Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Peter Shor's MIT Fall 2022 course lecture notes on quantum computing

math.mit.edu

Post reply on HN
Print view View original

21–30 of 48 posts

Re: Peter Shor's MIT Fall 2022 course lecture notes on quantum computing

#21

Post by light_hue_1 »

Obscurity4340 wrote: post #20
abdullahkhalids wrote: post #2

I have taught a course on quantum computing a few times, mostly to CS students who have no background in quantum mechanics. The way I proceed is to * First introduce classical reversible computation. I model it using linear algebra, meaning classical n-bit states are 2^n length binary vectors, and the gates are 2^n x 2^n binary matrices acting on theses states. Exponential, yes, but a faithful model. The critical fea…

Do you know how qubits are physically implemented? Like, what is a qubit made of and how does it reify computation?

Have a look at "Quantum Computing: Fundamentals, Implementations and Applications " by Bhat et al. from 2022 https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=9783210

It's kind of a crappy paper and the explanations are mediocre at best, but it provides a decent survey of the main physical implementations in language that is simple to follow.

Re: Peter Shor's MIT Fall 2022 course lecture notes on quantum computing

#22

Post by [deleted] »

abdullahkhalids wrote: post #2

I have taught a course on quantum computing a few times, mostly to CS students who have no background in quantum mechanics. The way I proceed is to * First introduce classical reversible computation. I model it using linear algebra, meaning classical n-bit states are 2^n length binary vectors, and the gates are 2^n x 2^n binary matrices acting on theses states. Exponential, yes, but a faithful model. The critical fea…

[deleted]

Re: Peter Shor's MIT Fall 2022 course lecture notes on quantum computing

#23

Post by hexane360 »

Obscurity4340 wrote: post #20
abdullahkhalids wrote: post #2

I have taught a course on quantum computing a few times, mostly to CS students who have no background in quantum mechanics. The way I proceed is to * First introduce classical reversible computation. I model it using linear algebra, meaning classical n-bit states are 2^n length binary vectors, and the gates are 2^n x 2^n binary matrices acting on theses states. Exponential, yes, but a faithful model. The critical fea…

Do you know how qubits are physically implemented? Like, what is a qubit made of and how does it reify computation?

Just like a physical bit, qubits are basically an abstraction over an analog world; they can be implemented in any physical medium you can make a quantum measurement with.

Most current implementations are "trapped ion" computers. This is exactly what it sounds like, an ion trapped in an electromagnetic field. However, people are working on many systems, including:

- Photonic (photon) - Superconducting (Cooper pair) - Diamond/silicon carbide (single dopant) - Liquid NMR (molecular spin)

Re: Peter Shor's MIT Fall 2022 course lecture notes on quantum computing

#24

Post by FabHK »

To download all of the pdfs into the current directory:

  wget -r -np -nd -l 1 -A pdf https://math.mit.edu/~shor/435-LN/
(There might be more elegant ways, but this does the job.)

  -r,  --recursive          specify recursive download.
  -np, --no-parent          don't ascend to the parent directory.
  -l,  --level=NUMBER       maximum recursion depth (inf or 0 for infinite).
  -A,  --accept=LIST        comma-separated list of accepted extensions.
  -nd, --no-directories     Do not create a hierarchy of directories

Re: Peter Shor's MIT Fall 2022 course lecture notes on quantum computing

#26

Post by currymj »

jahsome wrote: post #3
abdullahkhalids wrote: post #2

I have taught a course on quantum computing a few times, mostly to CS students who have no background in quantum mechanics. The way I proceed is to * First introduce classical reversible computation. I model it using linear algebra, meaning classical n-bit states are 2^n length binary vectors, and the gates are 2^n x 2^n binary matrices acting on theses states. Exponential, yes, but a faithful model. The critical fea…

On behalf of my fellow English majors, may I just say: What?? I love Hacker News because it exposes me to a great deal of things like this. I intend to do as deep a dive I can muster into the provided lecture notes. But boy howdy, are certain topics I encounter here humbling. If I were fully honest with myself I would avoid a certain subset of the content on hn. Sometimes I think it only fuels my impostor syndrome.

trying to elaborate on the OP a little by avoiding math terminology:

part 1 here is essentially the idea of logic circuits. you can write these down in terms of large vectors of 0s and 1s, and operations transforming them as large matrices -- which is useful because it takes familiar ideas (to a CS student) and casts it using mathematical formalisms that are later required for weird quantum stuff.

this could be unfamiliar if you haven't learned about matrix/vector multiplication. but ultimately it's just a different way of talking about combinations of AND/OR/NOT on truth values.

part 2 just says, go from vectors of 0s and 1s to probabilities between 0 and 1. the "L1 norm" (aka Manhattan or taxicab distance) in this situation just means that all the values together have to sum up to 1, the way probabilities do. this includes part 1 as a special case, and extends it naturally.

part 3 is indeed where the weird quantum stuff comes in. no easy explanation, you do have to get an idea of how complex numbers work. but again, the familiar logic circuits of part 1 are still a special case. the "L2 norm" for real numbers is just the regular straight-line distance -- I can't provide a good intuition for complex numbers though.

Re: Peter Shor's MIT Fall 2022 course lecture notes on quantum computing

#27

Post by abdullahkhalids »

__rito__ wrote: post #25

Quantum Computing made sense to me for the first time, when I came across Umesh Vazirani's MOOC on Coursera. It is not there anymore. It can be found on YouTube.

That is indeed a beautiful course. UZ has a way with explanations. Here is a link of the course lecture videos https://www.youtube.com/watch?v=VPsl_5RQe1A&list=PLnhoxwUZN7...

Re: Peter Shor's MIT Fall 2022 course lecture notes on quantum computing

#29

Post by AmIDev »

When learning classical computing, I have done the following things that gave me a deeper understanding of how things work.

1. Learned logic gates and built(in simulators) small circuits which can do addition/multiplication.

2. Used a 8085 board to write assembly programs for search/sort etc.

3. Learnt C programming and Operating systems(primarily Linux)

4. Learnt higher level programming languages and paradigms(OOP, compilation, etc).

What set of courses/topics would lead to a similar level of understanding in the quantum domain? I have learnt about the quantum gates, but I do not have to context to understand how they fit in the larger picture.

Re: Peter Shor's MIT Fall 2022 course lecture notes on quantum computing

#30

Post by fastneutron »

robbinliuli wrote: post #7
abdullahkhalids wrote: post #2

I have taught a course on quantum computing a few times, mostly to CS students who have no background in quantum mechanics. The way I proceed is to * First introduce classical reversible computation. I model it using linear algebra, meaning classical n-bit states are 2^n length binary vectors, and the gates are 2^n x 2^n binary matrices acting on theses states. Exponential, yes, but a faithful model. The critical fea…

Your approach sounds very interesting. Do you have any course materials to share or recommend?

This video, “Quantum Computing for Computer Scientists” is quite approachable: https://m.youtube.com/watch?v=F_Riqjdh2oM&pp=ygUeTWljcm9zb2Z...
Post reply on HN