What makes quantum computing so hard to explain?
quantamagazine.org
quantamagazine.org
Let's take the simplest phenomenon in quantum computing: superposition. People get very confused about superposition. Something being both 0 and 1 at the same time? Like fuzzy logic? Is it 0 and 1? Is it 0 or 1? No, superposition is a linear combination of 0 and 1 which can be collapsed according to certain measurement rules. It can also be manipulated with quantum logic gates. There is no simpler way of explaining it.
With a follow-up blog post focusing on entanglement: https://ahelwer.ca/post/2018-12-07-chsh/
There's also this video which walks through how quantum computers solve a very specific factoring problem (Shor's Algorithm) in a way that classical computers cannot. https://www.youtube.com/watch?v=lvTqbM5Dq4Q
Why? Because he asserts that there is no measurement problem, and that the EPR paradox and violations of Bell's Inequality don't exist: They are based on misunderstanding what QM is actually predicting and what QM observers are actually observing. Likewise, there is no wave function collapse, no need for MWI, no hidden variables, etc.
To sum up the physics, badly....
Background: Relativity took as its principles that physics is universal (the universe is isotropic), that there are no fixed reference frames (all measures of speed, and therefore of a few other things, like energy) are relative to the observer making the measurement), and that the speed of light is a fixed constant. From that we space-time curvature, etc.
Relational QM takes this same perspective: Measurement is relative to the measurer, which can mean an observer or anything else affected by whatever is manifesting itself, like another particle, e.g.
Manifesting is a deliberate word: Absent manifestation, nothing has properties. Properties only make sense in the context of interactions.
What is the charge or spin of an isolated electron? 無 (mu): the question makes no sense, because charge and spin and everything else only arise, are only measurable, in interactions.
So take EPR: There is no paradox, because when Alice measures the spin of one of the entangled particles, she may "know" that Bob will measure or will have measured opposite spin, but she doesn't "know" this yet unless and until she interacted with Bob.
It is only after this slower-than-light communication that the two opposite spins - and the predictions of QM - are confirmed.
Until A and B interacted, entangling their states, the states A-observes-S1 and B-observes-S2 were independent. The interaction between A and B, state "A+B share information re S1+S2", took place without anything ever being FTL, without violations of locality, etc.
What I do not yet know, and have not had enough to look into, is whether and how Relational QM might or does change what we expect of quantum computing. At some point, I'll seek out some Aaronson on the subject, e.g.
Read the book, well worth it.
When you imagine a fair coin being flipped and describing that with a probabilistic mathematical model, you can always imagine a classical story of what actually occurred. How you went from a spread out of possibilities to witnessing a single definite outcome. So I can understand the ontology because there is a classical ontology.
What QM is forcing us to do is write down as much classical story as possible, THEN SOMETHING TRULY RANDOM OCCURS. I can't imagine in my head any possible classical story. Both the coin and quantum "measurement" use probability theory in a similar way, but this is an important distinction.
When you say develop a new ontology, I really think you mean develop a recipe. I see no way to even comprehend anything but classical ontologies. I'm not sure if it's a limit of our, biology, imagination, or intuition. There is no classical ontology, nor settled ontology for that matter to describe the "measurement" of superpositions process.
You can't simulate that (fundamental randomness) purely classically. The classical world can be simulated with Turing machines, however. And we know infinite pen-and-paper maths can simulate any Turing machine.
How do I get from pen-and-paper maths (doing simple turing-machine-like operations/computations) to a truly random event, a necessary component for a quantum measurement? So when I'm doing my pen-and-paper maths, I have to go grab a radioactive atom and use the time it decays to somehow seed a random event into my simulation.
I do not know of a way to think beyond classically, or beyond the above notion of pen-and-paper maths.
Or are you saying some abstract high-dimensional vector really does ontologically exist in some even higher dimensional space? What space? Not spacetime, that is 4D. And even then how do we reduce that spread out WF to definite values in your ontology.
Math is not an ontology, unless you want to go the Mathematical Universe route.
The refusal of the majority of QM theoreticians to accept MWI is the root cause of the "mystery".
I'm sure decades after Copernicus, there were still astronomers going on and on about the complex interplay of the wanderers, and how the retrograde motion could only be explained with circles up circles, and spheres upon spheres.
This is no different.
I think it's unfair to criticize too harshly those who aren't ready to dive in with MWI. It's not that incomprehensible or too crazy, but it is far beyond what current physics says exists. We'd go from spacetime to some infinite or extremely high-dimensional space. Why should we need to go that far when other interpretations maybe ask less of us.
https://cloudflare-ipfs.com/ipfs/bafykbzacebhd6s3rewniz2q6b3...
pp. 21-35 307-355 355-368 (and more) if you or anyone wants some critiques of MWI
It's so much simpler to model the wanderers as moving along the surface of a celestial sphere! Adding depth adds nothing to our understanding when the current mathematical models can already predict their motion to high accuracy. It's all isomorphic anyway.
Look, just go away with your heretical notions, I have calculations to perform!
Quantum mechanics is completely deterministic. But the point from which we are observing it is random. (Not our origin in space, but our origin in possibilities.) The spread of a waveform is deterministic, but it seems random because we can't predict from which outcome our perspective will originate.
That's why the multiverse interpretation is (imo) the simplest way to reason about QM.
From the article: The goal in devising an algorithm for a quantum computer is to choreograph a pattern of constructive and destructive interference so that for each wrong answer the contributions to its amplitude cancel each other out, whereas for the right answer the contributions reinforce each other.
"In order to maintain a quantum superposition, we have to follow very strict rules imposed by quantum mechanics. We can't make operations depend on the state, so nothing like an if statement is available. Also all operations have to be reversible, so we don't have logical 'and' or 'or'. A relative handful of programs can follow these rules and get a huge speedup from quantum parallelism. The vast majority of useful computer programs can't be rewritten this way and get little or no speedup."
In fact, "trying all possibilities at the same time" is a ubiquitous phenomenon in Nature. Light rays find their trajectory by tryin out all possible paths and only the one with the highest constructive interference survives (this is what Feynman discovered in Quantum Electrodynamics, which is referenced in the article).
The real trick in quantum computing is manipulating qubits through quantum gates such that the outcome that gets assigned the highest probability is the correct one. This is indeed hard as the environment usually interferes and spreads out the probabilities across all outcomes, leading to a junky, random outcome.
DECLARE result BIT
H 0
MEASURE 0 result
Others might say the “Bell pair” is the hello world, and that looks like this:
H 0
CNOT 0 1
Similar to how you can have hello world in both ruby and python, but arrive at them with different syntax and compilers.
The troll answer of simulating a qbit using a qbit excluded.
To see quantum circuits that do something useful, check out the "Example Circuits" links that show up in the Quirk simulator: https://algassert.com/quirk
via https://algassert.com/2016/05/22/quirk.html via https://news.ycombinator.com/item?id=11752421
So for the time being quantum is not a real thread to cryptography and there sound technical reasons to assume that it never will be.
[0] https://en.wikipedia.org/wiki/Integer_factorization_records#...
There is a lot of arguments around that quantum computing will scale in a Moore's Law way (wrt qubits, so doubly exponential in compute power) and thus will be useful in the near future.
These are extremely optimistic.
Quantum computing hardware just came out of academic lab in the last few years and was subjected to actual engineering, hence the massive growth in capabilities. However these were mostly the result of solving all kind of low hanging fruits. To give an example of what I mean, I talked to a physicist doing superconducting qubit work at a conference in 2015 and at the time the cavities used to hold qubit wavefunction where machined by the Dept machine shop, using a mill. He told me they would just keep making them until they had enough that were of sufficient quality for computation. If I remember properly something like 1 was kept and 20 thrown. Using proper manufacturing can get you a lot farther but...
It's unclear how far, and modern (non quantum resistant) encryption would require thousands of time more qubits to solve on QC than are currently there.
https://www.technologyreview.com/2019/05/30/65724/how-a-quan...
https://arstechnica.com/information-technology/2015/08/nsa-p...
[1] https://crypto.stackexchange.com/questions/59795/largest-int...
> Accompanying the Quanta piece is a 10-minute YouTube explainer [1] on quantum computing, which (besides snazzy graphics) features interviews with me, John Preskill, and Dorit Aharonov.
[1] https://www.youtube.com/watch?v=jHoEjvuPoB8&t=6s
I get all my quantum computing info from Aaronson. I'm grateful for his efforts, but I sure hope he knows what he's talking about!
Two questions, for anyone who knows these things:
* Perhaps it's just not perfectly edited, but the above says the amplitudes are related to the probabilities that the qubit is 0 or 1. Shouldn't that say will be 0 or 1, because the qubit is currently in a superposition?
That may seem like nitpicking over typos, but it's necessary to the next question:
* Why have two amplitudes rather than one? The probabilities of either of two exclusive results, such as the two states of a resolved qubit, are P and 1-P. Given that amplitudes are directly proportional to those probabilities (in the last sentence of the above quote), how could the amplitudes change independently of each other? If the probability of one outcome increases, the other must proportionally decrease. And why not use one amplitude, because (it seems) if you know one amplitude you can easily determine the other? I suspect I'm misunderstanding something, perhaps that last sentence.
The thing to understand is that amplitudes are not actually just probabilities. For a single qubit, they are a pair of complex numbers a and b such that |a|^2+|b|^2=1. If you force a and b to be positive real numbers, then they really can be thought of as (square roots of) probabilities, and knowing one determines the other. However, since they can be complex, there are actually three real degrees of freedom, not one.
On the face of it, it’s not really clear what this buys you since measurement does force these complex numbers into their plain old, squared-norm probability. The interesting part is that there are quantum computational operations which only make sense in the complex world; there’s no way to realize them in the vanilla “probabilistic computing” world (that is, where all amplitudes are positive real).
Where things really start to get interesting is with “entanglement” of qubits, where now you have complex linear combinations of all possible n-bit states (where again the squared-norms must sum to 1). If you think of these linear combinations as elements of C^{2^n}, then quantum gates can be thought of as matrices acting on this space. Again, the “secret sauce” here is when you have gates that don’t come from classical computation (permutation matrices) or even probabilistic computation (real matrices with positive coefficients).
That being said, QM and QC is not particularly hard to explain, but the explanation sounds as believable as something else that could be completely made up, without some underlying knowledge, that intrinsically is seen as harder to understand than something that just leads logically from familiar experiences.
So lots of people will believe it and retweet it and talk knowingly about it on Reddit?
The approach I've started taking is to ask people if they know about mechanical or water powered computers. That at least implants the idea that there's a variety of ways to make a computer work.
Why is this question so important? I can see how it's interesting, but if the quantum computer does the job faster than the known classical solution, why not use it? You wouldn't delay shipping your classical code until you could prove that nobody will ever find a better solution.
A classical algorithm can be run immediately on commodity hardware tomorrow. And, most of the time, novel quantum algorithms actually can be matched or beaten classically.
Given that it makes sense to spend a small fraction of the cost of the needed quantum computer looking for the classical alternative. Preferably before you start investing in building the quantum computer.
See https://www.scottaaronson.com/blog/?p=3192 for an example of this back and forth.
Knowing little about QC, and based on reading that, it seems a qbit would be better called a qgate. It's not the store of data as much as the physical component that manipulates it, based on inputs. - Is that even approximately on target?
A q-bit really is a store of data that is equivalent to a bit. For example it can be a single trapped particle whose spin is in some superposition of up and down. What makes it different than a regular bit is that you can have 2 q-bits that are correlated, for example they are both in a superposition of up and down, but if one is up then the other is down and vice versa. Which means that an n q-bit system winds up being in some superposition of possible states, each of which is a sequence of n bits.
The problem with explaining QC to me lies in the quantum mechanics : it is a theory that is stochastic by nature but governed by deterministic principles. In a way we can't really explain QM properly or satisfactory to ourselves, hence how can we explain any of the quantum techs naturally ?
Quantum bullshit hype doesn't help either.
For example, when somebody need to predict trajectory of a car, he will not try to predict position of car tires in the every moment of the trajectory, because it's too complex. He will just assume that tires are "rotating" (i.e. in superposition of all tire states), unless tire state is important for the calculation, e.g. when braking.
PS.
Sorry for my English.
You can take two approaches : either in the Schrodinger's picture states are moving and operators (hence, measurable quantities) are static, or in the Heisenberg picture operators are moving but states are described as static. Defining trajectories themselves in QM is a daunting task (but can be done, through quantum trajectories, which can be interpreted as the ensemble of realizations of all possible outcomes of the system).
When you are dealing with superposition, in pure states, you might be in actuality in a stationary case and can only rely on measurements, which by themselves pose ontological problems (see the measurement paradox for more info). The determining factor of selection of the next outcome is philosophically unresolved and at the time I don't know if it can be explained through any case of quantum fluctuations.
At the moment for example I am working with arbitrary qubit selection with Ramsey interferences, the experimental setup can make by interferating one photon to another any superposition of two frequency states (thus manipulating the probability to be in a frequence or in other over an average of realizations of the experiment), thus an arbitrary Qubit.
In our case, we could freeze time and the outcome would be the same, in fact, time poses absolutely no role in any part in our description. I know some top physicists who lose sleep over this question of being able to describe past, present and future of quantum states in dynamical context all at once, without even considering time.
To put it simply, there's two sources of probabilities in QM : intrinsic to the random nature of QM (pure states) and probabilities due to our lack of knowledge (mixed states). When dealing with highly controlled system we can assume we are in pure states conditions, selection is automatic, and not due to any lack of description, at least to our current understanding.
The way I understand it now, is based on the double slit experiment. If you want to know the outcome of the "double spilt operator", you need to run it many times. The outcome of the calculation, is the combination of all the runs. The way to visualize is to think of the waves passing through.
QC itself is nothing more than chaining different operators, that influence how waves interact.
For small problems, it's work flawlessly, e.g. when you need to find an odd number, the network will be in solution state 99,99999999999999% of the time.
However, large networks are loosing their quantum properties very fast. Large objects have no properties of quantum objects — this is the corner stone of QM. The network can lose solution faster than it can find it, so when you sample, most of samples contains no solution to the problem, so you need to be lucky.
Currently, QC math doesn't account this, so we have a "measurement problem", because physical reality doesn't match math abstraction, but mathematicians don't want to adjust their formulas.
If you want to develop intuition, just look at reproduction of double slit experiment in macro[0]. It's just self-interference.
BTW: If you have resources, can I ask you to help to reproduce Stern–Gerlach experiment in macro? We need fresh blood (and money for experiments).
definitely not something a non-technical person would understand in 35 seconds!