For factoring 2048 RSA integers, the technique proposed in the paper would require ~430 million memory qubits (see the table at top of page 16).
...would be like bringing mathematics to Mesopotamia.
It could also be possible to use the technology developed for the precise control and measurement of qubits to "rebuild" natural phenomena like the interaction of chemical molecules, something which is currently extremely hard to simulate.
No it won't
We don't know either way. relationship between BPP, BQP, P, NP are all open.
Most of the time, the 'weight' flows back and forth between a and b according to certain equations over time. When you measure the system- that is, when the bit interacts with the outside world, hopefully your measuring apparatus- you see a 1 or a 0, with probabilities |a^2| and |b^2| respectively.
So what you can do is get a whole bunch of these quantum bits- qubits together, and set things up so that the time-evolution of their quantum state is correlated and probabilistically moves towards something you're interested in. Say you can set things up so the bit array- which, at first, will give you a mere perfectly random bit string on measurement- becomes more and more likely to give you, say, a prime factor, or the answer to some other question.
So yes, the quantum phenomenon is that the bits of the computer are quantum objects as opposed to classical.
(qubits I've seen explained many times, but setting things up so that qubits are probabilistically correlated is the part I've never understood anyone else to be saying)
The math on quantum computers checks out, it's "just" an engineering challenge at this point, and many are doubtful whether these challenges will ever be overcome to build a quantum computer of sufficient complexity.
Essentially, some "unitary evolutions" are complex to implement, as in requiring a lot of quantum "gates". This causes an accumulation of error and a whole lot of other problems, which limits the complexity of the calculations that can currently be performed.
I guess you meant to write high power as in high electrical power consumption? Or low power in the sense of low processing power? Anyway: Performance per Watt is probably pretty bad for current quantum computers ;)
It might not look that way because there's a lot of (relatively) mainstream investment in quantum computing. However it's pretty common for speculative physics research to be pursued for years without ever coming to fruition. Especially when there are promising early results before it's shown that scaling the work reduces to an intractable problem.
Of course, I’m saying it’s reasonable to be more optimistic, not that we have a proof we will certainly be able to scale to enormous machine sizes. But it’s definitely more than “speculative physics”: real machines have been built and demonstrated to exhibit truly measurable quantum effects that allow for programmable computation.
(To be sure, there is hype, there is a lot of cash sloshing around, and there are totally bogus claims some companies are publicly making.)
No they didn't. Not in any meaningful sense.
How exactly what that machine does can be called a "computation"? in what sense is it "programmable"?
The gate-model systems have shown that they are pursuing a much more difficult path, one that may indeed be fruitless for years or decades before they can approach our raw qubit count. We also have examples of nontrivial, paying-customer use cases that become more compelling with each new announcement. Factoring integers is indeed an interesting hard problem which would have a massive (negative?) impact on the world if realized, but besides Shor's and Grover's algorithms, it's not like gate-model QPUs have a ton of use cases significantly better than what a quantum annealer can accomplish.
I like to think of it this way: we're basically at the point of an ENIAC scale machine, if you liken quantum computing progress to classical computing. Fills up a room, very specific environmental and power requirements, little or no "memory" to speak of, esoteric and hard for anyone without years of training to master. Only a few decades later, the state of the art machine was thousands of times more capable, far cheaper and smaller, more reliable, more accessible in every way. Imagine describing the Internet as we use it today to an ENIAC operator, or a speculative investor considering IBM, Honeywell, etc. - it would sound like an impossible, Asimovesque dream, not something that children would literally be playing with sixty years later.
The only difference is that so far, we don't really seem to have a real exponential Moore's Law effect in quantum computing. Google et al. still have very low numbers of qubits without any real promise that they'll be able to deliver more of them in any consistent timeframe. At D-Wave we've done better on the scaling front, and we've been trying to keep up to our former founder's "Rose's Law" of qubit scale growth, but fabrication is an incredibly expensive, complicated, competitive endeavour that necessitates incredible quality control in order to produce processors that are up to spec. There are also other factors beyond the raw qubit count; the bigger advantage in our latest Advantage chip may actually be the higher connectivity between qubits on the graph, rather than their raw number.
Of course, we expect that we'll continue to push the envelope in this regard, and given enough time and investment, some of the early applications we're seeing now may well eventually be integrated into large scale products people use every day.
I don't think I understand this metaphor.
We may not have 13k qubit systems today, but we do have qubit systems already. Expecting us to get better at them is pretty reasonable.
Quantum systems don't scale that way. In order to get the quantum speedup you need to be able to maintain the larger quantum state which gets a lot harder the larger these systems get.
This is like saying we already have 7nm process today for silicon so expecting us to get better, like 1nm, 10 angstrom... or we have a plane that goes 2000 miles per hour, expecting 10kmph, 100kmph, 2000kmph... physics doesn't work like that.
How expensive is quantum memory relative to quantum compute, over the long term? Expectations about the answer to this question strongly affect whether or not you find this paper relevant. And the answer depends on the pieces you build your quantum computer out of, e.g. hypothetical photonic architectures have a bigger ratio than hypothetical superconducting qubit architectures.
It is currently very much an open question whether or not quantum computers will have a memory hierarchy.
After DRAM goes SSD and after SSD goes disk. The difference in price per GB for SSD and disk is about four (4x) times, I looked for that numbers recently. The difference between tape and disk is, again, about 4-10 times (from memory).
https://cdn.wccftech.com/wp-content/uploads/2020/11/AMD-Ryze...
If the price/density difference was anywhere near that much you'd see a lot more chips with fat onboard DRAM caches.
Also, please consider bandwidth here. 1TB of RAM can max at ten times the bandwidth of 1TB SATA hard disk drive, if not more. The difference in price is 80-fold, but if you factor in bandwidth requirements, the price difference drops to lower levels (10 drives, more SATA or specialized controllers, etc).
Is this also a hypothetical structure, or have they been built and shown to be able to reliably store and retrieve quantum state in such spatial modes? 430 million is a much, much larger number than their headline 13436 qubits...