# Nobel Prize challenge: Could neutrinos be used for quantum information processing?

We know that two scientists, Takaaki Kajita and Arthur B. McDonald, working on Neutrinos have just been awarded the 2015 Nobel Prize in Physics. My question as a Nobel Prize Challenge Question is: could neutrinos be used for quantum information processing?

Requirements based the DiVincenzomy criteria and my preliminary thoughts:

1. A neutrino has to be able to serve at least as a qubit. That is to say, at least two fiducial states of neutrinos can be used to represent $|0\rangle$ and $|1\rangle$ states. You can use motional states, spin states or any other neutrino quantum states for the fiducial states. Arbitrary superpositions of those fiducial states and entangled states can be constructed easily. Certainly, you can have more than two fiducial states to form qutrits or qudits.

2. There must be a way to bring in a robust interaction mechanism between neutrinos, or between neutrinos and other particles. Based on the interaction mechanisms, the neutrino state can be prepared/initialized at least to a uniform state (say all in $|0\rangle$ state).

3. At least universal single qubit gates and two-qubit gates can be constructed stably to interact with the qubits. For instance, gates like CNOT, Pauli Z (or NOT)/X/Y, T and S (SU(2) rotations with some angles) gates. The processing time per gate must be shorter than the storage time and neutrino's decay time.

4. To make the system easier to control and to make information storable, it would be nice if neutrino systems are able to exchange information with other local qubit units which can be easily controlled and stored coherently. If this exchange mechanism is hard to satisfy, it will at least require a robust quantum memory protocol for neutrino themselves which has a storage time longer than its decay or life time.

5. There should be a way to robustly read-in and read-out quantum information as classical information so that human beings can recognize the information processed or to be processed.

6. A neutrino itself can be a fly qubit, of course. This is required for quantum communication and transporting quantum information, which may be the best thing that people want to use due to the super-weak interaction between neutrinos and other matters. If all the other criteria fail, conditions 2, 5 and 6 themselves can make neutrinos a good candidate for quantum communications for extreme needs.

I am not working on neutrino science, but I would like to see how experts of neutrino science say about whether the criteria above could be satisfied at least in theory. Thanks.

• You would have to find a way to contain something that can virtually pass through anything. – Horus Oct 7 '15 at 15:47
• Yeah, that is the read-in and read-out requirement. I am sure if this can be done by exchanging some sort of information between abandon neutrinos and other particles. – Xiaodong Qi Oct 7 '15 at 16:29
• Even if it's theoretically possible, I wouldn't rely on it. Everything, which reacts with its environment only via weak interactions (and gravity), is too hazard to be practically usable. – Newbie Oct 8 '15 at 9:12

In principle: I don't know. Preparing the states would be hard.

In practice: of course not.

Consider the fractional interaction rates. We routinely measure atmospheric neutrino that have come right through from the other side of the planet.

• I guess the property that a neutrino can pass through almost any objects is a coin with two sides. Certainly this is a big challenge, but can you also comment on other criteria? Feel free to let me know where is not clear for non-quantum-information scientists. Thanks. – Xiaodong Qi Oct 7 '15 at 16:32
• When you mention state preparation, do you mean that even single-qubit state preparation would be difficult? How difficult would it be to prepare a "flavour eigenstate" of a neutrino? The difficulties with creating entangling gates are obvious, in the absence of some kind of exotic matter that would interact strongly with neutrinos. – Mark Mitchison Oct 7 '15 at 16:40
• Making a flavor eigenstate is easy (because the flavor eigenstates are defined to be the neutrinos that take part in interactions with the corresponding charged leptons). But keeping a neutrino in a flavor eigenstate is nearly impossible and doing anything else is also hard. – dmckee Oct 7 '15 at 16:42
• @XiaodongQi "Big challenge" should be replaced with "insurmountable challenge." You could bring all the matter in the galaxy together into a roughly spherical neutrino apparatus, and still you'd lose 99.9% of all your neutrinos as they escaped without doing any computation for you. Also your device would collapse to a black hole, so there's that. – user10851 Oct 7 '15 at 20:43
• @XiaodongQi Error correction only works if you can measure your qubits, so using millions of neutrinos as a redundant resource is not an option. – Norbert Schuch Oct 12 '15 at 6:11

Neutrinos are leptons with spin-1/2, so there's at least some quantum storage that they can provide. The real problem is getting them to stay in one place. You can do this with a strong gravitational field for a dense object: since they'll be going near the speed of light you need a massive object which is entirely contained within three times its Schwarzschild radius, which does happen for neutron stars at least. But, since we're not sending humans to another star any time in the next millenium (and certainly not to the nearest neutron star, which is hundreds of light years away) that is pretty much a non-starter for anything interesting in the near future. Let's confine ourselves to things that can be achieved in the next few millenia.

There is some possibility to contain them instead with magnetism: they might have an unbelievably tiny magnetic moment (the strongest magnetic fields we have ever created would have an interaction energy $~10^{-22}\text{ eV}$) and you might therefore someday be able to contain them with a strong magnetic field. Unfortunately Earnshaw's theorem says that this sort of magnetic trapping is incredibly difficult and cannot be accomplished with a static magnetic field. There are some magnetic trap designs, though. We might also be able to confine the neutrino in circular motion with a co-rotating magnetic field; Earnshaw's theorem says that all minima are saddle points but maybe we can make the "down" direction the polar one if we are careful. Probably this still has to happen in space (and then we can take it out towards Pluto where the solar neutrino flux has dissipated considerably), but at least it's reasonably close to home and could potentially be realized in this millenium, maybe.

That might also be a trick to store a quantum state with them: normally we don't do positional superpositions because they interact with environments, but neutrinos hardly interact with anything. If Penrose is wrong or we can run the experiment for short enough times, we can simply have a neutrino circling in two different paths in some insanely strong magnetic trap. Your "detectors" will consist of turning off the magnetic trap and guiding the neutrino into a straight line trajectory out of the apparatus, into a Super Kamiokande-style detector. So that could give you criterion 5.

Issue #2 is much trickier. Magnetic interactions are going to go with the square of tininess, so we can ignore those. Neutrinos are presently modeled to only interact with the W and Z bosons, which are massive. Furthermore, their interactions with the W bosons will convert them into other particles due to charge conservation; the neutrinos don't have charge while the $W^\pm$-es do. The only direct interaction they'll have is going to be very short-range interactions mediated by the Z field. The LHC is able to "see" that in 20% of cases their Z bosons seem to "disappear" and this is thought to be a straightforward conversion to a neutrino-antineutrino pair, which would prove that neutrinos would also interact via the Z field through relativity (if a Z turns into a neutrino-antineutrino pair, then that diagram rotated 90 degrees in spacetime becomes a neutrino scattering off of a Z). But you may be able to reach something interesting.

Issue #3, qubit gates, is probably the hardest topic. If we're doing the path-superposition then you're going to need to make two orbits which cross, and they need to interact with something in the middle. The problem is that the insane magnetic fields we're talking about are presumably going to rip apart any matter known to man, so you can't place an object inside there. The only thing I can think is that you might create a particle accelerator with insane power requirements which beams relativistic Z particles directly through the crossover point, with their half-life being time-dilated to the point where they don't normally decay within the apparatus. The W particles you're generating will need to be filtered out before they hit the apparatus and destroy it; the Z particles should pass right through the apparatus as not having any normal magnetic moment. But that's going to be a monumental engineering challenge.

• Don't overlook that so far as we know we can only get one helicity for matter and the other for anti-matter without absurd boosts, so using the spin state for storage is tricky. Unless they're Majorana in which case those two degrees of freedom are the same. – dmckee Oct 7 '15 at 16:44
• Yeah, a neutrino spin qubit is more "if you could get the neutrino to slow down somehow," which maybe we could solve in the next few millenia. – CR Drost Oct 7 '15 at 16:46
• So detailed... Photons can be almost stopped AFAIK. Ignoring the technical details, what if a neutrino stops translational motion for storage purpose? The flavor or state will be changed? My ignorance here. – Xiaodong Qi Oct 7 '15 at 20:26