Superposition does not fork the world. This common misconception arises due to confusion between superposition and the many-worlds interpretation of quantum mechanics, but it’s easy to see that the two are only superficially similar. States in a superposition still interfere—that's the essence of the double-slit experiment.
In contrast, when arguing that the timeline 'splits' due to measurements, the resulting universes do not interact at all and remain completely unaware of each other—they can never even know if the others exist.
If quantum computers truly 'forked' the world, they would be equivalent to non-deterministic Turing machines (capable of solving NP-complete problems in polynomial time), but quantum computing experts agree that they can still be modeled as deterministic Turing machines.
It's better to think of quantum computers as a type of analog computer, capable of solving certain problems that fit their model well, but not generally more powerful. It’s like an Intel CPU having SIMD or AVX instructions that allow it to perform certain operations faster, but these don't fundamentally change its capabilities. The no-free-lunch theorem applies.
Correct - superposition doesn't fork the world - measurement does. And correct, you can't communicate with the other universe after the split has happened [1]. I'm glad you mentioned that quantum computers can't solve NP-complete problems - my next blog post was going to be about why. Here's an overview of what I plan on saying:
A typical quantum algorithm like Shor's works by sending every possible input through a gate, and so you get every possible output out in a superposition. If you were to just measure that, you'd get a random result - so instead, you need to somehow interfere the output to get the actual result. You do this by taking advantage of the fact that the superposition is a periodic function and the amplitude repeats. This is literally the core assumption of the algorithm.(a common way of doing this using the QFT).
Every quantum algorithm requires some kind of structure in the output like this. Deustch's algo, dumb ones like Simon's algo, etc. NP-Complete problems have no structure to them, so even if you build a gate that creates the superposition you want, it's not possible to destructively interfere it to get an answer (I don't know how to prove that there's no structure to NP-Complete outputs - it just feels trivial, since they're only solvable in exponential time, so there must be an exponential amount of "structure" there).
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[1] The only way to communicate with the other universe would be to try to use quantum mechanics with something like an entangled pair. But no information can be communicated through an entangled pair if all you just have 1 of the 2 particles! Measurement collapses a state nonlocally, and if you could somehow measure one particle and change the probability distribution of the other, you'd be communicating faster than light. The measurement genuinely changes the state and the amplitudes, but not in a way that the other person can detect. It's really interesting and leads to stuff like teleportation.
Since quantum computers can stimulate classical computers, presumably they can solve NP-complete problems, since classical computers, by definition, can. Perhaps you mean that they can’t solve NP-complete problems in polynomial time, but we don’t even know that of classical computers, so you would presumably have shown that P≠NP, which would be fairly impressive.
Where is the best place a layman can dig into this statement “You do this by taking advantage of the fact that the superposition is a periodic function and the amplitude repeats.”? I’ve seen articles hinting at this in an obtuse way but I’d love to see something more approachable to help wrap my head around it.
I just tried finding a good resource and I can’t. All of them are mile long page scrolls… I don’t know how they have so much stuff to spew. Qiskit had amazing lessons with cool illustrations (although they did spew at the end) but I can’t even find that anymore on their site.
Don’t worry though, even the professional researchers I’ve worked with think it’s a waste of time. The field is screwed.
Here’s a quick explanation from me-
The state |x> means you have some qubits that represent the number x. Say you want to represent the number 13, that just means you have |1,0,1,1>, it just means you have 4 qubits in this configuration (quits can be 0 or 1). It’s also written |13>. If you want the state “13 AND 14 AND 15” in superposition where qubits are both 0 and 1, that’s represented by |1,0,1,1> + |1,1,0,0> + |1,1,0,1>. It’s in that superposition and can interact with itself until you choose to measure it. When you do go to measure it, you might measure any of the values (you dont get to choose which). Maybe you measure 15, that means the state is now |1,1,0,1>, you just deleted all the terms that aren’t 15.
If you look at the pic, main idea is the first layer of H’s creates the state sum_x=0…2^n-1 |x, 0>, then gate U turns that state into sum_x |x, f(x)>, then the measurements measure which f(x) you have, deleting all the terms that don’t have that f(x) in them, so for example if you measure that f(x) is 13, the state is now |0, 13> + |15, 13> + |30, 13> + |45, 13> + …
This is the periodic state. Now that we have it we can just apply a gate that takes the QFT (finds the frequency, which here turns the state into roughly |15, 13>), and then measures it, giving the answer period=15.
Yep, they're essentially giant brute force machines. You can find the period of a function by passing all the inputs through it at once and destructively interfering the result.
Why is there a speedup in quantum, though? Why can't you just brute force classically? The answer is that whether quantum or classical, you can always build a hard-coded circuit that essentially swaps the time and space complexity - just make it so that for every operation you were doing in time, instead, every operation happens at its own place in space.
Quantum is special because it also takes the "log" of the space complexity b/c n qubits represent 2^n bits. So quantum lets you swap space with time and then take the log of time, lol. Superposition, interference, etc aren't really even needed in the explanation.
This is potentially useful because people can be very impressionable when it comes to quantum magic. I think if I could build some kind of shiny heavy tangible apparatus to interface with the IBM compute service, with like seven segment LEDs (resist the urge to use Nixie tubes, this is a serious, practical device) with a big loud trigger and some kind of boutique radio, I would have a potentially very persuasive magic 8 ball I could use to influence and manipulate people, with carefully chosen false dichotomies.
Okay team, we’ve effectively entangled the success of our endeavor with the quantum dead man’s switch by all swearing to comply with the protocol. It’s time to start letting the universe tell us what works. QUESTION 1 for the Profit Manifold: promote yours truly to director or stay the course? Click bang hiss: 01.
Note to self: cut “universe B” (or just B? It’d hurt less) into my thigh with a razor blade 6 months before demonstrating The Device, as a plot device to be exploited for purposes TBD.
Rick: OK, Morty, this program runs by spawning a new universe for each parallel subtask, destroying the universes that throw an exception instead of returning a value, and then aggregating the remaining results. Are you ready to experience quantum hyperspatial optimization, Morty? This'll strap a warp drive to the ass of your gamer shit for sure.
Morty: Aw, geez, Rick, I don't think we ought to--
We are all incessantly forking the universe with every single decision we make. We probably have at least as many universes by now as the number of atoms in this one. And now it's one more, where I decided to leave this comment.
If you roll a regular coin without any quantum effects, every version of you will either see only heads, or only tails. You need quantum in order to make the choice nondeterministic.
How do I know they won't just give me a cached output from someone else's identical job, or from a simulator? I don't really trust IBM to not mess it up.
I keep getting "500 Internal Server Error" when trying to login. It's not logging in. I get this error after entering the "IBM verify code" which I receive in an email.
1 fork per 4 seconds? That's so inefficient. Just observing Geiger counter will fork the universe faster than article's very inefficient implementation.
I generally try not to comment on work-related stuff in public but I almost fell out of my chair when I saw that sampling rate. Surely they can do better, and that's just a limitation of the free API?
> The outcome provably does not exist until you measure it.
My preferred interpretation:
There is a density function across all possible realities (Hilbert space).
Schrodinger's cat has equal density of being alive and dead.
The person who opens the box can be happy or sad.
The density of cat being alive is entangled with the observer being happy. And the opposite for the death.
The original cat distribution did not "collapse" or "resolve" per se. The cat is still equal parts alive and dead. But it did become non-uniformly entangled with the distributions of rest of the universe.
It doesn't change much in practice. If the event is influenced by a state outside of its past light cone, you (that is observer inside the universe) cannot predict the outcome even theoretically.
Watch the Remedial Chaos Theory episode of Community to see why it is a bad idea to play around with making decisions that can spawn alternative worlds and timelines based off a single unnatural random event. (also probably one of the best episodes ever)
The "split" happens contantly outside the lab/quantum-computer. Just get a geiger counter, the atoms split randomly using a quantum process. Or just get a digital camera, the photons are absorved in the CCD sensor randomly using a quantum process. Or ...
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