sf.backends.BosonicBackend¶

class
BosonicBackend
[source]¶ Bases:
strawberryfields.backends.base.BaseBosonic
The BosonicBackend implements a simulation of quantum optical circuits in NumPy by representing states as linear combinations of Gaussian functions in phase space., returning a
BosonicState
state object.The primary component of the BosonicBackend is a
BosonicModes
object which is used to simulate a multimode quantum optical system.BosonicBackend
provides the basic APIcompatible interface to the simulator, while theBosonicModes
object actually carries out the mathematical simulation.The
BosonicModes
simulators maintain internal sets of weights, means and covariance matrices for all the Gaussian functions in the linear combination. Note these can be complexvalued quantities.Attributes
Methods
add_mode
([n])Adds new modes to the circuit each with a number of Gaussian peaks specified by peaks.
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)cubic_phase
(gamma, mode)del_mode
(modes)Delete modes from the circuit.
displacement
(r, phi, mode)Apply the displacement operation to the specified mode.
gaussian_cptp
(modes, X[, Y])Transforms the state according to a deterministic Gaussian CPTP map.
Return a list of the active modes for the circuit.
init_circuit
(prog)Instantiate the circuit and initialize weights, means, and covs depending on the
Preparation
classes.is_vacuum
([tol])Test whether the current circuit state is vacuum (up to given tolerance).
kerr_interaction
(kappa, mode)loss
(T, mode)Perform a loss channel operation on the specified mode.
mb_squeeze_avg
(mode, r, phi, r_anc, eta_anc)Squeeze mode by the amount \(re^{i\phi}\) using measurementbased squeezing.
mb_squeeze_single_shot
(mode, r, phi, r_anc, …)Squeeze mode by the amount \(re^{i\phi}\) using measurementbased squeezing.
measure_fock
(modes[, shots, select])Measure the given modes in the Fock basis.
measure_heterodyne
(mode[, shots, select])Perform a heterodyne measurement on the given mode.
measure_homodyne
(phi, mode[, shots, select])Measure a phase space quadrature of the given 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.
passive
(T, modes)Perform an arbitrary multimode passive operation
prepare_cat
(a, theta, p, representation, …)Prepares the arrays of weights, means and covs for a cat state:
prepare_cat_real_rep
(a, theta, p, ampl_cutoff, D)Prepares the arrays of weights, means and covs for a cat state:
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, mode)prepare_fock
(n[, r])Prepares the arrays of weights, means and covs of a Fock state.
prepare_fock_state
(n, mode)prepare_gaussian_state
(r, V, modes)Prepare a Gaussian state.
prepare_gkp
(state, epsilon, ampl_cutoff[, …])Prepares the arrays of weights, means and covs for a finite energy GKP state.
prepare_ket_state
(state, mode)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.
run_prog
(prog, **kwargs)Runs a strawberryfields program using the bosonic backend.
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.

add_mode
(n=1, **kwargs)[source]¶ Adds new modes to the circuit each with a number of Gaussian peaks specified by peaks.
 Parameters
n (int) – number of new modes to add
 Keyword Arguments
peaks (list) – number of Gaussian peaks for each new mode
 Raises
ValueError – if the length of the list of peaks is different than the number of modes

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) – Hilbert space truncation dimension (for Fock basis backends only)
batch_size (int) – (optional) batchaxis dimension, enables batched operation if > 1 (for the TF backend only)

cross_kerr_interaction
(kappa, mode1, mode2)¶

cubic_phase
(gamma, mode)¶

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

gaussian_cptp
(modes, X, Y=None)[source]¶ Transforms the state according to a deterministic Gaussian CPTP map.
 Parameters
modes (list) – list of modes on which
(X,Y)
actX (array) – matrix for multiplicative part of transformation
Y (array) – matrix for additive part of transformation

get_cutoff_dim
()¶

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]

init_circuit
(prog)[source]¶ Instantiate the circuit and initialize weights, means, and covs depending on the
Preparation
classes. Parameters
prog (object) –
Program
instance Raises
NotImplementedError – if
Ket
orDensityMatrix
preparation usedCircuitError – if any of the parameters for nonGaussian state preparation are symbolic

is_vacuum
(tol=1e10, **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)¶

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

mb_squeeze_avg
(mode, r, phi, r_anc, eta_anc)[source]¶ Squeeze mode by the amount \(re^{i\phi}\) using measurementbased squeezing.
Here, the average, deterministic Gaussian CPTP map is applied.
 Parameters
mode (int) – mode to be squeezed
r (float) – target squeezing magnitude
phi (float) – target squeezing phase
r_anc (float) – squeezing magnitude of the ancillary mode
eta_anc (float) – detection efficiency of the ancillary mode

mb_squeeze_single_shot
(mode, r, phi, r_anc, eta_anc)[source]¶ Squeeze mode by the amount \(re^{i\phi}\) using measurementbased squeezing.
Here, the singleshot map is applied, returning the ancillary measurement outcome.
 Parameters
mode (int) – mode to be squeezed
r (float) – target squeezing magnitude
phi (float) – target squeezing phase
r_anc (float) – squeezing magnitude of the ancillary mode
eta_anc (float) – detection efficiency of the ancillary mode
 Returns
the measurement outcome of the ancilla
 Return type
float

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_heterodyne
(mode, shots=1, select=None, **kwargs)[source]¶ Perform a heterodyne measurement on the given mode.
Updates the current state of the circuit such that the measured mode is reset to the vacuum state.
 Parameters
mode (int) – which mode to measure
shots (int) – number of measurement samples to obtain
select (None or complex) – If not None: desired value of the measurement result. Enables postselection on specific measurement results instead of random sampling.
 Returns
measured value
 Return type
complex

measure_homodyne
(phi, mode, shots=1, select=None, **kwargs)[source]¶ Measure a phase space quadrature of the given mode.
For the measured mode, samples the probability distribution \(f(q) = \bra{q_\phi} \rho \ket{q_\phi}\) and returns the sampled value. Here \(\ket{q_\phi}\) is the eigenstate of the operator
\[\hat{q}_\phi = \sqrt{2/\hbar}(\cos(\phi)\hat{x} +\sin(\phi)\hat{p}) = e^{i\phi} \hat{a} +e^{i\phi} \hat{a}^\dagger.\]Note
This method is \(\hbar\) independent. The returned values can be converted to conventional position/momentum eigenvalues by multiplying them with \(\sqrt{\hbar/2}\).
Updates the current state such that the measured mode is reset to the vacuum state. This is because we cannot represent exact position or momentum eigenstates in any of the backends, and experimentally the photons are destroyed in a homodyne measurement.
 Parameters
phi (float) – phase angle of the quadrature to measure (x: \(\phi=0\), p: \(\phi=\pi/2\))
mode (int) – which mode to measure
shots (int) – number of measurement samples to obtain
select (None or float) – If not None: desired value of the measurement result. Enables postselection on specific measurement results instead of random sampling.
Keyword arguments can be used to pass additional parameters to the backend. Options for such arguments will be documented in the respective subclasses.
 Returns
measured value
 Return type
float

measure_threshold
(modes, shots=1, select=None, **kwargs)[source]¶ 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)¶ 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

passive
(T, modes)¶ Perform an arbitrary multimode passive operation
 Parameters
T (array) – an NxN matrix acting on a N mode state
modes (int or Sequence[int]) – Which modes to prepare the state in.
Details and Conventions
Acts the following transformation on the state:
\[a^{\dagger}_i \to \sum_j T_{ij} a^{\dagger}_j\]

prepare_cat
(a, theta, p, representation, ampl_cutoff, D)[source]¶ Prepares the arrays of weights, means and covs for a cat state:
\(\ket{\text{cat}(\alpha)} = \frac{1}{N} (\ket{\alpha} +e^{i\phi} \ket{\alpha})\),
where \(\alpha = ae^{i\theta}\).
 Parameters
a (float) – displacement magnitude \(\alpha\)
theta (float) – displacement angle \(\theta\)
p (float) – Parity, where \(\phi=p\pi\).
p=0
corresponds to an even cat state, andp=1
an odd cat state.representation (str) – whether to use the
'real'
or'complex'
representationampl_cutoff (float) – if using the
'real'
representation, this determines how many terms to keepD (float) – for
'real'
representation, quality parameter of approximation
 Returns
arrays of the weights, means and covariances for the state
 Return type
tuple

prepare_cat_real_rep
(a, theta, p, ampl_cutoff, D)[source]¶ Prepares the arrays of weights, means and covs for a cat state:
\(\ket{\text{cat}(\alpha)} = \frac{1}{N} (\ket{\alpha} +e^{i\phi\pi} \ket{\alpha})\),
where \(\alpha = ae^{i\theta}\).
For this representation, weights, means and covariances are realvalued.
 Parameters
a (float) – displacement magnitude \(\alpha\)
theta (float) – displacement angle \(\theta\)
p (float) – Parity, where \(\phi=p\pi\).
p=0
corresponds to an even cat state, andp=1
an odd cat state.ampl_cutoff (float) – this determines how many terms to keep
D (float) – quality parameter of approximation
 Returns
arrays of the weights, means and covariances for the state
 Return type
tuple

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, mode)¶

prepare_fock
(n, r=0.05)[source]¶ Prepares the arrays of weights, means and covs of a Fock state.
 Parameters
n (int) – photon number
r (float) – quality parameter for the approximation
 Returns
arrays of the weights, means and covariances for the state
 Return type
tuple
 Raises
ValueError – if \(1/r^2\) is less than \(n\)

prepare_fock_state
(n, mode)¶

prepare_gaussian_state
(r, V, modes)[source]¶ Prepare a Gaussian state.
Note the different basisordering from the
GaussianBackend
.The specified modes are traced out and replaced with a Gaussian state provided via a vector of means and a covariance matrix.
 Parameters
r (array) – vector of means in \((x_1,p_1,x_2,p_2,\dots)\) ordering
V (array) – covariance matrix in \((x_1,p_1,x_2,p_2,\dots)\) ordering
modes (int or Sequence[int]) – Which modes to prepare the state in. If the modes are not sorted, this is taken into account when preparing the state. I.e., when a two mode state is prepared with
modes=[3,1]
, the first mode of the given state goes into mode 3 and the second mode goes into mode 1.
 Raises
ValueError – if the shapes of r or V do not match the number of modes.

prepare_gkp
(state, epsilon, ampl_cutoff, representation='real', shape='square')[source]¶ Prepares the arrays of weights, means and covs for 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
ampl_cutoff (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, mode)¶

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

run_prog
(prog, **kwargs)[source]¶ Runs a strawberryfields program using the bosonic backend.
 Parameters
prog (object) – sf.Program instance
 Returns
a tuple of the list of applied commands and the dictionary of measurement samples
 Return type
tuple
 Raises
NotApplicableError – if an op in the program does not apply to the bosonic backend
NotImplementedError – if an op in the program is not implemented in the bosonic backend

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()
.For the bosonic backend, mode indices are sorted in ascending order.
 Returns
object containing all state information
 Return type
BosonicState

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
