Can a photonic neural network be input to a vacuum state with all zeros?

In the Strawberry Fields article, the photonic neural network initialization cannot be all zeros in bosonic sampling and Gaussian bosonic sampling. However, it seems that the inputs can be vacuum states in instantaneous polynomial and Gaussian cloning circuits. Does it then make practical sense to use vacuum-state inputs for photonic neural networks that are not based on bosonic sampling?

Hi @RX1 , can you please link the Strawberry Fields article you’re mentioning?
Vacuum states are indeed used often for initialization but this will depend on what you want to do exactly.

May I ask if a photonic neural network initialized with a vacuum state can get the corresponding probability distribution in the same way as superconductivity? Instead of following bosonic sampling?

Hi @RX1 ,

I think there’s a lot of confusion here.

On one hand there are many approaches to photonic quantum computing. Xanadu for example has developed several generations of quantum computers based on squeezed-state qubits (qumodes) which were designed to perform Gaussian Boson Sampling. The new devices that we’re in the process of building are part of our measurement-based quantum computing architecture, which uses similar components but in a different way. There are even other approaches which other companies are pursuing, with photonics but different architectures. Superconducting quantum computers also have their own architectures.

If you’re interested in a gaussian-boson sampling problem, then our old devices were the best tool for that. The new ones are being designed for universal quantum computation and they’re based on GKP states, which are our qubits. The goal is that you can program circuits like you do normally on PennyLane and then our compilers can turn it into something that can run on the machine. We’re not ready yet, building a quantum computer takes time, but that’s where we’re heading.

So the question is, what do you want to do with your quantum neural network (QNN)? If you just want to study the Hafnian or the Permanent or Gaussian Boson Sampling then you don’t need a QNN, you need something like Borealis. If you want it to do something you can run in a superconducting circuit too then it’s better to think of gate-based quantum computing and think already about the Fault-Tolerant devices of the future instead of what exists at the moment.

Let me know if you have any follow-up questions :smiley:

By the way, our Xanadu YouTube videos can help you a lot to understand the architectures of the different computers we’ve built over the years.

Thanks for the reply, my real idea is: on a photonic computer, initialize all to 0 (i.e., initialize in the vacuum state), then go through a series of photon gates (making it structurally equivalent to a hardware effective ansatz) and then start training with the Adam simulator, and then finally make measurements on a Pauli Z-base to get the probability distribution.I’m not sure if such a construction makes practical sense for optical systems, and if it is physically possible.

Hi @RX1 ,

Not really. Starting with the fact that the measurements are different so there’s no PauliZ measurement. You can learn more about CV measurements here and here.

In the future you will indeed be able to do something like a PauliZ measurement but with our 2019 device and with Strawberry Fields you can’t.

If you want to do something like hybrid optimization you can do something like this demo where we train a CV circuit on a simulator to produce a specific output of the number operator. Note that this requires an older version of PennyLane (v0.29 or below) and the pennylane-sf plugin.

For most practical purposes I would recommend sticking to PennyLane. But of course feel free to explore the fascinating world of quantum photonics! Have you gone through this PennyLane demo? It’s an amazing guide into this field.

Can I realize the following optical circuit with a photonic computer? Is it practically feasible?

Hi @RX1,

In principle yes. However Xanadu doesn’t currently have a computer available online where you can code this since D gates aren’t supported on X8. I’m not sure what measurement you have there, X8 only works with photon counting.

Thank you for your reply. My measurements are constructing a Pauli operator |{{0}^{\otimes n}}\rangle \langle {{0}^{\otimes n}}|. Is the photonic circuit scheme in the above picture feasible and can it be realized with Pennylane-sf?

Hi @RX1 ,

Unfortunately to perform Pauli measurements you would need Homodyne measurements in the device, and these are not available in X8. Only photon-counting measurements are allowed in this device.