[HN Gopher] Quantum Computation Lecture Notes (2022)
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Quantum Computation Lecture Notes (2022)
Author : ibobev
Score : 153 points
Date : 2025-06-09 07:54 UTC (4 days ago)
(HTM) web link (math.mit.edu)
(TXT) w3m dump (math.mit.edu)
| revskill wrote:
| How can a person become so good at researching ?
| lightbendover wrote:
| (1) be naturally gifted, (2) avoid falling down wells of
| distraction, (3) be lucky. Don't sleep on (3), it's easy to
| call it capitalizing on opportunity in hindsight when it was
| honestly just luck.
| TechDebtDevin wrote:
| luck in terms of natural intelligence and focus. But
| generally people can approve their ability to avoid falling
| down the "wells of distraction". This year I set time filters
| for apps on my phone and its made a stark difference. Even
| though I can turn off "work mode" to get around it, that
| little reminder has saved me hundreds of hours as I usually
| just put down the phone when I see it.
| jasonhong wrote:
| I'd also add (4) be incredibly curious about lots of things;
| (5) surround yourself with other smart, curious, and
| committed people who have a culture of critiquing ideas; and
| (6) devote a lot of time to deep thinking.
| rwoerz wrote:
| (8) be good in counting things, (h) be consistent in your
| thinking, (10) have a good memory, (11) be good in counting
| things, (12) refrain from making silly comments
| xeonmc wrote:
| just get nerd-sniped.
| gaze wrote:
| I don't know how else to say it but you just have to do it.
| It's like asking how to get good at running. You run.
| graycat wrote:
| > How can a person become so good at researching ?
|
| My time in my Ph.D. program and some of the work in my career
| (getting paid) suggest that I was "good at researching". But I
| left such research due to wanting to get paid more, and settled
| on starting a business, owning it, and making it valuable. If
| some research can help the business, fine, but the real goal is
| just the money from a successful business.
|
| On (academic) research, one lesson no one ever mentioned to me
| but eventually I formulated: Pick a field of research. Then in
| that field a lot about what is expected, respected, intended,
| valued or not, ..., is not much spoken about and not made clear
| -- clear that have fertile ground for politics. Then, for such
| questions, the answers you guess or get in some one field will
| likely be quite different in another. In some fields can get
| reminded of the old quip: "Haydn wrote 101 symphonies or one
| symphony 101 times?" Or at times can believe that with high
| probability, a paper gets read by just two people, the peer
| reviewer and the author; as a result of that case, the only
| accomplishment of papers, good or bad, are that they get
| counted as in someone with 50 papers is regarded as better than
| someone with only 4. Ah, tough to prove that the paper will
| never get 1000 readers!
|
| For research, one approach is to study a (assume an academic)
| field, crawl down some narrow alley or rabbit whole, see a
| question with no answer, consider the broad status of the
| field, then if making progress on the question seems not
| obviously impossible, give it a try. By a few days or weeks
| should have an answer, a partial answer, or hints that by
| continuing you might get something.
|
| Another approach is to pick a problem mostly on your own and
| not from, trying to extend, published research. You might
| follow some instance of personal curiosity or something from
| some other field, e.g., do some math, optimization, statistics,
| ... research from problems in the environment (why the ups and
| downs of lobsters in east Canada?), medical testing, the supply
| chain, some engineering problem, some business problem, etc.
|
| Do note that in the US, after radar, the proximity fuze,
| submarine acoustics, code breaking, jet engines, the "bomb",
| the US military had plenty of both money and problems, and that
| funded a lot of US research. Now there seems to be a general
| view: We don't know what research directions will yield
| powerful results, but since we can't afford to miss out on some
| big results or _fall behind_ , we will continue to fund
| research. Non-military research seems less eager for results
| and to have less money.
|
| Ah, be good at the politics, e.g., even follow "Always look for
| the hidden agenda." If working in an organization, beware of
| "goal subordination", i.e., others working to have you fail.
| 11101010001100 wrote:
| What, if any, did you port from the research career to the
| business?
| graycat wrote:
| I derived some math, new at least to me, based on my pure
| math background, e.g., Rudin in measure theory some
| functional analysis, probability based on measure theory
| from Neveu, _tightness_ in probability once used in some
| statistics for _computer science_ , presented at NASDAQ,
| some optimization via the Kuhn-Tucker conditions, some
| stochastic optimal control, etc.
| polamolo wrote:
| I feel like I've seen/done this before. Could I be stuck in a
| groundhog day?
| zara_is_reading wrote:
| I've 70.71% seen it before and 70.71% not seen it before.
| rvz wrote:
| Well right now I am very skeptical, but I think we have somewhat
| given quantum computing plenty of time (we have given it decades)
| unless someone can convince me that it is not a scam.
|
| Right now it hasn't amounted to anything useful, other than
| Shor's and 'experiments' and promises and applications that are
| no better done on a GPU rack right now.
| adastra22 wrote:
| Tab is the equivalent of "there will be worldwide demand for
| 4-6 computers."
| dandanua wrote:
| Who are "we"? And why those "we" think that a branch of
| fundamental science that have people involved all around the
| globe could be a scam? It's nowhere close to the cryto mania,
| where there is only one end goal.
| n4r9 wrote:
| For quantum computing, as a rule of thumb I generally look to
| what Scott Aaronson says. And as you suggest, while some cool
| stuff is being done both in industry and academia, we are
| nowhere near general quantum computers. I haven't checked what
| his outlook is for the next 5-10 years.
| honzaik wrote:
| this may give you an idea about his current outlook
| https://www.youtube.com/watch?v=DQFyQgA_GE4
| bradly wrote:
| Not quantum computation, but quantum mechanics are being used
| in QKD satellites today to hedge against RSA being broken.
| Pretty neat.
| bawolff wrote:
| Quantum computers is not a scam, but QKD basically is. There
| is no scenario where QKD actually makes practical sense.
| Viliam1234 wrote:
| I am not an expert, but seems to me it is caused by two things:
|
| 1) While quantum computers are potentially exponentially
| faster, they also seem to be _exponentially more expensive_
| given the number of qubits, so you actually can 't save money
| by building a huge quantum computer. This may or may not change
| in future. Also, there was a problem with error correction,
| which is made much harder by the nature of quantum computing.
| Smart people are working on that, I don't know the current
| state of progress.
|
| 2) Despite the hype, only _some_ problems can be calculated
| exponentially faster using a quantum computer, not all of them.
| This is analogical to parallel computing: having two CPUs
| instead of one will allow you to calculate some things twice as
| fast, but some other things will require exactly the same
| amount of time because their steps need to be done
| sequentially. Similarly, a quantum computer is like a network
| of billions of computers that are spread across the multiverse,
| but they need to all run the same code, and to compress the
| results of the gigantic computation into about dozen bytes. So
| it 's great for highly parallelizable tasks where the entire
| required output is a "yes or no" or a single number... and less
| useful for everything else. That still includes some important
| scientific problems, such as simulating atoms and molecules.
| But those are not the things we typically use computers for.
| japanuspus wrote:
| > Well right now I am very skeptical, but I think we have
| somewhat given quantum computing plenty of time (we have given
| it decades) unless someone can convince me that it is not a
| scam.
|
| Shor's paper on polynomial time factoring is from 1997, first
| real demonstration of quantum hardware (Monroe et al.) is from
| 1995: Yes, quantum has had decades -- but only barely, and is
| has certainly only now started to have generations.
|
| To look at the kind of progress this means, take a look of some
| of the recent phd spinouts of leading research groups (Oxford
| Ionics etc.): There are a lot of organisations with nothing but
| engineering to go before they reach fault tolerance.
|
| When I came back to quantum three years ago, fault tolerance
| was still to be based on the surface code ideas that floated
| when I did my phd ('04). Today, after everyone has started
| looking harder, it turns out that a bit of long-range
| connectivity can cut the error correction overhead by orders of
| magnitude (see recent public posts by IBM Quantum): The
| goalposts for fault tolerance are moving in the right
| direction.
|
| And this is the key thing about quantum computing: you need
| error correction, and you need to do it with the same error-
| prone hardware that you correct for. There is a threshold
| hardware quality that will let you do this at a reasonable
| overhead, and before you reach this threshold all you have is a
| fancy random number generator.
|
| But yes, feel free to be a pessimist -- just remember to own it
| when quantum happens in a few years.
| William_BB wrote:
| "When quantum happens in a few years" -- do you mean NISQ
| (i.e. VQA, QAOA) or actual fault tolerant quantum computing
| that can run Shor?
| ttshaw1 wrote:
| We're already at NISQ
| William_BB wrote:
| I meant practically usable NISQ
| andrewla wrote:
| I'm a skeptic as well, but calling it a "scam" is a bit
| extreme. I think QC proponents are acting in good faith, and I
| believe that it is worth chasing a little longer since we don't
| yet have a convincing model for why QC will or won't work
| (although I think the Gil Kalai's work in this area is
| intuitively correct I don't think that we have a physical
| explanation for why quantum error correction would not work).
|
| The current emphasis on NISQ systems is a bit of a desperate
| measure because the most we can get out of such systems is
| evidence that quantum computing can work in theory; they do not
| advance us towards having a workable quantum computer.
| wasabi991011 wrote:
| Fwiw:
|
| The last paper I saw posted on hackernews from Gil Kalai
| included a few explicit predictions about what would be
| impossible in quantum error correction.
|
| This was a paper from a few years back.
|
| The problem is that now Google has published results which
| imply that some Kalai's predictions turned out false.
|
| The paper in question is Google's recent "below
| threshold"/"beyond break-even" QEC paper. I believe Kalai was
| predicting below threshold QEC to be impossible IIRC, among
| other things.
|
| Not sure if Kalai has responded or updated his predictions, I
| haven't been following him closely.
| n4r9 wrote:
| Although I agree that "scam" is extreme, the commercial side
| was sullied in the early 2010s by D-Wave selling what they
| described as "quantum computers" for $10m and spinning up a
| bunch of misleading PR. Of course you expect a certain deree
| of "fake it til you make it" in such companies, but they'd
| been going for over a decade at that point. This was all
| kicking off as I was doing my PhD in the field. It was eye-
| opening to see how little attention was paid to serious
| academics vs hucksters, and how companies like Google could
| be duped into spending millions on basically nothing.
| dheera wrote:
| > we have given it decades
|
| Decades is a short amount of time in human history. Many things
| took centuries to invent.
|
| The silicon valley approach of a year or two of runway is how
| apps are built, but that's not how science is built.
| vonneumannstan wrote:
| It's not a scam. There are many applications in materials
| science for example. Your ignorance of them doesn't make it a
| scam.
| bawolff wrote:
| You should stop viewing it as a tech start up and view it more
| as a physics experiment.
|
| In some ways it is similar to fusion. People have been working
| on it for a long time. The benefits are potentially significant
| (shor is cute and all but really the big deal would be a cheap
| way to simulate other quantum systems) but the challenges are
| also significant. Real progress is being. Things that were
| super challanging 10 years ago are solved now. The field is
| advancing. But we still have a long way to go.
|
| It is not a scam itself, but a lot of scammers use the language
| of quantum to sell their scams. You should treat anyone
| convincing you that they will have a useful quantum computer in
| the next 5 years the same way as someone offering you a fusion
| reactor (i.e. full of shit).
|
| Its still a worthwhile pursuit, even just as a physics
| experiment. It pushes the "weirdness" of quantum physics to the
| limit - by literally disproving the extended church turing
| thesis. If we make a real quantum computer - that is proof that
| quantum physics is really how are world works. Its not just
| something else that is being misinterpreted.
| DebtDeflation wrote:
| This is exactly it. QC right now is a series of very cool
| science experiments that are being marketed to [Government
| Officials, CEOs, Investors, the General Public] as product
| development, which it is not. We're at the stage of
| scientists in the 1910s creating the first vacuum tubes and
| noting the ability to amplify and control small currents with
| larger ones but these companies are pretending it's instead
| the early 1980s with the PC and 8088 and Moore's Law getting
| ready to take off like a rocket.
| JBits wrote:
| There are multiple competing quantum computing hardwares, so
| you haven't given all of them the same length of time.
| JanisErdmanis wrote:
| A scam is a strong word, giving the impression that there are
| malicious interests in selling it without working towards
| making returns to the investors. But a dead horse, for sure, it
| now looks like.
|
| The next big challenge will be mounting the controlling
| hardware, currently connected via coaxial cables, onto the chip
| while preventing the introduction of new sources of
| interference so that error correction can run. That will take a
| miracle.
|
| Of course, an alternative is a million coaxial cables connected
| to a chip cooled close to mK temperatures.
| addaon wrote:
| I agree completely. We gave programmable machines a full
| century after Babbage, and it was clearly a waste and a scam.
| Can you imagine if we had continued to invest in that garbage
| and built some "Electronic Numerical Integrator and Computer"
| or other nonsense? Clearly if an idea isn't mature in a couple
| decades, it has no possible future development or impact.
| EvgeniyZh wrote:
| There has been steady progress in metrics, that, if keep
| improving, will eventually lead to fault tolerant quantum
| computing. We also do not know any fundamental reason why we
| won't be able to keep improving them. It's true that the
| progress is not fast, because the problem is hard, but I don't
| see why would you call it scam (there are definitely scammers
| in the field, but there are in any field).
| m3kw9 wrote:
| As soon as a math equation comes up I get lost.
| ofjcihen wrote:
| Thanks for this.
|
| I've recently become very interested in QC and purchased and read
| Quantum Computation and quantum Information which I think is the
| standard book on the subject right now.
|
| I'm even more interested in applying what I've learned but I'm at
| a loss as to how to begin working in the industry. Aside from
| getting a new masters degree I wouldn't know where to begin and
| resources on the matter are understandably sparse.
| abdullahkhalids wrote:
| You can definitely work at QC companies even without having a
| degree in the field. Many QC companies hire people from other
| fields because they require that expertise, say people with
| experience in numerical optimization. Of course, many QC
| companies also hire software engineers because they have
| complex internal software. If you are a software engineer, you
| can start there and then start to move laterally within the
| company.
|
| Source: work at a QC company as a scientist.
| ofjcihen wrote:
| That's something I didn't think about. Thank you
| dheera wrote:
| It's actually not that difficult to pick up quantum mechanics
| and quantum computing if you have a solid foundation in linear
| algebra. QC really just reduces down to "applied linear algebra
| on crack".
|
| If you're in AI, you might be pleased to know that the
| probability distribution of a particle in its various energy
| states is related to the softmax of the negative values of
| those energies times temperature, which is where the concept of
| LLM "temperature" comes from. If you have linear algebra
| background, those energies are the eigenvalues of a
| Hamiltonian. Physics is actually quite beautiful.
|
| Getting into industries is another issue though, it seems every
| company favors credentials over learning ability these days. If
| you haven't published 1500 papers on the subject you're
| automatically rejected.
| qnleigh wrote:
| Yes that's still a great book, though it's starting to get a
| bit outdated. Some recent developments that would belong in an
| updated edition:
|
| - The section on error correction is still gold, but it doesn't
| cover "scalable codes" like the Surface Code (and other LDPC
| codes; lots of exciting progress there) - Superconducting
| Qubits: https://arxiv.org/abs/1904.06560. - Rydberg Atoms: see
| Nature Papers from Misha Lukin's group on the subject -
| Photonic quanum computing
|
| These might be hard to follow now, but if you make it through a
| good chunk of Nielsen and Chuang, then they might become quite
| readable. Make sure you solve lots of problems or it won't
| stick.
|
| Like other commenters have pointed out, quantum computing
| companies need lots of software engineers, so that's a very
| viable entry into the field for many people. Here's an
| arbitrary list of some relevant skills: - Qutip! You can learn
| sooo much quantum mechanics by playing around in Qutip, and
| it's quite easy to use. - Rust or C++ (depending on the
| company?) - FPGA programming - Python (ofc) - Linear algebra -
| ...
| fogof wrote:
| Very funny to me that lecture 21 is one of the only lecture
| titles that doesn't reference the name of the originator.
| hedgehog0 wrote:
| De Wolf's note is also one of the standards right now, and more
| up-to-date than the QC&QI book: https://arxiv.org/abs/1907.09415
| mikestorrent wrote:
| Of course, no discussion of quantum annealing, the only practical
| form of quantum computation that is likely to exist at scale in
| our lifetimes.
| adastra22 wrote:
| That's a strong statement. Regardless, the content of the
| course is explicitly targeted at gate-based quantum computing.
| msgodel wrote:
| Is it practical? The little I've messed with it it seemed
| borderline useless. All it can do is QUBO and encoding the
| problem into the machine topology itself is another QUBO
| problem that has to be done on a classical computer.
|
| People also keep talking about using it for AI but all you can
| train with it are Boltzmann machines because those are all that
| map into QUBO problems.
| husky8 wrote:
| I made a podcast in NotebookLM once I saw equations. Enjoy
| https://notebooklm.google.com/notebook/bc7616c4-1c71-4a04-b2...
| vismit2000 wrote:
| Getting this message - "Oops! This audio could not be loaded."
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