# Is it possible to simulate a quantum computer in Virtual Reality? If yes, how?

There have been a couple of simulations already made and I recently saw this high performance, hardware accelerated quantum computer simulator QCGPU and started to wonder about how to simulate quantum computing in VR. I would like to look at demonstrating the theory behind it. As a teaching experience. Then afterwards simulating the algorithms that could run on it.

The motivation is that VR doesn't have similar limitations we have in the physical world. Essentially it will graphically illustrate the quantum physics behind this computer and to show Mesoscopic physics at work. The VR will illustrate experiments of quantum physics and theory behind this computer but it will also illustrate speed and algorithm execution. For example, this is like showing the mainframe generation how a 7'th Gen CPU would function. From hardware to software, theoretically. It would simulate how algorithms would work on this machine.

Superposition and entanglement would be the main focus. For instance to show entanglement the player would interact with a photon, electron , molecule, or laser (polarization) .The distance between electrons can be scaled to show qubits that are separated by incredible distances interacting with each other instantaneously.

Is it possible to build such a research environment for enthusiast and professionals to refer to with authenticity?

• Comments are not for extended discussion; this conversation has been moved to chat. – heather May 5 '18 at 13:23
• I have edited in your comments into the post. However, even now a lot of things are unclear in your post. 1. How are you thinking of "graphically illustrating" entanglement and superposition? (Are you thinking of something like this? Or are you thinking of a 3D animation model?) 2. Do you want a simulation illustrates qubits getting entangled and their existence as superposition states as an animation corresponding to step-by-step execution of a quantum program? – Sanchayan Dutta May 6 '18 at 7:59
• (cont.) If so, that seems a more sensible question. However, calling that "Virtual Reality" would be incorrect. 3. In a physical quantum computer qubits wouldn't be separated by "incredible distances", so I'm not sure where you're going with that. – Sanchayan Dutta May 6 '18 at 8:00

Virtual reality in a classical computer is just a fancy front-end on top of a classical simulation. A classical computer can simulate all of the quantum physics happening inside a quantum computer, including all the phenomena referred to in the question, but only for a limited number of qubits.

A 45-qubit circuit was simulated using 0.5PB of RAM in 2017.
A 49-qubit circuit was simulated using 3TB of RAM in 2017.
A 64-qubit circuit was simulated using 8TB of RAM in 2018.

These were universal random circuits. If you allow the circuit to be non-random, as in the case of most specific quantum algorithms, you can simulate more qubits.

For example, Bravyi ad Gosset showed that circuits dominated by Clifford gates can be simulated in polynomial time with respect to the number of $T$ gates on a classical computer. Here is the arXiv link if you don't have access to PRL.

If you want to simulate a real physical system (for example for your VR demonstration for students) you need to also model decoherence, but a Lindblad master equation can approximate this with the same amount of RAM as the above "exact" simulations for closed systems. If you want to simulate the decoherence without a Markovian approxiation, there are programs on GitHub such as FeynDyn (Feynman Dynamics). In my answer to a recent question here, I simulated 3 qubits in the presence of non-Markovian decoherence in 62 seconds, and the authors of FeynDyn claim they can simulate up to 16 qubits with non-Markovian decoherence.

• Comments are not for extended discussion; this conversation has been moved to chat. – Mithrandir24601 May 6 '18 at 7:56
• Update: at the time of writing my answer the record was 64 qubits, now it is 81 qubits. – user1271772 Jun 28 '18 at 0:39
• @user1271772 please edit the answer with that information, if you like – beppe9000 Nov 20 '19 at 0:40

Virtual reality is just a pretty front-end on top of a computer program. So, anything the computer program can do can be given a VR interface. As I see it, what is really being asked for is nice, yet 'authentic' ways of visualising quantum mechanics. One thing that immediately springs to mind is a book I read as an undergraduate, Mr. Tompkins in Paperback. Alice in Quantumland may also provide inspiration, I haven't read it. Then there's the minecraft mod (which I haven't played).

The standard trick for doing the maths would essentially be to solve the Schrodinger equation but make the value of $\hbar$ much larger. That way, you should be able to get diffraction effects and similar at a macroscopic scale. This is a trick which probably works quite well for continuous systems (e.g. where you measure position), but I don't think it helps so much where you're talking about discrete systems (e.g. a qubit). In fact, there are probably some more fundamental questions you have to answer first, like 'What does an electron look like?' Is it really a nice little ball that you can pick up and play with, or is it something more diffuse and wavy? How do you represent its spin? (I don't think an arrow pointing in some direction is very authentic.) Part of the problem you rapidly get into here is that by looking at a quantum object, you're measuring it, and therefore changing it, and often making it so that it can't do the cool quantum trick you want it to do. So, I think you generally have to make some compromises to authenticity somewhere in order to create a representation that hopefully facilitates some sort of understanding.

As others have said, VR is just a way of visualizing an output from a computer. If the computer producing the output is classical, it will struggle to visualize a universal set of gates on a many qubit system.

Even so, there are ways to visualize systems of few qubits with a classical computer (though not with VR). The Bloch sphere is the well known example for a single qubit. There are also a couple of games that have visualizations for few qubits:

I’m sure there are others too. I’ll add them as I think of them, or as people point them out in the comments

Regarding VR specifically, the only project I know of is Quantum Breathing. So you might want to check that out.