sf.backends.GaussianBackend¶

class
GaussianBackend
[source]¶ Bases:
strawberryfields.backends.base.BaseGaussian
The GaussianBackend implements a simulation of quantum optical circuits in NumPy using the Gaussian formalism, returning a
GaussianState
state object.The primary component of the GaussianBackend is a
GaussianModes
object which is used to simulate a multimode quantum optical system.GaussianBackend
provides the basic APIcompatible interface to the simulator, while theGaussianModes
object actually carries out the mathematical simulation.The
GaussianModes
simulators maintain an internal covariance matrix & vector of means representation of a multimode quantum optical system.Note that unlike commonly used covariance matrix representations we encode our state in two complex matrices \(N\) and \(M\) that are defined as follows \(N_{i,j} = \langle a^\dagger _i a_j \rangle\) \(M_{i,j} = \langle a _i a_j \rangle\) and a vector of means \(\alpha_i =\langle a_i \rangle\).
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)cubic_phase
(gamma, mode)del_mode
(modes)Delete modes from the circuit.
displacement
(r, phi, mode)Apply the displacement operation to the specified mode.
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)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_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_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_state
(n, mode)prepare_gaussian_state
(r, V, modes)Prepare a Gaussian 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.
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]¶ 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) – 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

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]

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)¶

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_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.
See
BaseBackend.measure_homodyne()
. Keyword Arguments
eps (float) – Homodyne amounts to projection onto a quadrature eigenstate. This eigenstate is approximated by a squeezed state whose variance has been squeezed to the amount
eps
, \(V_\text{meas} = \texttt{eps}^2\). Perfect homodyning is obtained wheneps
\(\to 0\). 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)[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

passive
(T, modes)[source]¶ 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_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_state
(n, mode)¶

prepare_gaussian_state
(r, V, modes)[source]¶ Prepare a Gaussian state.
The specified modes are traced out and replaced with a Gaussian state provided via a vector of means and a covariance matrix.
Note
This method is \(\hbar\) independent. The input arrays are the means and covariance of the \(a+a^\dagger\) and \(i(aa^\dagger)\) operators. They are obtained by dividing the xp means by \(\sqrt{\hbar/2}\) and the xp covariance by \(\hbar/2\).
 Parameters
r (array) – vector of means in xp ordering
V (array) – covariance matrix in xp 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.

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

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
GaussianState

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
