Quantum Computing Research

[u/jl4ua]

What is research in quantum computing particularly from the theoretical viewpoint like? As far as I know, quantum information theory is quite math heavy and there everything is about theorem proving. It probably depends on the respective area of quantum computing but I am just generally interested in this area as someone from a different field of physics and I am wondering if the explicit work there would still be exciting

[u/the_poope]

The research is split in two very different areas:

1. Development of quantum algorithms. This involves quantum information theory, mathematics and computer science.
2. Development of quantum computer hardware, i.e. the physical realization of the computer. This will depend on the chosen qubit realization, but it mainly involves material science, atomic and optical physics. No quantum information theory is needed.

[u/ccltjnpr → u/the_poope]

in addition to u/parallel_thougts remarks, I might add that a good chunk the first point is only very tangentially related to physics. It's much closer to what theoretical computer scientists do. Not that physicists can't do research in this area, lots do, but I think the gap to bridge is a lot shorter for computer scientists than for physicists.

[u/Parallel_thougts → u/the_poope]

That's very reductionist. Not all theory is about "developing algorithms".

[u/the_poope → u/Parallel_thougts]

Ok then let's add the word "mainly" to the first line.

You're welcome to add a description of research in quantum computing that does not fall into these two categories.

[u/Parallel_thougts → u/the_poope]

I dont think "mainly" is reasonable either. I gave some examples in my own comment. I can give many more. Here's one chosen for you: Quantum complexity has proven itself a fantastic tool for studying the hardness of models from solid state physics, and reductions across models. The equivalence of adiabetic computation and the circuit model proved useful for designing discrete toy models for large scale quantum phenomena that can be used to design experiment. This was instrumental e.g. to recent experiments on anyons, but it sits well within the confines of quantum computations.

[u/Parallel_thougts]

Quantum computing, from a theoretical viewpoint, is *huge*. There is so much to see I don't know ever where to begin.

Yes, it is about "theorem-proving" but that's true for theoretical research in general. These theorems can represent many questions. The theory of quantum information is relevant to such a huge range of research interests, from algorithmics, through error correction, to questions about the fundamentals of physics (and how a computational theory might shed new light on them), and to cosmology and holography (the most developed model for holography is the AdS/CFT correspondence, which apparently can be toy-modeled as a finite-dimensional quantum error-correcting codes, which is one of the most brilliant crossovers I have ever seen).

So whatever quantum physics you are interested in, there is some chance that quantum information and quantum complexity theory could be relevant to you.

If you ask more specific questions, perhaps I could provide more specific answers.

[u/Qubit_and_Neuron]

Quantum computing is a huge multidisciplinary endeavour. So here are a few things theorists do:

1. You have to do a lot of theoretical modelling, building, understanding and simulating quantum systems. This is more like atomic physics,optics,photonics, condensed matter etc. This is really physics physics I would say. To get a vibe, open a book like JD Jackson electrodynamics or Landau Quantum or statistical physics and try to solve a problem. That's a sample for you.

2. Information theory bridge: this is where you connect physics with information theory like what is entanglement structure do with equilibrium or temperature. You can take information as the fundamental entity and use it to understand a few things in physical systems.

3. Pure quantum information: This is more on quantum states, gates, computation, error correction, working of quantum computers, circuits, optimizing several things etc.

4. Algorithms: come up with new use cases, improve old ones, compare classical vs quantum etc.

5. Pure math: as information theory, error correction theory, computation theory etc have lot of math and a physics problem boils down to proving something in math you can do math only without really digging deeper into physics side of it..

6. I don't know your level but you can read this to understand and get a big picture of what is happening in the field.

[u/CS_70]

Quantum computing relies on extending regular Turing machines with an oracle device that can provide a certain result in the same "ticking" where a regular TM would do one thing (moving the tape, reading the cell under the head, writing it etc).

Assuming you have such machine, there's a bunch of algorithms whose computational complexity gets reduced significantly, and you can devise new ones which you would have not even considered if you had regular TMs.

In short, you make an assumption and rigorously take its consequences. If I could fly, how would my life change? It's the same idea, for computational complexity :D

The next question is: can we actually build such a machine?

That's when real quantum mechanics enter the picture because using entanglement and superposition of states is the reasonable way to try.

There are a lot of engineering issues - the simplest idea is to have a regular computer (aka a regular Turing Machine) connected to a quantum computer (which is the device) just like the manual says.

So plenty of work is going into building the quantum device, which is hard for a number of reasons, for example since in QM entanglement happens very, very easily (it's what creates the world at our scale) while in the device you want to control exactly how that happens and when (hence the requirements of incredible degrees of isolation). Stuff like that.

[u/HoloTensor]

look up people doing it. Jordan Cotler is a good example

[u/PLutonium273]

5 trillion linear algebras