Scott tries to explain quantum computing as not really a matter of qubits being 0 and 1 at the same time, but rather probabilities being negative or complex, and interfering.
There is some merit to what he says. Schroedinger's cat is not really alive and dead at the same time. If qubits could be 0 and 1 simultaneously, then we would expect exponential speedup in certain search algorithms, and we do not.
Probabilities are not really negative, so he is careful to say "probability amplitudes", but he wants you to think of them as analogous to classical probabilities.
No, this is just nonsense.
It is a little more accurate to say that the qubit is a superposition of 0 and 1. And that measuring the qubit can give 0 or 1. But to the layman, that is just like being 0 and 1 at the same time.
Many physicists explain quantum computing as using superpositions to do simultaneous computations.
Sequentially operating on bits having 0 or 1 values gives us Turing machines, like all known computers. Operating on qubits that are superpositions of 0 and 1 is supposed to give us quantum supremacy, and faster computers for certain types of computations.
Scott says the core of the quantum voodoo is amplitude interference. But all sorts of classical phenomena have interfering waves, and that is not particularly mysterious. It only becomes mysterious when you think of those amplitudes as probabilities or generalized probabilities.
Saying that they are probabilities is just a sneaky way of pretending that the qubit really is a 0 or 1 (or both). The qubit is not a 0 or 1 or a probability. A measurement gives a 0 or 1, and we can give a probability based on our knowledge of how the system was set up, but that is not what the qubit is. It is not an amplitude either. The amplitude is just a way of codifying prior knowledge.
We have no numerical equivalent for the state of a qubit.
Scott concedes that quantum supremacy has never been demonstrated and we do not know whether or not it is possible. He sure is opinionated about something that may not exist.
LuMo likes the comic, altho he cannot resist some cheap shots. He agrees that complex numbers are fundamental to quantum mechanics, because [x,p] = xp-px is anti-symmetric, and hence has imaginary eigenvalues.
This argument is unpersuasive. Lots of real matrices have that property, such as the 2x2 matrix [(0,1),(-1,0)]. (Sorry I am not using mathjax.) [x,p] is not directly observable, so the imaginary eigenvalues pose no problems. It implies the uncertainty principle, whether using real or complex numbers.
LuMo buys into Scott's line almost verbatim:
The wave functions are closer to probabilities but they're not quite the usual probabilities. Instead, they're probability amplitudes which are complex and also have the ability to constructively or destructively interfere. When one is observing anything, the amplitudes are converted to the usual probabilities only. But when no one is looking, the probability amplitudes evolve as a new entity according to new rules that have no counterparts in classical physics.Sorry, but this is just not helpful. If you are doing classical mechanics, such as predicting the location of the Moon in 1000 years, you compute probabilities. The Moon's position has probabilities that evolve with time. Observations tell us where it really is (to within measurement error). All this talk of probabilities as being unique to quantum mechanics is misleading.
So is talk of probability amplitudes interfering. Classical waves interfere also. Probabilities do not really interfere in either classical or quantum mechanics.
There's no "splitting of the worlds" during a quantum computation. On the contrary, the splitting of the worlds may only make sense after a measurement which can only occur after decoherence – but the quantum computation depends on the absence of any decoherence (I will make the same observation again later). So a key necessary condition for the quantum computer to work – and do some things that are practically impossible on classical computers – is that there's no decoherence and no splitting of the world during the calculation.LuMo is right for the wrong reason. I say that there is never any splitting of the worlds, and never any quantum computation.
If a quantum supremacy computation did exist, it would have to somehow take advantage of a qubit staying in a superposition, and not decohering. In the lingo of many-worlds, the qubit has to straddle different worlds. Supposedly quantum supremacy is possible because qubits can leave this world and do some of its computation in a parallel world. I am not buying it, but that is the theory.