If we choose double-slit, can we put multiple "slits" and create calculation for just one algorithm (problem, solution...)?
Not general purpose quantum CPU, just for one.
Same question for Stern-Gerlach.
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2 Answers
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To all intents and purposes, the double-slit experiment is the same as the Mach-Zehnder interferometer (a photon can go one of two paths before interfering at the output). Since the Mach-Zehnder interferometer implements Deutsch's algorithm, you could claim that the double slit experiment will do the same. Effectively, what you'd be talking about is by putting a piece of glass (of the correct optical depth) over one of the two slits, or not, creating two different interference patterns. If you can tell which pattern you've got, you can tell if the piece of glass is there or not.
However, what you lose is any evidence of a speed-up. The Mach-Zehnder interferometer works with a single photon, so it has a clear interpretation as `a single run of the computation', compared to the equivalent classical calculation, which requires two runs. Once you go over to the double slit, you need to create an interference pattern. To observe that, you're going to need many photons.
The Stern-Gerlach experiment is basically just a measurement of a qubit in a specific basis. You need more than that for an algorithm....
answered Jun 11, 2020 at 6:53
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To get a quantum gate with single photons, you need something of the form:
$$(|0\rangle+e^{i*0}|1\rangle)|1\rangle \rightarrow (|0\rangle+e^{i\pi}|1\rangle)|1\rangle$$
Putting this in English, it means that a second photon causes a phase shift in the first photon. This type of interaction can't occur simply by overlapping or interfering photons, but requires a "nonlinear" interaction where one photon sort-of "pushes" the other. In a lab setting, this typically happens through some other material. For instance, a photon shining on a gas of atoms might change the energy of the gas, which will change the properties of the medium, and the second photon will experience a different phase as a result. (For example, maybe the first photon causes the medium to slow down the speed of the second photon).
Getting these types of interactions to work (where one photon changes the phase of a second photon) is extremely difficult and is an active field of research. If it was developed, then it would be a big deal - and we wouldn't just have another competitor for a new quantum computing architecture, but we would also be able to do some interesting things like quantum nondemolition measurement.