# sf.ops.Catstate¶

class Catstate(a=0.0, phi=0.0, p=0, representation='complex', ampl_cutoff=1e-12, D=2)[source]

Bases: strawberryfields.ops.Preparation

Prepare a mode in a cat state.

A cat state is the coherent superposition of two coherent states,

$\ket{\text{cat}(\alpha)} = \frac{1}{N} (\ket{\alpha} +e^{i\theta} \ket{-\alpha}),$

where $$N = \sqrt{2 (1+\cos(\theta)e^{-2|\alpha|^2})}$$ is the normalization factor and $$\alpha = a e^{i\phi}$$.

Warning

Cat states are non-Gaussian, and thus can only be used in the Fock and Bosonic backends, not the Gaussian backend.

Parameters
• a (float) – displacement magnitude $$|\alpha|$$

• phi (float) – displacement angle $$\phi$$

• p (float) – Parity, where $$\theta=p\pi$$. p=0 corresponds to an even cat state, and p=1 an odd cat state.

• representation (str) – whether to use the 'real' or 'complex' representation (Bosonic backend only)

• ampl_cutoff (float) – if using the 'real' representation, this determines how many terms to keep (Bosonic backend only)

• D (float) – for 'real' representation, quality parameter of approximation (Bosonic backend only)

Definition

The cat state is a non-Gaussian superposition of coherent states

$|cat\rangle = \frac{e^{-|\alpha|^2/2}}{\sqrt{2(1+e^{-2|\alpha|^2}\cos(\theta))}} \left(|\alpha\rangle +e^{i\theta}|-\alpha\rangle\right)$

with the even cat state given for $$\theta=0$$, and the odd cat state given for $$\theta=\pi$$.

Tip

Implemented in Strawberry Fields as a NumPy array by strawberryfields.utils.cat_state

In the case where $$\alpha<1.2$$, the cat state can be approximated by the squeezed single photon state $$S\ket{1}$$.

 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