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The Case Against Quantum Computing

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Re: The Case Against Quantum Computing

#71

Post by maththrowawtays »

Many of the comments have pointed out this flaw in the argument. I will try to post my own summary of this flaw:

The problem is that this case against quantum computing due to the sheer scale of the number of parameters is also a case against randomized computing, but randomized computing certainly exists in the real world (a computer with a coin flipper). A 'state' in randomized computing over N bits is specified by a probability being assigned to each of the 2^N possible states of the N bits.

For example, to describe the distribution after flipping 100 coins, you require 2^100 real numbers to specify the probabilities for each outcome, since there are 2^100 combinations of heads and tails you can get. But it is very clear that we can do this in real life. The point is, you don't need 2^100 parameters with full precision to flip a coin 100 times.

To be more precise, we can write the state as a 2^N length vector, and our operations (think logic gates) on the vector are called stochastic matrices (this is the type of matrix required to so that the operation maps states to states).

Quantum computing is no different, except that instead of using real numbers for probabilities, complex numbers are used and they are called amplitudes instead. Also, instead of stochastic matrices for operations, they are now unitary matrices. The point is, the scale of the number of parameters is the same, the only thing that's changed is that it is complex numbers instead of real numbers.

Now an argument might be that it is not possible to create gates with a very specific probability distribution with just a discrete and not very precise coin flipper, but it's actually possible to show that for randomized computing, you only need a constant factor more flips to get exponentially close to the distributions you want. A similar result was proved pretty early for the quantum case, and it is a foundational result. So this is not really a problem either.

Re: The Case Against Quantum Computing

#72

Post by maththrowawtays »

The_rationalist wrote: post #23
nixpulvis wrote: post #19

Earlier quoted context omitted.

OK, yes. This builds on the parts of my intuition that already exist. It's about building a system (from combinations of quantum operators) that maximizes the probability distribution of the result you want. I'm still unsure of the timeline of any quantum operator, and the "finding the interference" seems equivalent to saying something like "find the function" or something more classical.

Yes I would really like to understand if this is different than curve fitting. How isn't that classical ? What about causality ? Quantum mechanics to me are just an effective model for dealing with uncertainty AKA probabilistic/meta probabilistic reasoning. But it is about statistically predicting the state of a particle/particles (position, spin, mass, momentum, etc). How can this model uncertainety in algorithms is…

Firstly, you're going to run into walls if you try to fully understand why the mathematics of quantum mechanics are how they are. Physicists have been going at it for decades and from what I can tell the picture is not so clear yet. What has been done though is many thousands of experiments showing that the predictions the mathematical theory makes (even the wild, unintuitive ones) are correct.

Secondly, I think you're going too deep on this whole 'prediction' thing. The algorithms in quantum computing aren't trying to model something any more than a classical algorithm does. Currently, the notion of a quantum algorithm is just a series of special logic gates that act on qubits instead of bits. What the previous poster said above is correct. Quantum computers are like classical computers with randomization except instead of real probabilities it has what are called complex amplitudes. The way the complex amplitudes behave allow for the states to interact slightly different since they can now 'interfere' with each other to cancel each other out in very specific situations. This power gives quantum computers only slightly more power the classical ones (with randomization). (Most) experts don't think quantum computers can solve NP-hard problems. This power from the interference only helps in very specific problems.

Re: The Case Against Quantum Computing

#73

Post by gitgud »

catpolice wrote: post #18

The core argument here, concerning the number of variables that need to be manipulated, isn't very clear to me - I can't tell if that's because it's an unclear argument in general, or if the author tried to simplify it for laypeople to the extent that it became unconvincingly vague for people who know a thing or two about the subject area. Given the status of the author, I'm willing to give him the benefit of the dou…

> unconvincingly vague for people who know a thing or two about the subject area.

I feel like this phrase could be applied to many things I come across... unconvincingly vague

Re: The Case Against Quantum Computing

#74

Post by tezthenerd »

dhammack wrote: post #66
tezthenerd wrote: post #51

Earlier quoted context omitted.

Let me present it a different way. Someone comes to you with two formal models of computing. Both models involve representing the state of the computer as a vector of real numbers, they both involve finite dimensional subsystems combined with a tensor product, both involve gates defined over the reals also combined via the tensor product and so on. That is, both models are just about evolution of a vector in some (ve…

Hey I'm not familiar with this way of comparing classical and quantum computation. Can you point me to some more details? I have Nielson's book but don't remember seeing this analogy before!

I presume its explained in Scott Asronsons book, its implicitly there in Nielsen and Chuang. But the best way to understand it is by example - try to write out how you would describe classical probabilistic computation on two classical bits to mimic the quantum circuit type of picture, and if you succeed the generalization will be obvious.

Re: The Case Against Quantum Computing

#75

Post by wjhuggins »

tezthenerd wrote: post #62
mcguire wrote: post #61

" While a conventional computer with N bits at any given moment must be in one of its 2N possible states, the state of a quantum computer with N qubits is described by the values of the 2N quantum amplitudes, which are continuous parameters (ones that can take on any value, not just a 0 or a 1). " If nothing else, that seems to me to be the clearest description of quantum computing I've seen.

[typo note its 2^N quantum amplitudes] A clear description but potentially very misleading and one that will certainly screw up your intuition about what to expect from quantum computers. As pointed out below, a classical probability distribution of N bits is a 2^N dimensional vector of real numbers. There are many very good reasons to think of the quantum state as "more like" this classical vector than the physical…

Actually, if you send a physical system which encodes N quantum bits you can send up to 2N classical bits.

(check out https://en.wikipedia.org/wiki/Superdense_coding)

Re: The Case Against Quantum Computing

#76

Post by ThePhysicist »

catpolice wrote: post #18

The core argument here, concerning the number of variables that need to be manipulated, isn't very clear to me - I can't tell if that's because it's an unclear argument in general, or if the author tried to simplify it for laypeople to the extent that it became unconvincingly vague for people who know a thing or two about the subject area. Given the status of the author, I'm willing to give him the benefit of the dou…

Gate-based quantum computers are similar to classical computers in that you can decompose any operation into a combination of a small set of universal gates (like single-bit NOT and two-bit NAND for classical computers). Typically you combine arbitrary single-qubit rotations along the X, Y, Z axes with a two-qubit gate like CNOT or iSWAP to obtain a full set of universal gates. You can then decompose your algorithm into these gates for running it, which is often doable efficiently (e.g. the Grover algorithm can be implemented easily using the gate set described above). You can also efficiently implement any classical gate operations on a quantum computer using a set of universal, reversible gates (e.g. single qubit NOT and classical CNOT). Finally, you need to read qubit states so you have to provide a readout of individual qubits, typically you implement the projection operator along the Z axis.

Now, for each of these operations you can characterize your error rate. For the processor I built during my PhD those error rates were around 9 % for qubit readout, 10 % for the universal two-qubit gate and around 1 % for single qubit gates. These errors stemmed from qubit decoherence (dephasing and relaxation), limitations of the readout and limitations of the signal precision for the manipulation. Errors are often different for each qubit and depend on the operation and the state the qubits are in (there’s crosstalk and different decoherence depending on the qubit frequencies as well), but you can usually give an upper bound for the error. Systems today are much better already btw. Given the different error rates you can very easily see how much error you will accumulate during a given gate sequence and what algorithms you will be able to run. We were for example able to perform the 2-qubit Grover algorithm with more than 50 % fidelity, which demonstrated quantum speed up for that very simple case. For a small subset of your qubits you can also perform quantum state tomography and quantum process tomography to statistically characterize their state and the quantum evolution they went through (including errors and decoherence), which allows you to characterize the errors in your system experimentally in a more precise way. Again this technique is limited by the fidelity of single qubit operations and readout, but it can nevertheless provide very good data for error analysis. For larger qubit systems tomography becomes intractable but there are other techniques that can allow you to characterize errors for these systems as well (e.g. randomized benchmarking).

So please stop telling people that it’s not possible to quantify errors, it is simply not true. Quantum computers are like classical computers in the sense that they obey the laws of physics and have various error sources that can be measured and characterized. The precision that’s required is higher than for classical computers but there’s no fundamental reason why quantum computers can’t work, it’s just a though engineering problem.

Re: The Case Against Quantum Computing

#77

Post by lewisinc »

Shame on this article. We should be researching everything within moral limits. Everything. Research all of it so hard that there's no long any debate about whether this point or that has any standing because it's so well understood that we can just fucking move on. Regardless of the topic, if we aren't sure if it's of value - we learn as much as we can until we can allow ourselves as a species to move on. That's the only way to prove any point in the realm of curiosity that satisfies me. Articles that argue the validity of investgating an unknown for any reason other than "it would cause significant harm" don't hold any weight and should be disregarded as either being based in fear, self interest, or simple ignorance.

Re: The Case Against Quantum Computing

#78

Post by feanaro »

krastanov wrote: post #47
klodolph wrote: post #31

Earlier quoted context omitted.

The argument that quantum computing relies on manipulating continuous variables with "near-infinite precision" is flatly incorrect, if my understanding of the threshold theorem is correct. So no, quantum computers do not require extreme amounts of precision or extremely low error rates because it is possible to correct errors by making the computer larger. https://en.wikipedia.org/wiki/Quantum_threshold_theorem

Amusing historical note: The same arguments were made about classical computers and a similar theorem (by Von Neuman) exists there.

Do you have a more precise citation of this theorem? I'm curious.

Re: The Case Against Quantum Computing

#79

Post by carlmr »

lewisinc wrote: post #77

Shame on this article. We should be researching everything within moral limits. Everything. Research all of it so hard that there's no long any debate about whether this point or that has any standing because it's so well understood that we can just fucking move on. Regardless of the topic, if we aren't sure if it's of value - we learn as much as we can until we can allow ourselves as a species to move on. That's the…

Completely agree. Imagine people had given up on the transistor. It took many attempts until there was a workable transistor. And then manufacturing still wasn't clear.

Re: The Case Against Quantum Computing

#80

Post by ur-whale »

lewisinc wrote: post #77

Shame on this article. We should be researching everything within moral limits. Everything. Research all of it so hard that there's no long any debate about whether this point or that has any standing because it's so well understood that we can just fucking move on. Regardless of the topic, if we aren't sure if it's of value - we learn as much as we can until we can allow ourselves as a species to move on. That's the…

The article isn't entirely worthless, the illustrations are really nice.
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