Peter Shor
@PeterShor1
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Discovered Shor's algorithm for prime factorization on quantum computers.
Joined June 2019
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I've put my lecture notes from my Fall 2022 Quantum Computation course online.
I don't guarantee that there aren't any mistakes left in them, although I've tried to eradicate them all. If you find any, feel free to email me.
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True story: When I was checking into a hotel in Atlanta, GA, I was asked "Can I have your name, please." I replied "Shor." Then there was a long pause.
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35 years ago today, Richard Feynman's paper "Quantum Mechanical Computers" was published in 𝘖𝘱𝘵𝘪𝘤𝘴 𝘕𝘦𝘸𝘴. I think he'd be surprised and gratified to see everything that his original idea has led to.
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40 years ago IBM and MIT held a 𝘗𝘩𝘺𝘴𝘪𝘤𝘴 𝘢𝘯𝘥 𝘊𝘰𝘮𝘱𝘶𝘵𝘢𝘵𝘪𝘰𝘯 conference, where Feynman gave his seminal keynote address, later published in the 𝘐𝘯𝘵. 𝘑. 𝘛𝘩𝘦𝘰𝘳. 𝘗𝘩𝘺𝘴. Next Thursday, they are holding a 40th anniversary conference:
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When I was working on my quantum algorithm for factorization, I didn't tell anybody, because it seemed like such a long shot. Similarly, Wiles didn't tell anybody that he was working on Fermat's Last Theorem before he solved it, presumably for the same reason.
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Wonderful article about recent progress in theoretical cryptography and complexity theory (although we're still really a long way from proving P ≠ NP).
For more than 50 years, complexity theorists have tried and failed to solve the foundational question of their field. Why is it so hard to prove hardness?
@benbenbrubaker
reports:
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Quanta Magazine's story on the discovery of the Ising model, and how it revolutionized the field of statistical mechanics. via
@QuantaMagazine
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To celebrate this anniversary, I have summarized Feynman's paper in 4 lines of
#quantumpoetry
:
With our computers, we can’t model Nature;
To simulate her faithfully, we must
Go where she lives, and grasp her hand, and make her,
With clever tricks, perform the task for us.
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I am sure lots of mathematicians are currently working on famous problems without telling anybody. Is this a good aspect of the culture of mathematics? Maybe if all the mathematicians working secretly on the Riemann hypothesis got together and compared notes, they could solve it.
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With the Google quantum supremacy paper, the claims that quantum computers can’t possibly work keep on coming. It is becoming clear that reasoned arguments will not stop them.
I don’t think illogical poetry is going to work, either. But it’s fun to write.
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I find superdetermism just as "spooky" as Einstein's action at a distance ... it implies that decisions you think are being made at a given moment (say you set detector angles by rolling dice) actually were predetermined.
If this isn't "spooky", I don't know what is.
Okay, to finish, another word on superdeterminism. If you want a local explanation of the observations of Aspect, Clauser, and Zeilinger -- ie, one without "spooky action" -- then the only currently known way to do this is superdeterminism. 13/
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With respect to the recent Supreme Court decision, if it's legal to give preferential admissions to people whose grandfather went to Harvard, shouldn't it also be legal to give preference to people whose great-great-great-great-great-grandparents were enslaved?
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Great advice! If you think about a mathematical problem on your own first, you may come up with new ideas. Next, look at the literature to find the old ideas people have already tried. If you're lucky, you will see how to combine your new ideas with their old ideas to solve it.
How to use the research literature. When approaching a difficult mathematical problem, first think deeply upon it on your own, using all the ideas you can muster, before consulting the work of others. Push your own ideas as hard as you can first, and read only afterward.
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In celebration of Jian-Wei Pan's amazing quantum advantage experiment (which was in yesterday's print edition of 𝘚𝘤𝘪𝘦𝘯𝘤𝘦,) here is another poem for quantum computing skeptics.
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I guess it had to happen sooner or later.
Wordle 319 1/6
🟩🟩🟩🟩🟩
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Just figured out why I hadn't proved that mathematics was inconsistent.
I was really worried for a little while.
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April is poetry month. So here is some
#quantumpoetry
I wrote.
I am the spooky action at a distance,
The seething chaos that fills up empty space,
The wave function collapse that you shall never witness,
The living grin upon the dead cat’s face.
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Black hole evaporation is not unitary; black holes destroy quantum information.
Please quote tweet this with your most controversial quantum information opinion.
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Charles Bennett is going to be the next Shannon Lecturer at the 2020 International Symposium on Information Theory (ISIT) in L.A. This is maybe the most prestigious award in information theory. Congratulations to Charlie!
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Google's Quantum Summer symposium is going on right now. Hartmut Neven's keynote address: a million physical qubits with error correction by 2029 — that is extremely optimistic.
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Is calling something the Chinese remainder theorem rather than Sun-Tzu's theorem being implicitly racist?
And how about reverse Polish notation, the Hungarian method, the four Russians algorithm? Are these names some kind of cultural deprecation?
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@chaoyanglu
@jenseisert
@NobelPrize
Four of us won the Breakthrough Prize: Deutch, Bennett, Brassard, and me.
Three of us won the BBVA award and a different three won the Dirac Medal.
So the pessimist's prediction is that the Nobel Committee will wait for one of us to die, and award the Prize to the survivors.
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This Is No Clockwork Universe
If the eternal dance of molecules
Is too entangled for us mortal fools
To follow, on what grounds should we complain?
Who promised us that Nature’s arcane rules
Would make sense to a merely human brain?
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♫♫ There's a rich man who's sure that all speech should be free
And he's buying the network of Twitter,
When he gets it he knows QAnoners will use
It to spread their insane propaganda.
Ooh, ooh, ooh, ooh, and he's buying the network of Twitter.
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A retrospective of the most interesting papers (according to the editors) of the last 15 years in Nature Physics. It's worth reading.
Feature | Over the last 15 years, the content of Nature Physics has covered an enormous breadth of subjects at the forefront of physics. The journal’s past and present editors recount their favourite papers
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I cannot resist tweeting this SMBC comic, since it involves both physics and computational complexity:
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When our dil fridges all have overheated,
And 𝘚𝘺𝘤𝘢𝘮𝘰𝘳𝘦 and 𝘉𝘳𝘪𝘴𝘵𝘭𝘦𝘤𝘰𝘯𝘦 are long forgot,
Surely these lines, by endless tongues repeated,
Will be remembered still — well, maybe not.
In 200 years, they won't remember who built the first useful quantum computer, what error correcting code it used, or what algorithm it ran. They will remember
@preskill
and
@PeterShor1
as twin bards of the early quantum age.
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A word about the blockade of the Gaza Strip.
In World War II, the Allies blockaded Germany. Very little food got through. Ordinary Germans suffered badly from malnutrition. Belgium and Holland were even worse off. But the German army and Nazi party officials got plenty to eat.
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Once again quantum mechanics does something completely unexpected.
Chemistry students are taught that hydrogen bonds and covalent bonds are distinct, but a new study suggests they may exist on a continuum.
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@boundstate
@VictorGalitski
@quantum_graeme
Bell Labs worked because they hired the best people around. If they continued to do top-flight research, they were given free reign. If they didn't they were directed to work on problems that were more relevant to the company. So the D part of R&D had some amazing people.
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For R^6, Oskar Perron proved in 1940 that it was impossible using a detailed case analysis, in a 45-page paper that is quite readable (if you know German). For R^7, the computer spit out a 200-gigabyte proof of impossibility.
This shows the dangers of exponential growth.
In 1992,
@PeterShor1
proved that [unlike R^2 tiled with squares, R^3 tiled with cubes … R^6 tiled with 6-cubes], R^{10} tiled with 10-cubes need not have any tiles sharing (n–1)-cubes.
In 2002, Mackey proved the same for R^8.
Now n=7 has been settled!
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@protoniom
Do what your heart tells you to do, and don't take career advice from responses on Twitter.
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@SamanthaStrudel
I'm not sure it gets better. I got my PhD 35 years ago, and I still can't understand certain words/books/articles/theories/concepts.
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A Poem for Quantum Computing Skeptics
Quantum computers may at first sight seem
To be impossible. How dare we dream
Of solving problems that else would take more time
Than has passed since the cosmos’s Big Bang!
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A poem responding to Sean Carroll's recent New York Times editorial:
He asks “But what is the wave function? Is it a complete and comprehensive representation of the world? ... Or does the wave function have no direct connection with reality at all?”
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In 1605, on November 5, Guy Fawkes tried to blow up the Houses of Parliament. Luckily, he was discovered. It seems like the U.S. just foiled its own version of the Gunpowder Plot.
So can we establish a holiday where every year, on January 6, we burn effigies of Trump?
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@BeggyScammy
@PardonMyPain
@shishtaouk3
@big_cheddars
@ohJuliatweets
In STEM, there may only be one right answer, but often there are many, many different ways of getting to it.
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@nattyover
You might use a quantum computer to simulate the fusion reactions in the interior of the sun. It won't produce any energy.
You might also use a quantum computer to simulate a superconducting material. Good luck using it to replace our electric grid.
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But is there any reason to believe
The universe computes the way we do?
Nature is profligate with galaxies.
Why shouldn’t her extravagance hold true
For other things? Why mightn’t she achieve
Prodigious feats of computation, too?
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A portrayal of Dan Spielman in
@QuantaMagazine
, who solves very hard problems by failing to solve many more very hard problems: "I do get frustrated, but it doesn’t really stop me."
The Computer Scientist Who Parlays Failures Into Breakthroughs
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Philosophically, I'm not sure that there's actually a difference between an environmental unitary and an environmental projective measurement. If you believe the universe is unitary, every interaction is unitary if you take a large enough chunk of Hilbert space.
claims QEC is impossible because QEC can't correct unwanted projective measurements. Any sim of a QEC code immediately confirms that they do correct such errors. Here's that, done with the very first QEC code (Shor's 9 qubit code):
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I really don't like Netanyahu, but I'm hoping he doesn't repeat Olmert's mistakes.
Olmert made two really big mistakes:
1. He waited a long time before sending the army after Hamas.
2. He attacked all of Lebanon, and not just Hamas.
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Of course, today the reluctance scientists have to reveal their code may not be because they don't want other people to use it, but because they don't want others to see it — they're ashamed of how poorly written it is.
The people enabling open scientific data, open code, etc, today are in much the same spot as Oldenburg. It's challenging, a bit fraught, & requires much ingenuity. And will be looked on very kindly by history!
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Einstein speculated that animal senses might reveal new physics, something that may have recently happened, with the discovery that quantum effects are involved in birds' sensing of magnetic north. via
@scroll_in
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Consider a binary vector space of size 2^n. Pick at random two subsets of nonzero vectors, each of size 2^(n/2)-1. What is the probability that they are disjoint?
Now pick two subspaces of dimension n/2 and discard the zero vector. What is the probability that they are disjoint?
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@martinmbauer
Proving scientifically that something works has no effect on whether it works or not.
Lots of folk medicines have never been tested scientifically to see whether they work. So modern scientists are much too quick to dismiss folk medicine that hasn't been scientifically proven.
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It's amazing how a conjecture in operator algebras and a conjecture in quantum non-locality end up being nearly the same thing.
Thomas Vidick in Notices of the
@AmerMathSoc
on different guises of Connes' embedding conjecture in operator algebras, quantum complexity theory, and non-locality.
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@dajmeyer
Actually, I started by trying to find a problem that quantum computers would solve quickly. Then I saw Dan Simon's paper where he uses the quantum Fourier transform over binary strings. That was the key insight, but it took a lot more work to discover the factoring algorithm.
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John Preskill was really prescient when he tweeted this last week.
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Interesting interview with John Preskill (who always has interesting things to say).
John Preskill of
@Caltech
physics and
@IQIM_Caltech
remembers Wightman and Wheeler
@PrincetonPhys
, Weinberg and Coleman
@harvardphysics
, magnetic monopoles, the meaning of black hole information, Shor's Algorithm, and the origins of quantum computing
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Because today is National Bagel Day in the U.S., here is a poem: A Bagel Fable. (And the machine really exists!)
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@MarioKrenn6240
I hope you realize this can't go on forever. If each researcher in the field doesn't start publishing exponential numbers of papers, I think tweaks to existing infrastructure should be able to handle it. (But if the AI computers themselves start writing papers, we're in trouble.)
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And while the Allies probably couldn’t let food through the blockade without letting weapons through, the IDF can.
In the long run, Netanyahu’s policies are likely to destroy Israel. He should be deposed immediately.
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Matt Gaetz: your reasoning is seriously flawed. "If somebody can get struck by a car and killed crossing a suburban street, there's no reason that I shouldn't stroll across a six-lane superhighway." See how 𝘴𝘵𝘶𝘱𝘪𝘥 that sounds.
Rep. Matt Gaetz on Fox News Friday night:
“If this virus can get into the Oval, into the body of the president, there’s no place where it could not possibly infect one of our fellow Americans.”
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@cwalterswrite
The first paper I wrote went through on the first pass. It was written so badly that nobody understood it, and it had a mistake Pooya Hatami discovered 25 years later. Fixing the mistake was easy, but we needed to rewrite it completely to get it past the referees the second time.
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Wordle 228 4/6
⬛⬛🟩⬛⬛
⬛⬛⬛🟨🟨
⬛🟩⬛🟩🟩
🟩🟩🟩🟩🟩
Do we know the distribution of Wordle words? Suppose you've narrowed it down to two possible words and you have to guess. Is the most common one more likely, or do they have the same chance of being right?
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@wrichars
The Supreme Court is never going to agree that a wealth tax is constitutional. What you have to do is raise the capital gains tax. It's ridiculously low now, and the only rationale for its being so low is that the rich people don't have to pay taxes.
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I'd interpret the citation “foundational work in the field of quantum information” as saying they're honoring us for helping to found the field of quantum information. (Of course, we had a lot of help, from Feynman and others).
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In Italy, the largest population clogging the emergency rooms and overloading the medical system (requiring extreme medical intervention) seems to be elderly people. Here's a proposal for how to avoid it: free Meals on Wheels for all seniors living at home who want them.
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"Analog computer" used in its original sense ... you set up the computer so it behaves analogously to the system you want to investigate.
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The best, and funniest, summary of the Google-IBM controversy I've seen yet (even if he is biased because of his employer).
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You can call "teleporting quantum information" by the name "sending quantum information through a traversable wormhole". As far as I can tell, all this does is confuse the public. I don't see how a teleportation experiments can demonstrate anything about wormholes or black holes.
There's been some controversy over this generally excellent article by
@philipcball
, so I thought I would write some thoughts. Full disclosure: I'm friends with many of the authors of this paper and was acknowledged in it for a couple of tangentially related discussions 1/n
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@KikeSolanoPhys
@Microsoft
Have you ever heard of Moore's law? Do you have some reason to think it won't apply to quantum computers?
People currently making projections of useful quantum computers in five to ten years are hopelessly optimistic.
Projections of centuries are hopelessly pessimistic.
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The same thing is going on in Gaza today. Hamas and its army have enough to eat—there are undoubtedly large quantities of food stored in Hamas’s tunnels. The only thing the food blockade is doing is teaching Palestinians to hate Israel.
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I think it's time for Benny Gantz to quit the government of Israel and try to bring Netanyahu down. Does he really want to be complicit in the impending crime against humanity?
"Despite the tragedy unfolding under our watch, the Israeli authorities informed the UN that they will no longer approve any UNRWA food convoys to the north" of Gaza -
@UNRWA
More here ⤵️
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@wtgowers
People are calling for real-world examples of social considerations having an impact on mathematics.
I have a couple from quantum information theory.
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If Omicron is the most contagious virus ever seen, one wonders why there aren’t others. One possibility: they run through all their fuel, burn themselves out, and go extinct. And if Omicron does that, it will take all the other variants with it, and the pandemic will be over...
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I really don't want to say that ICE is as bad as the Nazis were, but this is absolutely the wrong excuse. Most Nazis were only enforcing the laws, as well.
ICE agents complain about Nazi comparisons, say they're only enforcing the laws
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@ThomasBurkhartB
@wrichars
@TheRealAdamKemp
If a college professor (like I am) makes $400,000 a year, they're taxed at a marginal rate of 35%. But Mr. John Dale Robberbaron VII makes $20 million a year in capital gains, and his income is taxed at 15%, a lot less than I actually pay. This is what Krugman is talking about.
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Variation on a Theme of von Neumann
(Theme: Anyone who considers arithmetical methods of
producing random digits is, of course, in a state of sin.)
Is it not blasphemous of us to hope
That all of Nature, in her boundless scope,
Can be reduced to voltage on a chip?
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If the Israeli Defense Forces don't have a strategy for a war with Hamas, which it currently appears they do not (of course, I can't say for sure), this is a failure of colossal proportions. They should have been preparing for this for the last fifteen years.
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@skdh
@dahankzter
The standard model does not work fine ... it does not explain galaxy rotation curves. For that we either need MOND, for which there is no experimental evidence (as opposed to observational evidence) whatsoever, or dark matter (ditto).
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@AGHamilton29
Most of the people Israrl has killed are NOT Hamas terrorists, but innocent Palestinian civilians. It seems to me that you are the one being naive.
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@ulysses313131
@skdh
I don't have a solution. I do have a question: why does everybody keep trying to come up with a classical mental picture of the universe when it's quantum?
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Experiments are catching up with quantum mechanical "paradoxes", not just in the area of quantum information but also in quantum tunneling, which happens faster than light by some measures.
I wrote about recent virtuoso experiments that have measured how long particles take to tunnel through walls. Physicists have obsessed over this question for nearly a century, because it raises a bigger question: What is time, even?
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Is that a Schrödinger cat?
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@Liv_Lanes
I think that this is one of the hazards (maybe the only one) of tweeting about quantum mechanics.
I don't know what to do about it, either.
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@skdh
If you're saying to give up on any problem people have spent 40 years on and haven't solved, that's crazy.
If you're saying physicists won't recognize a solution to the black hole information problem, that's true for some physicists, but I have more faith in the whole community.
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@skdh
You're making the same mistake that John Horgan
@Horganism
made in his book "The End of Science". There are fields where nobody has any real clue which direction to go in, and we extrapolate and say that nobody will ever find the solution. But solutions can come out of the blue.
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If God’s great handiwork does not have more computing power
Than do our jury-rigged contraptions, how are
We to believe that it could be His finest workmanship?
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@jen_keesmaat
@A_Aspuru_Guzik
The coronavirus is transmitted by people who are showing no symptoms. If everybody wears a mask, we cut down on asymptotic transmission and flatten the curve (by people who happen to be sick but have no symptoms yet). It won't work if everybody who's not symptomatic stays home.
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@newplatonism
I has a proof that no quantum algorithm [satisfying some conditions] could accomplish a certain task. And then I found an algorithm that accomplished it.
The resolution was that the conditions weren't satisfied. But it took me ridiculously long to figure this out.
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@skdh
I find superdetermism just as "spooky" as Einstein's action at a distance ... it implies that decisions you think are being made at a given moment (say you set detector angles by rolling a die) actually were predetermined.
If this isn't "spooky", I don't know what you think is.
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Mr. Trump, tear down this wall!
White House almost completely surrounded by more than a mile of fencing
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I make superconductors lose all their resistance,
I make the atom split, the laser gleam,
And although you might feel bewildered by my strangeness,
I am real; 𝘺𝘰𝘶 are living in a dream.
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@SJ_Powers
Funding decisions are made by panels of very smart researchers, but the dynamics of these panels tend to work against radical new untested ideas. Luckily, I didn't need a grant to work on quantum factoring (I was at Bell Labs), but I probably wouldn't have gotten one.
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For me, the obvious answer to this is “yes”. Do people always use an inner monologue thinking about math? (I sometimes do, sometimes don’t.)
Apparently, some people never think in inner monologues, which surprises me. But this shows the risk of generalizing from one example.
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@BarakShoshany
Or say 'I am very interested in your area of research,' without actually specifying what it is.
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This is a double-crostic, a type of puzzle generally only seen in the Sunday NYT. Its solution also contains the wonderful quote from her book "Kepler in later life became convinced the planets play music ... [he] concluded the earth sings mi fa mi. It wasn't his best work."
It took me a while to understand this image, but apparently the solution to Sunday's NYT crossword was "HOSSENFELDER LOST IN MATH". Probably the first and last time I'm the solution to anything 🙃
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A really interesting discussion of the recent controversies over the detection of Majorana fermions in 𝘕𝘢𝘵𝘶𝘳𝘦.
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This is St. Patrick's Day, so I'm posting a couple of limericks; hopefully, they will make a few people smile in these grim times.
There once was a rhyme-loving nerd
Whose limericks all were absurd,
For his rule was he must
In the last line put just
One
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Beautiful article by Claire Voisin on doing mathematical research.
"One may argue that a great theorem cannot actually depend on obscure and technical details, but this is only true a posteriori, once we are convinced that the result is true."
“I find it hard to do mathematical research full time. Hard because new ideas are so rare that we are faced most of the time with our own mediocrity…Yet…” Refreshingly honest, clear-eyed view by one of the greats of mathematics …
#mathematicallife
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I find it difficult to believe that our ancestors have been eating burnt meat for over a million years without evolving ways to digest it without getting cancer.
On the other hand, we've only been eating nitrite-drenched burnt meat for a century. So maybe avoid preserved meats.
Researchers are in another fight about whether or not meat is bad for you
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