3 ms·
The biggest obstacle to the realization of quantum computing is not technical, imo, but theoretical. it is well known, but not to laypeople, that a quantum com
by ouid 4y ago
The biggest obstacle to the realization of quantum computing is not technical, imo, but theoretical.
it is well known, but not to laypeople, that a quantum computer is efficiently (quadratic overhead) simulable if it only operates on the eigenstates of the generalized Pauli matrices with the so called Clifford operators. This is a really fancy way of saying that this group action is not dense in the unitary operators, which is itself a fancy way of saying that it behaves like rolling a die, instead of like rolling a ball.
In order to achieve density in the unitaries it suffices to construct a single state that is not one of these magic states (their language, not mine), to a sufficiently high level of purity.
The much touted paper which claims to do this only succeeds in showing that the problem is equivalent to some other problem which we also do not know how to solve, (creating many, worse separable copies of this state) and there is no particular reason to believe that it can be. Moreover given what it would be able to do, it seems much more likely to me that there is a proof, waiting to be discovered, that there is a fundamental obstruction to harvesting such a state without at least waiting as long as you would have to wait to do your computation the old fashioned way.
- Strilanc 4y agoCould you cite the "much touted paper" you're talking about? In my view, making the noisy physical magic states is the easy part of the distillation process. You reset a qubit, then rotate it 90° around the Y axis, then 45° around the Z axis. That's the magic state. Note that the tolerance on those rotations is forgiving: getting them to within 10°, 95% of the time, is sufficient. All the error correcting code stuff that follows has fidelity requirements an order of magnitude stricter. As you note, there'd need to be some unforeseen obstacle for state prep to be the showstopper. Given how apparently easy it is to make these states, I think any obstacle like that would basically have to falsify quantum mechanics as we know it. It would be like finding out that light can't be diagonally polarized.
- ouid 4y agoThe ability to rotate 45 degrees is equivalent to the construction of a magic state, as you have correctly identified, as it is not a clifford operator, and adding it to your generators gives universal quantum computation on its own. You have pushed the problem sideways. This is the paper, https://arxiv.org/abs/quant-ph/0403025 https://arxiv.org/abs/quant-ph/0403025, and it is well understood by the paper that the independence of the noisy magic states is necessary for the distillation process to proceed. Note that the probability of having some entanglement between your partial states goes up rather dramatically with the number of them that you have, and not obviously in a way that you can do anything about.
- Strilanc 4y agoThanks for the reference. > Note that the probability of having some entanglement between your partial states goes up rather dramatically with the number of them that you have Entanglement is not binary, it is continuous. If you start with states like CPHASE(5°)|TT>, a few rounds of distillation will have turned them into states like CPHASE(0.0000000000000001°)|TT>. Sure the output states are "still entangled", but the amount of entanglement is so negligible that you don't have to care. Such small distortions won't prevent trillion step computations from working.
- raziel2701 4y agoNo it definitely is technical, we need a lot of materials science and RF electronics to get things to work better with each other. We need better material growth and device fabrication techniques and better readout schemes.