modes.
begin_circuit
(num_subsystems, **kwargs)Instantiate a quantum circuit.
cross_kerr_interaction
(kappa, mode1, mode2)Apply the two mode crossKerr interaction \(\exp{(i\kappa \hat{n}_1\hat{n}_2)}\) to the specified modes.
cubic_phase
(gamma, mode)Apply the cubic phase operation to the specified mode.
del_mode
(modes)Delete modes from the circuit.
displacement
(r, phi, mode)Apply the displacement operation to the specified mode.
Returns the Hilbert space cutoff dimension used.
Return a list of the active modes for the circuit.
is_vacuum
([tol])Test whether the current circuit state is vacuum (up to given tolerance).
kerr_interaction
(kappa, mode)Apply the Kerr interaction \(\exp{(i\kappa \hat{n}^2)}\) to the specified mode.
loss
(T, mode)Perform a loss channel operation on the specified mode.
measure_fock
(modes[, shots, select])Measure the given modes in the Fock basis.
measure_homodyne
(phi, mode[, shots, select])Perform a homodyne measurement on the specified mode.
measure_threshold
(modes[, shots, select])Measure the given modes in the thresholded Fock basis, i.e., zero or nonzero photons).
mzgate
(phi_in, phi_ex, mode1, mode2)Apply the MachZehnder interferometer operation to the specified modes.
prepare_coherent_state
(r, phi, mode)Prepare a coherent state in the specified mode.
prepare_displaced_squeezed_state
(r_d, phi_d, …)Prepare a displaced squeezed state in the specified mode.
prepare_dm_state
(state, modes)Prepare the given mixed state in the specified modes.
prepare_fock_state
(n, mode)Prepare a Fock state in the specified mode.
prepare_gkp
(state, epsilon, ampl_cutoff[, …])Prepares the Fock representation of a finite energy GKP state.
prepare_ket_state
(state, modes)Prepare the given ket state in the specified modes.
prepare_squeezed_state
(r, phi, mode)Prepare a squeezed vacuum state in the specified mode.
prepare_thermal_state
(nbar, mode)Prepare a thermal state in the specified mode.
prepare_vacuum_state
(mode)Prepare the vacuum state in the specified mode.
reset
([pure])Reset the circuit so that all the modes are in the vacuum state.
rotation
(phi, mode)Apply the phasespace rotation operation to the specified mode.
squeeze
(r, phi, mode)Apply the squeezing operation to the specified mode.
state
([modes])Returns the state of the quantum simulation.
supports
(name)Check whether the backend supports the given operating mode.
thermal_loss
(T, nbar, mode)Perform a thermal loss channel operation on the specified mode.
two_mode_squeeze
(r, phi, mode1, mode2)Apply a twomode squeezing operator to the two specified modes.

add_mode
(n=1, **kwargs)[source]¶ Add modes to the circuit.
The new modes are initialized to the vacuum state. They are assigned mode indices sequentially, starting from the first unassigned index.
 Parameters
n (int) – number of modes to add
 Returns
indices of the newly added modes
 Return type
list[int]
 Keyword Arguments
peaks (list) – number of Gaussian peaks for each new mode (for bosonic backend only)

beamsplitter
(theta, phi, mode1, mode2)[source]¶ Apply the beamsplitter operation to the specified modes.
 Parameters
theta (float) – transmissivity is cos(theta)
phi (float) – phase angle
mode1 (int) – first mode that beamsplitter acts on
mode2 (int) – second mode that beamsplitter acts on

begin_circuit
(num_subsystems, **kwargs)[source]¶ 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 reassigned 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. Parameters
num_subsystems (int) – number of modes in the circuit
 Keyword Arguments
cutoff_dim (int) – Numerical Hilbert space cutoff dimension for the modes. For each mode, the simulator can represent the Fock states \(\ket{0}, \ket{1}, \ldots, \ket{\text{cutoff_dim}1}\).
pure (bool) – If True (default), use a pure state representation (otherwise will use a mixed state representation).

cross_kerr_interaction
(kappa, mode1, mode2)[source]¶ Apply the two mode crossKerr interaction \(\exp{(i\kappa \hat{n}_1\hat{n}_2)}\) to the specified modes.
 Parameters
kappa (float) – strength of the interaction
mode1 (int) – first mode that crossKerr interaction acts on
mode2 (int) – second mode that crossKerr interaction acts on

cubic_phase
(gamma, mode)[source]¶ Apply the cubic phase operation to the specified mode.
Applies the operation
\[\exp\left(i \frac{\gamma}{6} (\hat{a} +\hat{a}^\dagger)^3\right)\]to the specified mode.
Note
This method is \(\hbar\) independent. The usual definition of the cubic phase gate is \(\hbar\) dependent:
\[V(\gamma') = \exp\left(i \frac{\gamma'}{3\hbar} \hat{x}^3\right) = \exp\left(i \frac{\gamma' \sqrt{\hbar/2}}{6} (\hat{a} +\hat{a}^\dagger)^3\right).\]Hence the cubic phase gate \(V(\gamma')\) is executed on a backend by scaling the \(\gamma'\) parameter by \(\sqrt{\hbar/2}\) and then passing it to this method, much in the way the \(\hbar\) dependent X and Z gates are implemented through the \(\hbar\) independent
displacement()
method.Warning
The cubic phase gate can suffer heavily from numerical inaccuracies due to finitedimensional cutoffs in the Fock basis. The gate implementation in Strawberry Fields is unitary, but it does not implement an exact cubic phase gate. The Kerr gate provides an alternative nonGaussian gate.
 Parameters
gamma (float) – scaled cubic phase shift, \(\gamma = \gamma' \sqrt{\hbar/2}\)
mode (int) – which mode to apply it to

del_mode
(modes)[source]¶ Delete modes from the circuit.
The deleted modes are traced out. As a result the state may have to be described using a density matrix.
The indices of the deleted modes become invalid for the lifetime of the circuit object. They will never be reassigned to other modes. Deleting a mode that has already been deleted raises an
IndexError
exception. Parameters
modes (Sequence[int]) – mode numbers to delete

displacement
(r, phi, mode)[source]¶ Apply the displacement operation to the specified mode.
 Parameters
r (float) – displacement amplitude
phi (float) – displacement angle
mode (int) – which mode to apply the displacement to

get_cutoff_dim
()[source]¶ Returns the Hilbert space cutoff dimension used.
 Returns
cutoff dimension
 Return type
int

get_modes
()[source]¶ Return a list of the active modes for the circuit.
A mode is active if it has been created and has not been deleted.
 Returns
sorted list of active (assigned, not invalid) mode indices
 Return type
list[int]

is_vacuum
(tol=0.0, **kwargs)[source]¶ Test whether the current circuit state is vacuum (up to given tolerance).
Returns True iff \(\bra{0} \rho \ket{0} 1 \le\)
tol
, i.e., the fidelity of the current circuit state with the vacuum state is within the given tolerance from 1. Parameters
tol (float) – numerical tolerance
 Returns
True iff current state is vacuum up to tolerance tol
 Return type
bool

kerr_interaction
(kappa, mode)[source]¶ Apply the Kerr interaction \(\exp{(i\kappa \hat{n}^2)}\) to the specified mode.
 Parameters
kappa (float) – strength of the interaction
mode (int) – which mode to apply it to

loss
(T, mode)[source]¶ Perform a loss channel operation on the specified mode.
 Parameters
T (float) – loss parameter, \(0\leq T\leq 1\).
mode (int) – index of mode where operation is carried out

measure_fock
(modes, shots=1, select=None, **kwargs)[source]¶ Measure the given modes in the Fock basis.
Note
When
shots == 1
, updates the current system state to the conditional state of that measurement result. Whenshots > 1
, the system state is not updated. Parameters
modes (Sequence[int]) – which modes to measure
shots (int) – number of measurement samples to obtain
select (None or Sequence[int]) – If not None: desired values of the measurement results. Enables postselection on specific measurement results instead of random sampling.
len(select) == len(modes)
is required.
 Returns
measurement results
 Return type
tuple[int]

measure_homodyne
(phi, mode, shots=1, select=None, **kwargs)[source]¶ Perform a homodyne measurement on the specified mode.
See
BaseBackend.measure_homodyne()
. Keyword Arguments
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).

measure_threshold
(modes, shots=1, select=None, **kwargs)¶ Measure the given modes in the thresholded Fock basis, i.e., zero or nonzero photons).
Note
When :code:
shots == 1
, updates the current system state to the conditional state of that measurement result. When :code:shots > 1
, the system state is not updated. Parameters
modes (Sequence[int]) – which modes to measure
shots (int) – number of measurement samples to obtain
select (None or Sequence[int]) – If not None: desired values of the measurement results. Enables postselection on specific measurement results instead of random sampling.
len(select) == len(modes)
is required.
 Returns
measurement results
 Return type
tuple[int]

mzgate
(phi_in, phi_ex, mode1, mode2)[source]¶ Apply the MachZehnder interferometer operation to the specified modes.
 Parameters
phi_in (float) – internal phase
phi_ex (float) – external phase
mode1 (int) – first mode that MZ interferometer acts on
mode2 (int) – second mode that MZ interferometer acts on

prepare_coherent_state
(r, phi, mode)[source]¶ Prepare a coherent state in the specified mode.
The requested mode is traced out and replaced with the coherent state \(\ket{r e^{i\phi}}\). As a result the state may have to be described using a density matrix.
 Parameters
r (float) – coherent state displacement amplitude
phi (float) – coherent state displacement phase
mode (int) – which mode to prepare the coherent state in

prepare_displaced_squeezed_state
(r_d, phi_d, r_s, phi_s, mode)[source]¶ Prepare a displaced squeezed state in the specified mode.
The requested mode is traced out and replaced with the displaced squeezed state \(\ket{\alpha, z}\), where \(\alpha=r_d e^{i\phi_d}\) and \(z=r_s e^{i\phi_s}\). As a result the state may have to be described using a density matrix.
 Parameters
r_d (float) – displacement amplitude
phi_d (float) – displacement angle
r_s (float) – squeezing amplitude
phi_s (float) – squeezing angle
mode (int) – which mode to prepare the squeezed state in

prepare_dm_state
(state, modes)[source]¶ Prepare the given mixed state in the specified modes.
The requested modes are traced out and replaced with the given density matrix state (in the Fock basis). As a result the state will be described using a density matrix.
 Parameters
state (array) – Density matrix in the Fock basis. The state can be given in either matrix form, with two indices, or tensor form, with two indices per mode. For backends supporting batched mode, state can be a batch of such matrices or tensors.
modes (int or Sequence[int]) – which mode to prepare the state in If modes is not ordered this is take into account when preparing the state, i.e., when a two mode state is prepared in modes=[3,1], then the first mode of state goes into mode 3 and the second mode goes into mode 1 of the simulator.

prepare_fock_state
(n, mode)[source]¶ Prepare a Fock state in the specified mode.
The requested mode is traced out and replaced with the Fock state \(\ket{n}\). As a result the state may have to be described using a density matrix.
 Parameters
n (int) – Fock state to prepare
mode (int) – which mode to prepare the Fock state in

prepare_gkp
(state, epsilon, ampl_cutoff, representation='real', shape='square', mode=None)[source]¶ Prepares the Fock representation of a finite energy GKP state.
GKP states are qubits, with the qubit state defined by:
\(\ket{\psi}_{gkp} = \cos\frac{\theta}{2}\ket{0}_{gkp} + e^{i\phi}\sin\frac{\theta}{2}\ket{1}_{gkp}\)
where the computational basis states are \(\ket{\mu}_{gkp} = \sum_{n} \ket{(2n+\mu)\sqrt{\pi\hbar}}_{q}\).
 Parameters
state (list) –
[theta,phi]
for qubit definition aboveepsilon (float) – finite energy parameter of the state
amplcutoff (float) – this determines how many terms to keep
representation (str) –
'real'
or'complex'
reprsentationshape (str) – shape of the lattice; default ‘square’
 Returns
arrays of the weights, means and covariances for the state
 Return type
tuple
 Raises
NotImplementedError – if the complex representation or a nonsquare lattice is attempted

prepare_ket_state
(state, modes)[source]¶ Prepare the given ket state in the specified modes.
The requested modes are traced out and replaced with the given ket state (in the Fock basis). As a result the state may have to be described using a density matrix.
 Parameters
state (array) – Ket state in the Fock basis. The state can be given in either vector form, with one index, or tensor form, with one index per mode. For backends supporting batched mode, state can be a batch of such vectors or tensors.
modes (int or Sequence[int]) – Modes to prepare the state in. If modes is not ordered this is taken into account when preparing the state, i.e., when a two mode state is prepared in modes=[3,1], then the first mode of state goes into mode 3 and the second mode goes into mode 1 of the simulator.

prepare_squeezed_state
(r, phi, mode)[source]¶ Prepare a squeezed vacuum state in the specified mode.
The requested mode is traced out and replaced with the squeezed state \(\ket{z}\), where \(z=re^{i\phi}\). As a result the state may have to be described using a density matrix.
 Parameters
r (float) – squeezing amplitude
phi (float) – squeezing angle
mode (int) – which mode to prepare the squeezed state in

prepare_thermal_state
(nbar, mode)[source]¶ Prepare a thermal state in the specified mode.
The requested mode is traced out and replaced with the thermal state \(\rho(nbar)\). As a result the state may have to be described using a density matrix.
 Parameters
nbar (float) – thermal population (mean photon number) of the mode
mode (int) – which mode to prepare the thermal state in

prepare_vacuum_state
(mode)[source]¶ Prepare the vacuum state in the specified mode.
The requested mode is traced out and replaced with the vacuum state. As a result the state may have to be described using a density matrix.
 Parameters
mode (int) – which mode to prepare the vacuum state in

reset
(pure=True, **kwargs)[source]¶ Reset the circuit so that all the modes are in the vacuum state.
After the reset the circuit is in the same state as it was after the last
begin_circuit()
call. It will have the original number of modes, all initialized in the vacuum state. Some circuit parameters may be changed during the reset, see the keyword args below. Parameters
pure (bool) – if True, initialize the circuit in a pure state representation (will use a mixed state representation if pure is False)
 Keyword Arguments
cutoff_dim (int) – new Hilbert space truncation dimension (for Fock basis backends only)

rotation
(phi, mode)[source]¶ Apply the phasespace rotation operation to the specified mode.
 Parameters
phi (float) – rotation angle
mode (int) – which mode to apply the rotation to

squeeze
(r, phi, mode)[source]¶ Apply the squeezing operation to the specified mode.
 Parameters
r (float) – squeezing amplitude
phi (float) – squeezing angle
mode (int) – which mode to apply the squeeze to

state
(modes=None, **kwargs)[source]¶ Returns the state of the quantum simulation.
See
BaseBackend.state()
. Returns
state description
 Return type

supports
(name)¶ Check whether the backend supports the given operating mode.
Currently supported operating modes are:
“gaussian”: for manipulations in the Gaussian representation using the displacements and covariance matrices
“fock_basis”: for manipulations in the Fock representation
“bosonic”: for manipulations of states represented as linear combinations of Gaussian functions in phase space
“mixed_states”: for representations where the quantum state is mixed
“batched”: allows for a multiple circuits to be simulated in parallel
 Parameters
name (str) – name of the operating mode which we are checking support for
 Returns
True if this backend supports that operating mode.
 Return type
bool

thermal_loss
(T, nbar, mode)¶ Perform a thermal loss channel operation on the specified mode.
 Parameters
T (float) – loss parameter, \(0\leq T\leq 1\).
nbar (float) – mean photon number of the environment thermal state
mode (int) – index of mode where operation is carried out

two_mode_squeeze
(r, phi, mode1, mode2)[source]¶ Apply a twomode squeezing operator to the two specified modes.
 Parameters
r (float) – squeezing magnitude
phi (float) – squeezing angle
mode1 (int) – first mode that twomode squeezing gate acts on
mode2 (int) – second mode that twomode squeezing gate acts on