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Google Quantum AI

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Re: Google Quantum AI

#171

Post by vtomole »

adrian_b wrote: post #167
vtomole wrote: post #131

Earlier quoted context omitted.

> It is still open whether we can build quantum computers with sufficiently low noise to run Shor‘s algorithm. This statement should delimit between theory and experiment. Theoretically, the question of building a quantum computer with low enough noise to run Shor's has been solved. In fact it was solved by Shor himself in the 1990s: https://arxiv.org/abs/quant-ph/9605011 . Experimentally, we are just getting started…

That paper of Shor just shows how a quantum computer with a large number of bad qubits can be the equivalent of a quantum computer with a small number of good qubits. The paper does not prove anything about the upper limit for the number of bad qubits that are physically realisable. There are doubts that this upper limit, which is unknown yet, is high enough for most practical applications.

> The paper does not prove anything about the upper limit

Nothing can prove how many qubits can be realizable except trying to realize them. There will never be a theorem that says "The maximum number of qubits that can ever be controlled in a lab is X". That's what experiment is for.

I will say, it's difficult to doubt that the upper limit to the number of qubits we can realize is infinity. We can now trap ~10 million atoms and efficiently control hundreds of them: https://www.nature.com/articles/s41586-023-06927-3. The question is not "Could we ever realize billions of qubits?". It's "When can we realize billions qubits?". The answer could be decades or centuries but as long as people are building these devices, it will happen eventually.

Re: Google Quantum AI

#172

Post by vtomole »

hedora wrote: post #162
vtomole wrote: post #149

Earlier quoted context omitted.

> The cynicism stems from people telling others that practical quantum computers will change the world for at least a decade. Practical quantum computers will change the world (break RSA 2048). The question is "when". The people who have a timeline of ~10 years instead of decades contribute to what we in our community call "Quantum hype" and it's very much frowned upon by most of the members in the community. > combi…

How would breaking RSA change the world? Perhaps via some practical (non-crypto) application of factoring large numbers?

Breaking RSA changes the world by breaking crypto and implicitly by moving protocols to post-quantum crypto, which is already happening https://security.apple.com/blog/imessage-pq3/.

Quantum computers also change the world by solving circuit-SAT https://en.wikipedia.org/wiki/Circuit_satisfiability_problem more efficiently than classical computers than.

They also change the world by simulating quantum systems efficiently, which classical computers cannot do. This has profound implications for physics.

Re: Google Quantum AI

#173

Post by adrian_b »

fsh wrote: post #59
amelius wrote: post #54

Earlier quoted context omitted.

We currently can't even simulate a hydrogen atom.

We can absolutely simulate the hydrogen atom. This paper lists the equations and fundamental constants that allow calculating the hydrogen energy levels with around 13 digits of accuracy: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.93....

That is not a simulation and those are not fundamental constants.

Because a simulation is too difficult, there are approximate formulae for computing the quantities of interest, like the energy levels of the spectrum of the hydrogen atom.

These approximate formulae include a large number of constants which are given in the paper linked by you and which are adjusted to match the experimental results.

A simulation of the hydrogen atom would start from a much smaller set of constants: the masses of the proton and of the electron, the magnetic moments of the proton and of the electron, the so-called fine structure constant (actually the intensity of the electromagnetic interaction) and also a few fundamental constants depending on the system of units used, which in SI would be the elementary electric charge (determined by the charge of a coulomb in natural units), the Planck constant (determined by the mass of a kilogram in natural units) and the speed of light in vacuum (determined by the length of a meter in natural units).

Re: Google Quantum AI

#174

Post by fsh »

adrian_b wrote: post #170
fsh wrote: post #160

Earlier quoted context omitted.

This is completely wrong. My laptop can solve the equations in fractions of a second. I believe that with some optimizations it should be trivial to do the calculations on a 1960s mainframe.

That is not true. You can solve such equations in fractions of a second only for very low precisions, much lower than the precision that can be reached in measurements. For higher precision in quantum electrodynamics computations, you need to include an exponentially increasing number of terms in the equations, which come from higher order loops that are neglected when doing low precision computations. When computing…

I believe you might be confusing the QED calculations of hydrogen with those of the electron g-factor. Just have a look into the paper I linked (section VII). Most of the QED corrections are given analytically, no computers involved at all. You could in principle calculate this with pen-and-paper (and a good enough table of transcendental functions).

The most accurate hydrogen spectroscopy (of the 1S-2S transition) has reached a relative accuracy of a few parts in 1E15 which is around an order of magnitude above the precision of FP64 numbers.

Re: Google Quantum AI

#175

Post by jacobsimon »

edanm wrote: post #113
jacobsimon wrote: post #79

Earlier quoted context omitted.

I thought one of the main advantages of QC was that it could (theoretically) solve existing problems that have exponential time complexity with more efficiency. Isn’t the idea that it could make everything faster? Or did I fall for the marketing.

> Isn’t the idea that it could make everything faster? If that is your understanding, then yes, you have unfortunately fallen for the very mistaken reporting on this. There are specific algorithms that Quantum Computing can solve faster than regular computers. Some of these algorithms are incredibly important, and a faster solution to them would cause serious changes to the world, namely Shor's algorithm, which would…

Huh yeah I guess I need to learn more. My layman’s assumption was that it would help with a lot of NP problems that involved recursion or backtracking algorithm would benefit from it. From some quick googling it seems like they have already designed QC algorithms for traveling salesman etc. Isn’t that sort of meaningful or am I missing something?

I could totally see the argument that they are physically impractical and therefore not likely to be actually used vs parallelizing conventional computers.

Re: Google Quantum AI

#176

Post by fsh »

adrian_b wrote: post #173
fsh wrote: post #59

Earlier quoted context omitted.

We can absolutely simulate the hydrogen atom. This paper lists the equations and fundamental constants that allow calculating the hydrogen energy levels with around 13 digits of accuracy: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.93....

That is not a simulation and those are not fundamental constants. Because a simulation is too difficult, there are approximate formulae for computing the quantities of interest, like the energy levels of the spectrum of the hydrogen atom. These approximate formulae include a large number of constants which are given in the paper linked by you and which are adjusted to match the experimental results. A simulation of t…

The inputs of the formulas for the hydrogen energy levels in the paper are: The Rydberg constant, the fine structure constant, the electron-to-proton mass ratio, the electron-to-muon mass ratio, the Compton wavelength of the electron, and some nuclear properties (charge radius, Friar radius, and nuclear polarizability). All inputs except the nuclear properties are as fundamental as it gets according to our current understanding of physics (note that the Rydberg constant and Compton wavelength are simple combinations of other physical constants). Nuclear physics is dominated by quantum chromodynamics which is not nearly as well developed as QED.

The constants are determined by fitting the theory to the best available measurements (not only in hydrogen). This is exactly what fundamental constants do: They convert unit-less theory expressions into measurable quantities.

Re: Google Quantum AI

#177

Post by adrian_b »

fsh wrote: post #174
adrian_b wrote: post #170

Earlier quoted context omitted.

That is not true. You can solve such equations in fractions of a second only for very low precisions, much lower than the precision that can be reached in measurements. For higher precision in quantum electrodynamics computations, you need to include an exponentially increasing number of terms in the equations, which come from higher order loops that are neglected when doing low precision computations. When computing…

I believe you might be confusing the QED calculations of hydrogen with those of the electron g-factor. Just have a look into the paper I linked (section VII). Most of the QED corrections are given analytically , no computers involved at all. You could in principle calculate this with pen-and-paper (and a good enough table of transcendental functions). The most accurate hydrogen spectroscopy (of the 1S-2S transition)…

The "few parts in 1E15" claim is applicable only to the absolute value of the frequency of the 1S-2S transition, which is 1 233 030 706 593 514 Hz.

That absolute frequency is computed from the ratio between an optical frequency and the 9 GHz frequency of a cesium clock, which is affected by large uncertainties due to the need for bridging the gap between optical frequencies and microwave frequencies.

The frequency ratios between distinct lines of the hydrogen atom spectrum or between lines of the hydrogen atom spectrum and lines in the optical spectra of other atoms or ions can be known with uncertainties in parts per 1E18, one thousand times better.

When comparing a simulation with the experiment, the simulation must be able to match those quantities that can be measured with the lowest uncertainty, so the simulated values must also have uncertainties of at most parts per 1E18, or better per 1E19.

This requires more bits than provided by FP64. The extended precision of Intel 8087 would barely be enough to express the final results, but it would not be enough for the intermediate computations, so one really needs quadruple precision computations or double-double-precision computations, which are faster where only FP64 hardware exists.

I have not attempted to compute the QED corrections myself, so I cannot be certain how difficult that really is.

Nevertheless, the section VII from this CODATA paper and also the previous editions of the CODATA publications, some of which had been more detailed, are not consistent with what you say i.e. with them being easy to compute.

For each correction there is a long history of cited research papers that would need to be found and read to determine how exactly they have been computed. For many of them there is a history of refinements in their computations and of discrepancies between the values computed by different teams, discrepancies that have been some times resolved by later more accurate computations, but also some where the right value was not yet known at the date of this publication.

If the computations where so easy that anyone could do them with pen and paper there would have been no need for several years to pass in some cases until the validation of the correct computation and for a very slow improvement in the accuracy of the computed values in other cases.

Re: Google Quantum AI

#178

Post by fsh »

adrian_b wrote: post #177
fsh wrote: post #174

Earlier quoted context omitted.

I believe you might be confusing the QED calculations of hydrogen with those of the electron g-factor. Just have a look into the paper I linked (section VII). Most of the QED corrections are given analytically , no computers involved at all. You could in principle calculate this with pen-and-paper (and a good enough table of transcendental functions). The most accurate hydrogen spectroscopy (of the 1S-2S transition)…

The "few parts in 1E15" claim is applicable only to the absolute value of the frequency of the 1S-2S transition, which is 1 233 030 706 593 514 Hz. That absolute frequency is computed from the ratio between an optical frequency and the 9 GHz frequency of a cesium clock, which is affected by large uncertainties due to the need for bridging the gap between optical frequencies and microwave frequencies. The frequency ra…

The accuracy of the hydrogen 1S-2S measurement was mainly limited by the second-order Doppler shift of the moving atoms (and to a lesser degree the AC Stark shift of the excitation laser and the 2S-4P quench light). The comparison between the laser frequency and the Cesium fountain clock was done with an optical frequency comb which introduces a negligible uncertainty (Isn't it fun to get your own field of expertise (wrongly) explained to you on the internet?

Edit: I never said that it is easy to derive the corrections listed in the CODATA paper. However, it is relatively easy to calculate them.

Re: Google Quantum AI

#179

Post by edanm »

cwillu wrote: post #132
edanm wrote: post #113

Earlier quoted context omitted.

> Isn’t the idea that it could make everything faster? If that is your understanding, then yes, you have unfortunately fallen for the very mistaken reporting on this. There are specific algorithms that Quantum Computing can solve faster than regular computers. Some of these algorithms are incredibly important, and a faster solution to them would cause serious changes to the world, namely Shor's algorithm, which would…

Public key crypto is vulnerable to period finding, but symmetrical key cryptography is pretty safe from quantum computing advances.

This might be true (I'm not that up to date on whether there are symmetrical algorithms that negate the advantage of QC), but most of the internet / world commerce relies on public key crypto.

Re: Google Quantum AI

#180

Post by fooker »

maxboone wrote: post #115
fooker wrote: post #15

The fact this prize exists is admitting that no one has figured out a use for quantum computers. I have heard this mentioned several times in the last decade or so : "The only thing a quantum computer definitively does better than a classical computer is simulating a quantum computer." Whether this capability is useful is up in the air. Note that in practice, classical computers are going to be better at factoring nu…

The origins of quantum computing give it a clear use: simulation of many-body systems. Number factorization and anything else in BQP is also an use for them.

N body problems are usually non linear.

Quantum-everything is linear, how is this distinction overcome?

Also, doesn't solving this problem hint at quantum gravity?

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