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Constructing a qubit requires something that can be represented as a linear combination of two states. The physical realizations are numerous

https://en.wikipedia.org/wiki/Quantum_computing

But I do not see the use of light polarization in this list. If we let |0> be vertically polarized light and |1> be horizontally polarized light, then a qubit can assume the polarization of light as a sum of these two components. It is easy to read the state of a qubit by measuring the residual brightness after passing the photon through a linear Polaroid filter. The polarization of a qubit can be changed by applying a magnetic field to the photon. The polarization can be stored in a hologram.

https://www.researchgate.net/publication/258369620_Polarization_Holography

Obviously there is a reason no one has done this so perhaps someone can enlighten me.

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    $\begingroup$ To make a quantum computer, you need to be able to implement a set of 2-qubit gates on any pair of qubits. This might be difficult with light. I think you'd need some kind of nonlinear multi-photon effect to implement such gates, and these phenomena might have very low probabilities of occurring. $\endgroup$ Apr 10 '20 at 16:33
  • $\begingroup$ why 2 qubit gates? photons can be entangled. and this reference (which I just found) en.wikipedia.org/wiki/Qubit lists light polarization in its first entry as a physical implementation. And this paper iopscience.iop.org/article/10.1088/1367-2630/15/5/053007 shows the use of photons with coherence times of ~500ns. $\endgroup$ Apr 10 '20 at 22:09
  • $\begingroup$ There is no issue with polarization representing a qubit. My point was about quantum gates acting on multiple qubits. Phrased alternatively, I'm making the argument that it seems difficult (although probably not impossible) to implement quantum gates that generate arbitrary types of entanglement. This is different from coherence also. To perform arbitrary types of quantum computation, you need arbitrary unitary operators on your composite space of all qubits. The standard way to do this is to choose a universal set of 2-qubit gates which you can compose into arbitrary unitaries. $\endgroup$ Apr 11 '20 at 1:33
  • $\begingroup$ Searching for "photon polarization qubits" gives loads of hits. I can't understand how you come to claim that this is not been done. $\endgroup$ Apr 11 '20 at 11:47
  • $\begingroup$ @NorbertSchuch (sigh) If you read my comment again, you will see I am NOT claiming that photon polarization has not been used to build qubits. I am claiming that coupling photon polarization qubits via 2-qubit gates is very difficult due to the need for non-linear optics effects which have low probabilities. $\endgroup$ Apr 15 '20 at 14:44
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Of course this is possible and has been done. For instance, photonic polarization qubits are explicitly listed on https://en.wikipedia.org/wiki/Qubit#Physical_implementations as a physical implementation. Indeed, it is easy to convert polarization into other encodings of a qubit with photons, such as a "which-way" encoding, by using polarizing beam splitters.

There are some difficulties which are specific to photonic qubits, most importantly the necessity to create a large number of photons at the same time ("on demand"), and the difficulty of coupling qubits, which requires non-linear media.

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  • $\begingroup$ Bad intellectual habit - searching on stack exchange before searching google. Yes I realized later (and included the wiki link in my comment) that light waves have been explored as the physical basis of quantum computing. However I still cannot understand your two provisos. Making a lot of photons at once happens in a laser. And are these photons not entangled? Splitters are used in experiments assuming they are. Your second point of ‘coupling’ eludes me. Doesn’t entanglement imply coupling? $\endgroup$ Apr 16 '20 at 15:14
  • $\begingroup$ @aquagremlin No, they are not entangled. And they are indistinguishable. But the real problem is: You want to create single photons, in different paths (or otherwise distinguishable), at the same time. 100 qubits = 100 photons, but of course not all in a huge pile, but distinguishable. And they have to be there at the same time, otherwise how would you couple them? And yes, entanglement implies coupling. But this happens with very low probability - one reason why it is hard to create entangled photon. (Story on its own.) And in a quantum computer, you have to run gates ... $\endgroup$ Apr 16 '20 at 15:48
  • $\begingroup$ ... those have to couple the qubits on demand, with high probability. That's why teleoprtation-based schemes (KLM) are used for photonic quantum computing. $\endgroup$ Apr 16 '20 at 15:50

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