[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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