Quantum mechanics forces you to reassess what you think space and time are. We know information is something physical, but then we get told that quantum states don't need to be (considered to be physical objects). This is as if they have more degrees of freedom than classical information does in 3 + 1 dimensions, which are the only ones we can observe in. So, you could consider quantum computers are exploiting these "hidden" dimensions; you could also consider that the quantum domain is where space and time come from. We take for granted that we can collect scattering data and put it all in the same frame, but doing something like that seems to mean a whole lot more--we ignore it because we're evolved to think classically. For instance, the two-slit apparatus: does this encode particles with "position information" in 3 + 1 dimensions, or does it encode space and time, and if so, in what physical basis?
This thread has moved around a bit but I get the impression your real interest is in quantum logic/computing. Banal 'safe' comments or even some of our better posts given earlier probably are of little use if one needs specialist feedback. Have you tried Googling 'quantum computing blogs'? Seems to come up with multiple avenues to pursue. As for interpretations not being relevant, maybe so but I know of one individual claiming to have proven a LHV interpretation of QM, and is adamant it does not permit the expected exponential speedup that QC crowd are all claiming will eventually materialize. Then again, a very smart gent has also claimed to prove in-principle exponential speedup by exploiting not QM but electrical noise based logic circuits!
My interest is in things electronic, like computers. I have a degree and I've worked on some large scale contracts putting stuff together for fibre-optics network companies. Fibre optics has to be right there in the quantum-classical domain. Engineers keep squeezing information into light signals, the ways you can multiplex a signal onto a carrier wave these days is probably close to some limit. But that's what communications is all about, squeezing as much bandwidth as possible out of the system. The predications on the arrival of true quantum computers, or predictions, seem to get closer every year. The Time magazine cover story was of a D-wave which some say doesn't do any better than silicon.If you've been keeping track of developments in the likes of photonics research, or just news feeds from Science/Nature about new tech, there seems to be something that looks promising for quantum computers about every week or so. I've heard the rumours about IBM being close to an announcement, maybe this year, but we'll see. I'm also interested in the connections between information and thermodynamics. I have to admit that some of the ideas people publish papers about are beyond me, but engineering stuff isn't.
Fibres themselves are simply dielectric waveguides, these days single-mode for the most part. Whether you send a single or multiple photons down the line is incidental. On the other hand reliable single-photon routing, filtering etc. & logic operations via integrated photonics chips likely does require specific QM knowledge. The fella I mentioned re noise-based logic is imo a true genius - Laszlo B Kish: https://engineering.tamu.edu/electrical/people/lkish A scathing critic of quantum computing as hype that will fail for fundamental reasons. Just check out the various links. Mind blowing is not an exaggeration.
Just about every interpretation of QM chooses a hidden variable to model the interpretation. A hidden variable interpretation of QM. ?
I think it's still an interesting science because of the way it seems to have everything backwards. We can design quantum computers "out there" but haven't built any yet. We can encode signals in space and time (fibre optic signalling) but this seems to be switched around somehow in the quantum domain--the space and time are the "encodings" it "makes for us" contrarily. It laughs at our need to see sequentiality, the hallmark of computation. We have algorithms that we are sure about, they are mathematically correct, but haven't got the quantum computers beyond a few qubits in scale to demonstrate more than that the algorithms are scalable. So, one of the algorithms, Shor's algorithm, when explored from the "how it works" angle in a computational setting, seems to say that a suitably scaled number of qubits can factor numbers larger than the number of particles in the universe, so the question seems to be about resources, or maybe it's about what we think numbers are.
Yes, signal processing is about Fourier transforms, what's known in the trade as homodyne or heterodyne detection. You design optical filters in this domain. Interestingly, this is pretty much Fraunhofer diffraction and the Huygens principle, it's nearly three centuries old. So, ok, I know a bit about computers at a practical and a theoretical level. I know that a computer is essentially a switching network, and so if just about anything can be a switch, just about anything can be a computer. It needs to be physical though. If it is a switching network, there should be distinct non-intersecting paths for signals and no loss of information. If, say, it's a network of rail tracks, the consequences of intersecting paths and loss of trains or wagons is obvious. In trying to take this context to quantum interactions, you "lose" half the information, and there are no distinct paths except probable ones. A quantum gate is a probability switch, type of thing. So the "it has to be physical" argument changes to: it has to have a probability of being physical half the time, or something totally weird like that. A coin has a probability of landing heads or tails, but suppose the coin "is" a probability, is it still physical?
Ah cha, you have the notion of the probability of a coin landing heads or tails. Forget about the physical coin but "use" its probability--flip the coin inside a box, then turn it over (which of course we know are physical actions). Now we can describe the probability of the coin being heads or tails, and still forget about the coin. The coin and the box that means you can't see the coin are the framework with its two probable paths--we reason that when we look at the coin, the history tells us it was initially the other way up. It sounds so obvious, but its the same logic we apply in quantum experiments. It's why we think a particle, an electron, has either passed through a pair of slits or through one of them, and made a dot on a screen.
So I think I've managed to reason so far, about the computational framework, that the diagrams of quantum gates like controlled-NOT are another way to write tensor diagrams. So a Toffoli gate is a representation of a braid on 3 strands, one is the 'control', a generalised phase operator (on qubits). The two other strands can be a single particle in a linear superposition of states. So this is what embeds in \( SU(2) \). This is something to do with the difference between classical logic gates and their diagrams, or the algebra and diagrammatic representations of Boolean logic, and a similarly faithful map of quantum logic. The latter is a tensor algebra whereas classical logic 'resolves' to a 2-dimensional space--we forget about the third dimension and assume non-intersecting paths for distinct signals. Ultimately trying to apply classical ideas--coins, switching networks etc--is unsatisfactory, you have think in \( \mathbb C^2 \).
This links to a quite tolerable online course on quantum computation: http://www.arturekert.org/quantum/. Artur Ekert is an Oxford professor, his style is quite readable and if you aren't scared of diagrams and mathematics it's quite good as an introduction. He points out that in this framework, the NOT operation acting on a single qubit is the composition of two operations, each the "square root of NOT". To be a NOT gate in QIS, you have to be a CNOT gate. This is the first major difference between Boolean and quantum logic, where in the first case a NOT gate is a single input-single output gate. Here's a sample: "You can convince yourself that the square root of NOT does exist by experimenting with beam-splitters." How can this be like inverting a 0 to a 1, or a 1 to a 0? You assign these numbers to the paths in the beam splitter for a single photon, and recombine the paths with a second beam-splitter (along with reflecting mirrors, of course), so one path is the inverse of the other. The square root of NOT is what each beam-splitter represents, but logically. The logic is infallible because it's how nature works, q.e.d.. But wait, you send two photons to the first beam-splitter and there are two detectors (of photons as path information). Well, one of them has to be the control qubit, which flips the state of the other if it's in the |1> state, and does nothing if it's in the |0> state. You just need to connect the idea of a path labeled 0 or 1 with this kind of logic, which is to say, reason that path states exist.
