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

math.mit.edu

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

#41

Post by havnagiggle »

anthk wrote: post #40
havnagiggle wrote: post #39

Earlier quoted context omitted.

Here's a brief example paired to some of the nomenclature in the parent post: Linear algebra are equations that do not have exponential independent variables. For example (a,b,c,d,e) are constants: aw + bx + cy + dz = e. You won't find an x^2, z^3, etc. Everything is of order 1. "classical n-bit states are 2^n length binary vectors": Binary is 1's and 0's. A binary vector is a list of them where each entry is a parti…

Enter 4 spaces before the text to write it monospaced [0, 1] [1, 0] ┌ ┐ │ 1 4 │ │ 2 5 │ │ 3 6 │ └ ┘

Brilliant, ty.

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

#42

Post by jmcqk6 »

pyinstallwoes wrote: post #36
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…

It happens to be the one the universe runs on? So there’s a physical quantum computer that exists? Where?

There is a common perspective that the physical world is computation. That doesn't mean that it's a simulation, only that information is being processed in a way that is very analogous to computation, and it is very useful for seeing it as such.

The world we live in is quantum in nature, and so it is very useful to think of the entire universe as a giant quantum computer.

In fact, one of the primary use cases for building a physical quantum computer we can program is the "simulation" of natural quantum systems, though that begins to stretch the word "simulation."

I'm not sure why you're so accusatory in this comment, but if you want to understand this better, I would recommend "Programming the Universe" by Seth Lloyd

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

#43

Post by nh23423fefe »

C-x_C-f wrote: post #37
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…

I'm curious, why L2 norm? Each qubit lives in C^2, does it not? I've only ever seen quantum computing formulated over finite dimensional Hilbert spaces (though to be fair it was only in a math context, no real physics there)

Real probabilities sum to 1 additively. Complex amplitudes don't. The L2 norm preserves unitarity.

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

#44

Post by jahsome »

havnagiggle wrote: post #39
jahsome wrote: post #3

Earlier quoted context omitted.

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.

Here's a brief example paired to some of the nomenclature in the parent post: Linear algebra are equations that do not have exponential independent variables. For example (a,b,c,d,e) are constants: aw + bx + cy + dz = e. You won't find an x^2, z^3, etc. Everything is of order 1. "classical n-bit states are 2^n length binary vectors": Binary is 1's and 0's. A binary vector is a list of them where each entry is a parti…

Thank you for this. I skimmed it while on a call, and this seems like a really good breakdown. I look forward to absorbing it with my full attention later.

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

#45

Post by abdullahkhalids »

C-x_C-f wrote: post #37
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…

I'm curious, why L2 norm? Each qubit lives in C^2, does it not? I've only ever seen quantum computing formulated over finite dimensional Hilbert spaces (though to be fair it was only in a math context, no real physics there)

We can't have a why, because the claim that the norm is L2 is axiomatic [1]. However, as the sibling comment notes, we can argue from consistency. Would any other norm give us a sensible theory? Or we can put quantum theory in a larger framework of theories and discuss why the L2 norm makes more sense within that framework. Scott Aaronson discusses some of these idea in his lecture [2].

[1] Feynamn on why https://www.youtube.com/watch?v=36GT2zI8lVA&pp=ygULZmV5bm1hb...

[2] https://www.scottaaronson.com/democritus/lec9.html

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

#48

Post by frognumber »

I have not reviewed these, but this course used to be co-taught by Peter Shor and Seth Lloyd.

Peter Shor was smarter, but a bad teacher.

Seth Lloyd was a much better teacher.

Together, the two made a good team. There's an obsession with finding the most famous person to teach, but on the whole, I'd pick Seth's lecture notes over Peter's any day.

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