This is a hardware question. You can have superposition of degree of freedoms in classical light. From a prior literature [2203.00994] Nonseparable states of light: From quantum to classical, I found that it is possible to emulate entanglement classically. My question: would it be practical to implement Shor factorization or Grover search on a classical optical computer?

Recently, complex structured light was used to
implement a quantum walk and largely enhance its ability of data correction [190, 191]. It was also proposed that
the use of quantum-like modes allow to emulate the evolution of a quantum walk in real time [192], which was
also recently realized experimentally [168], see Fig. 5g.
The classical quantum walk technique was also extended to
higher-dimensional topological state for more powerful optical computations [193].

A rephrase of my question: would it be simpler to implement a general computing framework that leverages superposition and entanglement on such classical system than on a quantum optical system? The experimental references in that paper didn’t implement any arbitrary quantum circuit (instead, mainly on quantum walks), and so, I wasn’t able to know about the advantages/limitations of this approach. A pointer or documentation on where I should look at would be appreciated!

I don’t know the answer for the specific cases that you mention, but in general you need actual quantum computation, not just a simulation of it, in order to solve very complicated problems in a variety of fields.

As an example, you can simulate quantum computers in classical ones but at some point you hit a memory limit if you try to simulate too many qubits. In the system you describe there may be some limits too. If, for example, you wanted to simulate problems in chemistry, I’m not sure that you could do it efficiently and to a high level of precision with the system you describe.

One of the reasons why people are looking into quantum computing is that most of the leading technologies here allow you to do universal computation, so you can solve many different kinds of problems. I don’t know whether this is the case with the technology you mention.

There are probably other advantages and disadvantages such as scaling capacity, error correction, an established information framework, etc. But I really don’t know the technology you mention so these are just things to consider and compare yourself.

Thank you for taking the time to answer. I may have misdescribed that the classical optical system “emulates” superposition and entanglement. I agree that while a GPU machine could implement superposition and entanglement, it is on the software layer emulation, and so is not efficient.

I think it is more accurate to say that the said classical optical system does have an inherent feature of superposition and nonseparability aspect of entanglement, on the hardware layer. The missing feature is nonlocality.

Regarding with universal computation, AFAIU, the requirement is that the degrees of freedom must at least exist in 2D or more. But given that this is not a quantum system, measuring the classical light degree of freedoms won’t provide the Born rule.
Regarding with error correction, given that no-cloning theorem applies to the linear operations on the optical degree of freedoms, it may require some form of quantum error correction, except that there is no decoherence.