What You Shouldn't Know About Quantum Computers
arxiv.org
arxiv.org
I am skeptical. 36 years is a long time, but in the past 10 years there hasn't been much progress:
year 2001: factorization of 15 (IBM)
year 2012: factorization of 21 (University of Bristol)
year 2019: factorization of 35 attempt, failed (IBM)
The “largest integer factored” metric is terrible for several reasons, which is well recognized by researchers and is why people rarely publish those sorts of claims any more. Without net-positive error correction, it’s basically a function of how low your error rate is and how many bits that allows you to compute on with low chance of error, but as soon as the error rate crosses the fault-tolerance threshold then suddenly your storage is limited only by how many qubits you can build. So you can’t use this metric (if people were even publishing it) to predict anything after fault tolerance is achieved.
On more meaningful metrics, there has been steady progress.
Additionally, I was under the impression that not all QCs being built are able of executing Shor’s algorithm which added additional challenges that aren’t solved.
My final impression is that having the QC algorithm run faster than a classical computer doing the same operation has also not necessarily gotten better so we don’t even know if we are actually closer to Quantum supremacy in terms of actually useful more general computation instead of the limited supremacy that Google achieved in 2019 on specific problems, similar to the (still ongoing?) controversy whether DWave built a QC or a quantum annealer capable of accelerating simulations of very specific physical properties.
Is this impression outdated and/or misinformed? Would love to update my priors.
In practice, the first useful QCs will probably be Q-Turing complete.
I'm confused here.
Everyone in the industry is basically fully occupied with coming up with a mechanism for active error correction. But based on what I've heard from the folks on the front lines, it's still 10+ years away at minimum.
https://en.wikipedia.org/wiki/Threshold_theorem
If it helps, there are plenty of historical analogies. Quantum-enhanced sensing took more than half a century between conception and practical use, but it is currently used daily at LIGO.
https://www.quantamagazine.org/the-argument-against-quantum-...
In any case, I'm happy to bet on this.
As for my own belief, I don't know how it will pan out, but I'm inherently sceptical of people who are too certain that it is one way or another, the hard evidence simply does not exist yet.
I'm personally most inclined to believe that the universe is computationally classical, and while quantum physics necessitates that there must be quite a lot more information and processing happening than a Newtonian model requires, it is still a finite, thus putting a finite limit on what speed-up we can gain from a quantum computer. Most likely this pans out as the error correction limit being impossible to reach, but there is also the possibility that more complicated quantum states result in higher per-gate error rates.
I'm open to other conjectures, but if you want to dispel mine I would like to see some hard evidence.
New fundamental physical principles are at this stage required in any case, quantum mechanics and general relativity don't fit together, meaning that at least one of them need to be overhauled into something that explains the same observations but doesn't have quite the same maths. The lacklustre performance of quantum computers could be a hint to what needs overhauling.
And which odds would you need on that?
If you wanted a useful machine, say factoring RSA-2048, you would need to push the date to more like 2050 or 2060.
Most of the uncertainty comes from the economy, engineering cost, public interest in QC, AI doom, etc. If we could somehow make a platonic bet on “is a large QC constructible if dedicated $10T/yr for 200 years”, then I am over 95-5.
Not to mention the fact that we still don’t know if the current candidate PQC protocols are actually secure. Security is mostly a game of back-and-forth over years, so it could take a while.
Which isn't to say that it's impossible, but it would be quite exciting if it were the case.
There is finite a threshold error rate (roughly 0.1-1%) at which you can produce a single logical qubit with an unbounded number of physical qubits (infinite overhead). For error rates below the threshold, the overhead becomes much less. People expect overheads in the thousands. See Fig. 1 in our paper. https://arxiv.org/pdf/2009.05045
> and it’s not actually known if we’re any closer on that metric vs other more easily achieved metrics.
We are getting lower error rates. But until we cross the error threshold, the overhead for a logical qubit is infinity.
> I was under the impression that not all QCs being built are able of executing Shor’s algorithm
Correct.
> which added additional challenges that aren’t solved.
Logical qubits enable general purpose quantum computing, which includes Shor's algorithm. As mentioned, we don't have logical qubits yet, and some people are trying to build less general devices to solve certain math problems in the meantime. But the overall goal for the field is still logical qubits, and there's steady progress on that.
> My final impression is that having the QC algorithm run faster than a classical computer doing the same operation has also not necessarily gotten better
I can't really parse the claim, but I think your impression is wrong. Supremacy has always been a fuzzy bound, since it's defined in terms of the best known classical algorithms. But the supremacy results have gotten more unambiguous over time.
By that I mean that integer factorization is still slower than classical machines even though the numbers that can be factored have gotten larger. Similarly, with the exception of very specific toy problems specifically constructed to demonstrate quantum supremacy, we haven't achieved supremacy on any interesting and useful problems (not sure if DWave's quantum annealing machine really has any useful applications but presumably it must, but also not clear that it's a meaningful step on the path to a QC).
36 years ago we didn't even know shor's algorithm existed, and didn't know quantum computers could non-exponentially factor integers at all.
So in a certain sense, we have made infinite progress in the last 36 years. Who knows what could happen in the next 36.
More generally, i think making science predictions that far out is basically impossible.
> Hear the story of Shor's Algorithm, straight from the source, Peter Shor.
Shor's part of the story starts in '81.
Though, I generally agree with the it is hard to make predictions that far out. We've got the math to do some higher things, but we still don't have flying cars and fusion power.
There's a threshold you need to reach for quantum error correction to work and we are approaching it pretty steadily on a log scale.
> Of course this should not be considered a serious demonstration of Shor’s algorithm. It does, however, illustrate the danger in “compiled” demonstrations of Shor’s algorithm. To varying degrees, all previous factorization experiments have benefited from this artifice. While there is no objection to having a classical compiler help design a quantum circuit (indeed, probably all quantum computers will function in this way), it is not legitimate for a compiler to know the answer to the problem being solved. To even call such a procedure compilation is an abuse of language.
I have never seen a result like that. Do you have a citation?
A recent result considers a generic error model and a subclass for particular kinds of prime numbers [1]. The important result is $epsilon > cn^{−1/3}$ where epsilon represents qubit error rate and n number of bits in the factorised number. As $n = 2^N$ where N is a number of qubits, the result:
error_rate < const/2^{N/3}
Therefore, the error rate must decrease exponentially with the number of logical qubits with which the computation is made.
Or, possibly, they are using “90% confidence” colloquially as “pretty sure.” If so, that should probably be made more clear. He’s using the fact that the researchers agree as an argument from authority, which is doubly wrong if the apparent authorities here were just giving their hunches.
I'm not sure about the field of physics but in deep learning there are hundreds of papers published every day while no more than a percent of them tries to make the paper less mythical and instead they keep inventing buzzwords and claiming positive results to make them even more mythical
BQP: Bounded-Error Quantum Polynomial-Time, bounded by a max error of 1:3
BQP is the complexity class thought to contain problems with practical solutions for quantum computers.
IIRC the main limit being the transition amplitudes are subject to the Church–Turing thesis and must be computable functions.
Hopefully useful buzzwords for those who want to dig deeper.
I'm more familiar with cryptography so the most famous problem in BQP for me is discrete logarithm. Once you have this primitive, the following things are very clear:
1. How Shor's algorithm for factorization works: it consists of a classical algorithm that reduces factorization to calculation of group order of an element (which is a special case of discrete logarithm), then uses a quantum computer to solve the group order problem. This breaks RSA.
2. Breaking elliptic cryptography: Modern elliptic cryptography constructs an elliptic curve (in the form of y^2=x^3+Ax+B) and defines multiplication on top of the points on the curve. It turns out that multiplication is very easy but discrete logarithm is hard and that hardness is used to prove that Diffie-Hellman key exchange is hard to break, but what if it's not? Moreover, elliptic curves usually only have 256~512 bits since it's sufficient to guarantee security in the classical case, compared to RSA with 2048~4096 bits. While it's harder to break elliptic curves using classical methods, it turns out to be even easier for quantum computers.
What quantum computers is NOT is a parallel computer with 2^n threads running in parallel that would collapse to the thread that gives the correct results. This would imply BQP=NP which is not known to be true and however many qubits we build it won't be any more likely to become true.
In the first "Myth" section, that "nobody understands this quantum stuff", the example is used of the transistor. It's true that we have no way of making a classical model of a transistor, and our understanding of how transistors work relies on quantum mechanics.
But we did not invent transistors from quantum physics -- we created transistors long before we had an explanation of how they worked, and we have continued to improve and iterate by making advances in material sciences and experimentation, not by applying first principles. Things like blue LEDs were invented by tinkering rather than by solving Lagrangians.
The final section was of particular interest to me; Gil Kalai's work on quantum error correction is very interesting to me and I am in the camp that believes that quantum computing is not possible in any useful sense; in particular a quantum computer will not be capable of being significantly more powerful than a classical computer, in the quantum supremacy sense.
Here the author reverts to a simplistic argument that "of course" quantum computers are possible, because we can model a quantum computer in a traditional computer. But this sidesteps the main claims, which are whether it is possible to scale error correction to the point where a useful result can be achieved.
Even in the domain of NISQ, which is roughly the equivalent of running fluid dynamics simulation in a bathtub, we have yet to produce results showing that we can scale significantly better than a quantum computer.
In a similar spirit ships were built, steam engines made and applications of superconductivity imagined long before the objects were understood from first principles. Creation often proceeded theory nevertheless it is still useful for optimizing designs at later stages.
Could you elaborate on that? I was under the impression that some companies are using Quantum Computers because quantum supremacy has been demonstrated (such as in molecular modeling for drug discovery or materials science) - but I'm a complete novice here, and would love to learn more. I'm probably quite wrong, and happy to be corrected.
Also, by not possible in a useful sense, do you mean that QCs as they are now versus in N years, or just in general?
There are companies selling and companies using "Quantum Computers". For example, D-Wave systems sells a computer that uses quantum annealing so solve a class of minimization problems.
To date, there is no quantum computer, in a commercial or a research setting, that has demonstrated it can compute anything faster than a classical computer (this includes the D-Wave systems).
The current trend is to try to establish quantum supremacy (and thus falsify the error correction is impossible thesis) through building extremely simple (non-general purpose) quantum systems. Most recently Google announced a successful attempt that has since been invalidated.
Maybe his arguments have improved over the decades. Does he now have a coherent argument that doesn't (i) take it as a point of religious faith that noise will be magically correlated in order to break error correcting codes (ii) also demonstrate the impossibility of classical computers
This possibility doesn't strike me as any more magical than QM's conjugate variables or its unusual correlations, which also seemed magical to classical physics. Arguably these + contextuality would make noise correlated with the system's configuration in some way, we just don't have a thorough enough understanding of measurement and decoherence to quantify it precisely. I think that's beginning to change, and that we'll have more clarity in the next 10 years or so.
You can't just go "QM has many surprising aspects" to "this other theory also has surprising aspects, it's probably true".
If we had been having this conversation before some of the more bizarre quantum effects had been observed it would have been a fair comparison, but we are way past that point.
I didn't say it's probably true because of this argument, you're saying it's probably false because it seems magical, and that's the implication I'm disputing with that analogy.
I do think it's plausible that noise could be correlated for the reasons I specified, but not because of the "magical" analogy.
My question too. I've had a vague feeling about this for a long time, waving my hands about thermodynamics with "It must get exponentially harder per qbit to eliminate thermal noise by cooling down closer to absolute zero," and I'd really like to get past my hand-waving and see what the dynamics really are.
Why? Cooling a large object is not exponentially harder than cooling a small object.
Per unit of volume, your body produces more heat than the sun, exactly because it is an exponential function.
x^3 is not an exponential function, in the sense relevant here.
Thus why IBMs largest refrigerator can only dissipate tiny amounts when cold.
> enabling close to ~10 mW at 100 mK cooling power, and over 24 W of cooling power at 4 K temperatures. Finally, the weight of the entire system — 6.7 metric tons
They aren't building single huge quantum processors, but networks of easy to cool parts.
IBM hopes that one GoldenEye refrigerator may be able to hold a million qbits but that isn't enough to break RSA.
RAND estimated 890 MWh per key to be broken.
It will be horizontal sprawl, not vertical integration.
Larger objects simply have to get hotter to expell the same watts per volume or increase surface area.
That is problematic for quantum computers.
Can you give a reference? Also, how is heat generated within the quantum processor as operations are unitary?
This is only true if the object enlarges in every direction equally. If it spreads out along a flat plane then the ratio is essentially constant, for example.
Let u(x) the temperature at location x. Let \alpha be the thermal diffusivity (assume to be constant throughout the material and over time). Assume that within the ball of radius R, \alpha \nabla^2 u = k for k the heat production density divided by the specific heat capacity (assumed to be constant over the range of temperatures involved) . For spherically symmetric u(x), a function of just distance from the center..
ok, so, need solutions of Laplace's equation, \nabla^2 u = f , where f is some constant times the indicator function of the ball of radius r? Uh, I was thinking to have a boundary condition at the surface of the ball, fixing a particular temperature there, and seeing what temperature enforced there is enough to produce a small enough temperature at the center of the ball... (In that case I guess f can just be a constant, rather than the indicator function of the ball)
uhh.. does this have an analytic solution? This is ending up as a more difficult computation than I anticipated...
edit: oh, for it to be steady state, the rate of heat going through any sphere centered at the origin, must be equal to the rate of heat produced within the ball that it bounds, so for r < R, (4/3) pi r^3 k going through 4 pi r^2 surface area, so heat transfer per surface area of (1/3) r k , and... uh, this is proportional to the gradient in temperature, and this gradient should be proportional to the derivative of temperature with respect to radius (as, gradient should be in a radial direction)
so, g'(r) ~ r ,
so g(r) - g(0) ~ r^2 .
So... if I haven't messed up too badly, I would think that, the difference in temperature of the center, and the temperature of the surface, should be proportional to (heat production per qubit) * ((radius of ball)^2) ~ (heat production per qubit) * ((number of qubits)^{2/3})
which... given a particular upper bound on working temperatures for the core of the ball, would put an upper bound on the number of qubits if packed in a ball like that. Though, I would imagine that if you instead have the inner (some number) fraction of the ball not have qubits, and not produce heat, then that wouldn't apply. Though this would require the surface area grow faster than (number of qubits)^{2/3} .
My thermodynamic instinct says that the cooling effort required rises with the resolving power — which is exponential with the number of qbits. But it's just instinct, not grounded very well in science or engineering.
Yes, more qbits also take up more space, but I hadn't thought of that as a major factor — but it certainly could be if they are physically large! Overall I think the bigger issue is cooling.
The article mentions error correction as an alternative to increased coherence among the qbits. Perhaps what that really means is "to increase meaningful interaction among qbits, make it as cold as you can, and then error correct until you get a meaningful answer." My intuition is that they are both a battle against entropy — the need for error correction will also increase exponentially with the number of qbits, simply because the number of possible combinations increases exponentially.
And the even larger outcome of all this is that if this intuition bears out, quantum computing will have no fundamental advantage over conventional computing — which also has an exponential cost for a linear increase in bits, for computations such as factoring large numbers.
tl;dr Experts in a domain are extremely poor at predicting the impact of a technology disruptive to their domain. It's not that they are trying to be dishonest. Just that there are too many fallacies waiting to trap them and they inevitably fall prey to one or more of them.
https://www.csferrie.com/books
https://www.amazon.com/Quantum-Computing-Babies-Baby-Univers...
For example, emphasizing spacetime curvature is, in my opinion, kind of a weird way to talk about the actual substance of general relativity (universal coupling of gravity, futility of trying to describe the world with any fixed four dimensional coordinate system). His quantum mechanics book has similar problems. When I try to explain physics to my young child I always try to get at the essence of the ideas, not the superficial pictures.
Maybe other people thought this didn't add much to the discussion, but I found it interesting.
[0] I am Chris Ferrie, father of four and happy husband. My day job is academic research where I follow my curiosity through the world of quantum physics. My passion for communicating science has led from the most esoteric topics of mathematical physics to more recently writing children’s books.[1]
Yet in all that time I never thought to write, much less did I actually write, a pithy book called “What You Shouldn't Know About Quantum Computers.” My colleague Chris Ferrie did. He's the same guy who coauthored the surprise bestseller “Quantum Computing for Babies.” Now he's back, with something for those babies to read when they're slightly older.
I enjoy his kids' books and read almost all of them to my kids. They aren't "perfect" (whatever that means for a kids' book), but my kids love them and they start to wrap their brains around otherwise inaccessible topics for their age.
It's a panel headed by Prof Al-Khalili. I suspect it will be a beginner level presentation.
>Professor Jim Al-Khalili CBE FRS is a theoretical physicist at the University of Surrey where he holds a Distinguished Chair in physics and leads the Quantum Foundations and Technologies Research Group in the School of Mathematics and Physics. As well as his academic work he is a well-known popular science author and broadcaster on BBC radio and television.
No affiliation, just may be of interest.
Important Nuance: the research is real, the science is real, but the narrative being sold about the future of quantum computing to ensnare investors is not a reasonable prediction and is a con.
AI has commercial applications right now. What commercial application is there for quantum computing right now?
https://s7d9.scene7.com/is/content/quantum/LQ_ErrorCorrectio...
the corrections significantly decrease the error rate but they need to do a lot of preselection, so it isn't quite useful yet.
Delusional, IMO. Without a proper understanding of how the non-linearity of the macroscopic world arises from the unitarity of QM, any scaling projections are wishful thinking. We just don't have a good enough understanding of the measurement problem and decoherence to make such projections.
How so?