In the strawberry fields documentation, there is the Fock() operation that can be used in the Fock backends. In real hardware, what are the limits of this Fock initialization (e.g. how high of a Fock state can you create, within reason)?

Hi @jange , I think it will largely depend on the hardware. I don’t have a specific number to give you but I’d suggest looking for papers that talk about using large Fock states.

Sorry I don’t have more information!

Hi @jange ,

Here’s a really good explanation from my colleague Eli.

In optics, to generate Fock states using just Gaussian operations and photon counting, the easiest way is to prepare a two-mode squeezed state, then to measure one half with a photon counting measurement. This will prepare the same number of photons in the corresponding mode since the two-mode squeezed state is maximally entangled in the Fock basis.In practice, there are several limiting effects to the ability to prepare high Fock states:

- the level of squeezing in the two-mode squeezed state dictates the probability distribution of higher photon numbers. The photon nubmer probability distribution tends to an exponential decay with the level of squeezing, so to generate high Fock states you need a lot of squeezing, which is hard.
- to maintain the maximal entanglement, you need to have as pure a state as possible, i.e. reduce photon loss and other mixing effects. This is also hard.
- how you generate the two-mode squeezed state (directly or with two single-mode squeezed states) will affect the purity of the state, and in turn how correlated the state is in the Fock basis.
- to generate a pure Fock state in the unmeasured mode, you need to perform a perfect photon counting measurement on the measured mode. The measurement device is limited by imperfections too — inefficiency, mischaracterization of the photon outcome due to electronic noise, saturation at higher Fock numbers, etc.

All this to say, it is very dependent on multiple pieces of hardware. What I’ve described is also just for probabilistic schemes based on two-mode squeezing in optics, as opposed to quantum dot sources or microwave optical systems.