How the photonic state mathematically describes its step-by-step evolution

Superconducting quantum states follow the rules of evolution of Dirac states, which are very easy to understand because each operator can be clearly expressed in terms of the unitary operator. But the more I read the SF docs, the more I wonder, are the qumode tensor relations with each other? Is there a tensor relation between the light quantum operators at each level?What about the step-by-step evolution of the qumode under the operation of the continuous variable operator?What exactly is the mathematical form of the anhilation and creation operators? Can you answer my above questions in detail with a continuous variable Grover’s algorithm?

Hey @RX1,

I’m afraid I don’t understand what you’re asking :sweat_smile:. Are you just wondering how photonic states evolve through a circuit?

Yes, I am better at deriving the evolution of superconducting quantum states, which are based on Dirac symbols as well as the unitary operator. And photonic quantum gates are really less clear, for one thing I have no way of knowing their matrix form (I don’t need the Heisenberg S-matrix)

Ah! If you’re working with a discrete basis, you can think of photonic circuits in the Fock basis. In that case, you can think of each mode as being like a qudit with as many levels as the Fock space cutoff chosen for the system. The gates can also be expressed in the Fock basis as multidimensional tensors acting on those qudits. Let me know if that helps!

Hi, I am very interested in what you are presenting, can you give me a relevant textbook or example. I would love to learn it, I would love to learn it!

Hey Isaac, please teach me about this, did you learn it from Pennylane please?

I think any introductory photonics textbook should work, and maybe supplement that with an introductory quantum mechanics textbook. There’s also good learning material on the strawberryfields website:

Let me know if that helps!