Posted by A_D_E_P_T 1 day ago
So the "useful quantum computing" that is "imminent" is not the kind of quantum computing that involves the factorization of nearly prime numbers?
Either this relation is not that strong, or factoring should "imminently" become a reasonable benchmark, or useful quantum computing cannot be "imminent". So which one is it?
I think you are the author of the blogpost I linked to? Did I maybe interpret it too negatively, and was it not meant to suggest that the second option is still quite some time away?
the other problem is that factoring 21 is so easy that it actually makes it harder to prove you've factored it with a functional quantum computer. for big numbers, your program can fail 99% of the time because if you get the result once, you prove that the algorithm worked. 21 is small enough that it's hard not to factor, so demonstrating that you've factored it with a qc is fairly hard. I wouldn't be surprised as a result if the first number publicly factored by a quantum computer (using error correction) was in the thousands instead of 21. By using a number that is not absolutely tiny, it becomes a lot easier to show that the system works.
Google have been working on this for years
Don't ask me if they've the top supercomputers beat, ask Gemini :)
Like if you were building one of the first normal computers, how big numbers you can multiply would be a terrible benchmark since once you have figured out how to multiply small numbers its fairly trivial to multiply big numbers. The challenge is making the computer multiply numbers at all.
This isn't a perfect metaphor as scaling is harder in a quantum setting, but we are mostly at the stage where we are trying to get the things to work at all. Once we reach the stage where we can factor small numbers reliably, the amount of time to go from smaller numbers to bigger numbers will be probably be relatively short.
In QC systems, the engineering "difficulty" scales very badly with the number of gates or steps of the algorithm.
Its not like addition where you can repeat a process in parallel and bam-ALU. From what I understand as a layperson, the size of the inputs is absolutely part of the scaling.
So it seems like it takes an exponentially bigger device to factor 21 than 15, then 35 than 21, and so on, but if I understand right, at some point this levels out and it's only relatively speaking a little harder to factor say 10^30 than 10^29.
Why are we so confident this is true given all of the experience so far trying to scale up from factoring 15 to factoring 21?
I don't think we have any "real" experience scaling from 15 to 21. Or at least not in the way shor's algorithm would be implemented in practise on fault tolerant qubits.
We haven't even done 15 yet in a "real" way yet. I susect the amount of time to factor 15 on fault tolerant qubits will be a lot longer than the time to go from 15 to 21.
In the case of quantum algorithms in BQP, though, one of those properties is SNR of analog calculations (which is assumed to be infinite). SNR, as a general principle, is known to scale really poorly.
As far as i understand, that isn't an assumption.
The assumption is that the SNR of logical (error-corrected) qubits is near infinite, and that such logical qubits can be constructed from noisey physical qubits.
This is an argument I've heard before and I don't really understand it[1]. I get that you can make a logical qubit out of physical qubits and build in error correction so the logical qubit has perfect SNR, but surely if (say the number of physical qubits you need to get the nth logical qubit is O(n^2) for example, then the SNR (of the whole system) isn't near infinite it's really bad.
[1] Which may well be because I don't understand quantum mechanics ...
The hard problem then remains how to connect those qubits at scale. Using a coaxial cable for each qubit is impractical; some form of multiplexing is needed. This, in turn, causes qubits to decohere while waiting for their control signal.
In comparison, there is no realistic path forward for scaling quantum computers. Anyone serious that is not trying to sell you QC will tell you that quantum systems become exponentially less stable the bigger they are and the longer they live. That is a fundamental physical truth. And since they're still struggling to do anything at all with a quantum computer, don't get your hopes up too much.
If what you are saying is that error rates increase exponentially such that quantum error correction can never correct more errors than it introduces, i don't think that is a widely accepted position in the field.
I have a degree in chemistry from that institution, and don't have a clue what this means beyond the $1,000,000,000 economic impact this facility is supposed to make upon our fair city, over the next decade.
[•] <https://quantumzeitgeist.com/vanderbilt-university-quantum-q...>
[0] In partnership with our government-subsidized "commercial quantum-ready" fiber network, EPB
Nevertheless, Planck did not understand well enough the requirements for a good system of fundamental units of measurement (because he was a theoretician, not an experimentalist; he had computed his constants by a better mathematical treatment of the experimental data provided by Paschen), so he did not find any good way to integrate Planck's constant in a system of fundamental units and he has made the same mistake made by Stoney 25 years before him (after computing the value of the elementary electric charge) and he has chosen the wrong method for defining the unit of mass among two variants previously proposed by Maxwell (the 2 variants were deriving the unit of mass from the mass of some atom or molecule and deriving the unit of mass from the Newtonian constant of gravitation).
All dimensionless systems of fundamental units are worthless in practice (because they cause huge uncertainties in all values of absolute measurements) and they do not have any special theoretical significance (for now; such a significance would appear only if it became possible to compute exactly from theory the values of the 2 constants of the electromagnetic interaction and gravitational interaction, instead of measuring them through experiments; until now nobody had any useful idea for a theory that could do such things).
For the number of independently chosen fundamental units of measurement there exists an optimum value and the systems with either more or fewer fundamental units lead to greater uncertainties in the values of the physical quantities and to superfluous computations in the mathematical models.
The dimensionless systems of units are not simpler, but more complicated, so attempting to eliminate the independently chosen fundamental units is the wrong goal when searching for the best system of units of measurement.
My point is that the values of the so-called "Planck units" have absolutely no physical significance, therefore it is extremely wrong to use them in any reasoning about what is possible or impossible or about anything else.
The "Planck units" are not unique, there also exists a very similar system of "Stoney units", proposed a quarter of century before the "Planck units", where the values of the units are different, and there are also other variants of dimensionless systems of units proposed later. None of them is better than the others and all are bad, the worst defect being that the huge experimental uncertainties from measuring the value of the Newtonian constant of gravitation are moved from that single value into the values of all unrelated physical quantities, so that no absolute value can be known precisely, but only the ratios between quantities of the same kind.
In a useful system of fundamental units, for all units there are "natural" choices, except for one, which is the scale factor of the spatio-temporal units. For this scale factor of space-time, in the current state of knowledge there is no special value that can be distinguished from other arbitrary choices, so it is chosen solely based on the practical ease of building standards of frequency and wave-number that have adequate reproducibility and stability.
The only historical value of the "Planck units" is that they provide a good example of how one should NOT choose a system of units of measurement. The fact that they are still frequently mentioned by some people in any other context than criticizing such a system just demonstrates the very sad state of physics education, where no physics textbook includes an adequate presentation of the foundation of physics, which is the theory of the measurement of physical quantities. One century and a half ago, Maxwell began his treatise on electricity and magnetism with a very good exposition of the state of metrology at that time, but later physics textbooks have become less and less rigorous, instead of improving.
The theoretical entropy for a Schwartzchild black hole is nicely expressed using the Planck area.
So…
No. Your assertion that they have no value in theory, is wrong.
(Also, like, angular momentum is quantized in multiples of hbar or hbar/2 or something like that.)
It may be true that they aren’t a good system of units for actual measurements, on account of the high uncertainty (especially for G).
But, there is a reason why it is common to use units where G=c=hbar=1 : it is quite convenient.
2^256 states are comfortably distinct in that many dimensions with amplitude ~1. Their distinctness is entirely direction.
The obvious parallels to vector embeddings and high-dimensional tensor properties have some groups working out how to combine them in "quantum AI", and because that doesn't require the same precision (like trained neurel nets still work usefully after heavy quantization and noise), quantum AI might arrive before regular quantum computation, and might be feasible even if the latter is not.
Forget the talk about amplitudes. What I find hard to believe is that nature will let us compute reliably with hundreds of entangled qubits.
Yes, that is exactly the point. The example statevector you guys are talking about can (tautologically) be written in a basis in which only one of its amplitudes is nonzero.
Let's call |ψ⟩ the initial state of the Shor algorithm, i.e. the superposition of all classical bitstrings.
|ψ⟩ = |00..00⟩ + |00..01⟩ + |00..10⟩ + .. + |11..11⟩
That state is factorizable, i.e. it is *completely* unentangled. In the X basis (a.k.a. the Hadamard basis) it can be written as
|ψ⟩ = |00..00⟩ + |00..01⟩ + |00..10⟩ + .. + |11..11⟩ = |++..++⟩
You can see that even from the preparation circuit of the Shor algorithm. It is just single-qubit Hadamard gates -- there are no entangling gates. Preparing this state is a triviality and in optical systems we have been able to prepare it for decades. Shining a wide laser pulse on a CD basically prepares exactly that state.
> Changing basis does not affect the number of basis functions.
I do not know what "number of basis functions" means. If you are referring to "non zero entries in the column-vector representation of the state in a given basis", then of course it changes. Here is a trivial example: take the x-y plane and take the unit vector along x. It has one non-zero coefficient. Now express the same vector in a basis rotated at 45deg. It has two non-zero coefficients in that basis.
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Generally speaking, any physical argument that is valid only in a single basis is automatically a weak argument, because physics is not basis dependent. It is just that some bases make deriving results easier.
Preparing a state that is a superposition of all possible states of the "computational basis" is something we have been able to do since before people started talking seriously about quantum computers.
https://en.wikipedia.org/wiki/Quantum_computational_chemistr...
The video is essentially an argument from the software side (ironically she thinks the hardware side is going pretty well). Even if the hardware wasn't so hard to build or scale, there are surprisingly few problems where quantum algorithms have turned out to be useful.
It's a good reason to implement post-quantum cryptography.
Wasn't sure if you meant crypto (btc) or cryptography :)
This feels like woo-woo to me.
Suppose you're compressing the text of a book: How would a quantum processor let you get a much better compression ratio, even in theory?
If you're mistakenly describing the density of information on some kind of physical object, that's not data compression, that's just a different storage medium.
If results in quantum computing would start to "go dark", unpublished in scientific literature and only communicated to the government/ military, shouldn't he be one of the first to know or at least notice?
Surely if someone managed to factorize a 3 or 4 digits number, they would have published it as it's far enough of weaponization to be worth publishing. To be used to break cryptosystems, you need to be able to factor at least 2048-digits numbers. Even assuming the progress is linear with respect to the number of bits in the public key (this is the theoretical lower bound but assume hardware scaling is itself linear, which doesn't seem to be the case), there's a pretty big gap between 5 and 2048 and the fact that no-one has ever published any significant result (that is, not a magic trick by choosing the number in a way that makes the calculation trivial, see my link above) showing any process in that direction suggest we're not in any kind of immediate threat.
The reality is that quantum computing is still very very hard, and very very far from being able what is theoretically possible with them.
The fact that error correction seems to be struggling implies unaccounted for noise that is not heat. Who knows maybe gravitational waves heck your setup no matter what you do!
The error correction milestone matters because it's the gate to scaling. Previous quantum systems had error rates that increased faster than you could add qubits, making large-scale quantum computing impossible. If Willow actually demonstrates below-threshold error rates at scale (I'd want independent verification), that unblocks the path to 1000+ logical qubit systems. But we're still probably 5-7 years from "useful quantum advantage" on problems like drug discovery or materials simulation.
The economic argument is underrated. Even if quantum computers achieve theoretical advantage, they need to beat rapidly improving classical algorithms running on cheaper hardware. Every year we delay, classical GPUs get faster and quantum algorithms get optimized for near-term noisy hardware. The crossover point might be narrower than people expect.
What I find fascinating is the potential for hybrid classical-quantum algorithms where quantum computers handle specific subroutines (like sampling from complex distributions or solving linear algebra problems) while classical computers do pre/post-processing. That's probably the first commercial application - not replacing classical computers entirely but augmenting them for specific bottlenecks. Imagine a drug discovery pipeline where the 3D protein folding simulation runs on quantum hardware but everything else is classical.
QC is not a panacea. There are a handful of algorithms that are in BQP-P, and most of those aren't really used in tasks I would imagine the average person frequently engaging in. Simultaneously, quantum computers necessarily have complications that classical computers lack. Combined, I doubt people will be using purely quantum computers ever.