# sf.ops.GKP¶

class GKP(state=None, epsilon=0.2, ampl_cutoff=1e-12, representation='real', shape='square')[source]

Bases: strawberryfields.ops.Preparation

Prepare a mode in a finite energy Gottesman-Kitaev-Preskill (GKP) state.

In their ideal form, square lattice GKP states are linear combinations of position eigenkets $$\ket{\cdot}_q$$ spaced every $$\sqrt{\pi\hbar}$$. Finite energy GKPs are attained by applying the Fock damping operator $$e^{-\epsilon\hat{n}}$$ to the ideal states.

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 $$\ket{\mu}_{gkp} = \sum_{n} \ket{(2n+\mu)\sqrt{\pi\hbar}}_{q}$$.

Square lattice GKPs have Wigner functions with peaks arranged on a square lattice, whereas alternative lattices, such has hexagonal GKPs, can be obtained by applying symplectic transformations to the square lattice GKPs.

Parameters
• state (list) – [theta,phi] for qubit definition above

• epsilon (float) – finite energy parameter of the state

• cutoff (float) – this determines how many terms to keep

• representation (str) – 'real' or 'complex' reprsentation

• shape (str) – shape of the lattice; default 'square'

 measurement_deps Extra dependencies due to parameters that depend on measurements. ns
measurement_deps

Extra dependencies due to parameters that depend on measurements.

Returns

dependencies

Return type

set[RegRef]

ns = 1
 apply(reg, backend, **kwargs) Ask a local backend to execute the operation on the current register state right away. decompose(reg, **kwargs) Decompose the operation into elementary operations supported by the backend API. merge(other) Merge the operation with another (acting on the exact same set of subsystems).
apply(reg, backend, **kwargs)

Ask a local backend to execute the operation on the current register state right away.

Takes care of parameter evaluations and any pending formal transformations (like dagger) and then calls Operation._apply().

Parameters
• reg (Sequence[RegRef]) – subsystem(s) the operation is acting on

• backend (BaseBackend) – backend to execute the operation

Returns

the result of self._apply

Return type

Any

decompose(reg, **kwargs)

Decompose the operation into elementary operations supported by the backend API.

See strawberryfields.backends.base.

Parameters

reg (Sequence[RegRef]) – subsystems the operation is acting on

Returns

decomposition as a list of operations acting on specific subsystems

Return type

list[Command]

merge(other)

Merge the operation with another (acting on the exact same set of subsystems).

Note

For subclass overrides: merge may return a newly created object, or self, or other, but it must never modify self or other because the same Operation objects may be also used elsewhere.

Parameters

other (Operation) – operation to merge this one with

Returns

other * self. The return value None represents the identity gate (doing nothing).

Return type

Operation, None

Raises

MergeFailure – if the two operations cannot be merged