The Gaussian device

The Gaussian device gives access to Strawberry Field’s Gaussian simulator backend. This backend exploits the compact (and fully classically tractable) representation of so-called Gaussian continuous-variable operations. However, the backend cannot simulate non-Gaussian gates, such as a Cubic Phase or a Kerr gate.

The Gaussian device does not require a cutoff dimensions and simulations are exact up to numerical precision.

Usage

You can instantiate the Gaussian device in PennyLane as follows:

import pennylane as qml

dev = qml.device('strawberryfields.gaussian', wires=2)

The device can then be used just like other devices for the definition and evaluation of QNodes within PennyLane.

For instance, the following simple example defines a quantum_function circuit that first displaces the vacuum state, applies a beamsplitter, and then returns the photon number expectation. This function is converted into a QNode which is placed on the strawberryfields.gaussian device:

@qml.qnode(dev)
def quantum_function(x, theta):
    qml.Displacement(x, 0, wires=0)
    qml.Beamsplitter(theta, 0, wires=[0, 1])
    return qml.expval(qml.NumberOperator(0))

We can evaluate the QNode for arbitrary values of the circuit parameters:

>>> quantum_function(1., 0.543)
0.7330132578095255

We can also evaluate the derivative with respect to any parameter(s):

>>> dqfunc = qml.grad(quantum_function, argnum=0)
>>> dqfunc(1., 0.543)
1.4660265156190515

The continuous-variable QNodes available via Strawberry Fields can also be combined with qubit-based QNodes and classical nodes to build up a hybrid computational model. Such hybrid models can be optimized using the built-in optimizers provided by PennyLane.

Device options

The Strawberry Fields Gaussian device accepts additional arguments beyond the PennyLane default device arguments.

hbar=2

The convention chosen in the canonical commutation relation \([x, p] = i \hbar\). Default value is \(\hbar=2\).

cutoff_dim

the Fock basis truncation to be applied when computing quantities in the Fock basis (such as probabilities)

shots=None

The number of circuit evaluations/random samples used to estimate expectation values of observables. The default value of None means that the exact expectation value is returned.

If shots is a positive integer or a list of integers, the Gaussian device calculates the variance of the expectation value(s), and use the Berry-Esseen theorem to estimate the sampled expectation value.

Supported operations

The Strawberry Fields Gaussian device supports all Gaussian continuous-variable (CV) operations and observables provided by PennyLane.

Supported operations:

Beamsplitter

Beamsplitter interaction.

CoherentState

Prepares a coherent state.

ControlledAddition

Controlled addition operation.

ControlledPhase

Controlled phase operation.

DisplacedSqueezedState

Prepares a displaced squeezed vacuum state.

Displacement

Phase space displacement.

GaussianState

Prepare subsystems in a given Gaussian state.

QuadraticPhase

Quadratic phase shift.

Rotation

Phase space rotation.

SqueezedState

Prepares a squeezed vacuum state.

Squeezing

Phase space squeezing.

ThermalState

Prepares a thermal state.

TwoModeSqueezing

Phase space two-mode squeezing.

Supported observables:

Identity

The identity observable \(\I\).

NumberOperator

The photon number observable \(\langle \hat{n}\rangle\).

TensorN

The tensor product of the NumberOperator acting on different wires.

X

The position quadrature observable \(\hat{x}\).

P

The momentum quadrature observable \(\hat{p}\).

QuadOperator

The generalized quadrature observable \(\x_\phi = \x cos\phi+\p\sin\phi\).

PolyXP

An arbitrary second-order polynomial observable.

TensorN

The tensor product of the NumberOperator acting on different wires.