Distributed quantum computing with classical communication

Question

I'm interested in the field of distributed quantum computing, i.e. using multiple smaller quantum devices/circuits to cooperate to be able to perform some task that would require a larger device (where large/small refers to the total number of qubits the device has).

I'm looking for simple, abstract problems that could be solved when such a paradigm is utilized. To be even more specific, I wonder if sharing entangled states between such devices is a must in this type of problems, or are there tasks that could be broken down in such a way that each device performs some quantum computation independently from the others, and they all use classical communication to share partial results etc.

Does anyone know any articles on the subject? Thanks!

Answer 1

One of the possible methods for distributed quantum computing is remote quantum entanglement. There is a proposal by Mihir Pant and others to develop protocols for quantum “repeater” nodes, which enable a pair of users to achieve large gains in entanglement rates in a linear chain of quantum repeaters, by exploiting the diversity of multiple paths in the network. They are trying to develop quantum repeater protocols that enable multiple user pairs to generate entanglement simultaneously at rates that can far exceed what is possible with repeaters time-sharing among assisting individual entanglement flows. Please find more details about this approach in the following research article published by Nature.

There is a paper published in arxiv about using Quantum Interconnects for Distributed Quantum Computing and Quantum Internet. It is more of a compilation of necessary distributed quantum computing modules for the realization of a quantum internet. Quantum interconnects (QuICs) are devices or processes that allow the transfer of quantum states between two specified physical degrees of freedom (material, electromagnetic, etc.), or, more broadly, connect a quantum system with a classical one. It will be nice if you can explore this paper to see the details of the QuICs components.

There is another recent work on the use of distributed quantum phase estimation algorithms with two different distribution schemes. Please find the summary of this paper shared in ResearchGate and EuropePMC.

Answer 2

The main appeal of quantum computing is that it can do some tasks faster than a classical computer. This relies on unique quantum phenomena such as entanglement, phase interference, etc. This requires that all qubits in the quantum memory can "talk" to each other. If subsets of qubits are physically separated and only linked through classical channels, you lose this property since the qubits from distinct subsets cannot be entangled.

Another way to look at this is if you have $N$ small quantum computers, then they can do at most $N$ times the work of one of those computers. So this model does not allow anything better than a linear improvement over what a single of the small quantum computers can achieve. Any quantum algorithm with better than linear speedup (e.g. Grover or Shor) cannot be implemented in this model.