These are rather old lecture notes for the course CS 766/QIC 820 Theory of Quantum Information , taught at the University of Waterloo in odd-numbered fall terms (2011, 2013, … , 2021). Use OCW to guide your own life-long learning, or to teach others. Incidentally, Petter S: Thanks so much for your Python script that automatically regenerates a combined file! This entry was posted Basically, on one side is everything we observe as espoused by the Standard Model, QFT, and so on. Natural origin of a Speed of Light limit? on Sunday, August 26th, 2018 at 6:06 pm and is filed under Complexity, Quantum. When I first thought of this idea about 6 or 7 years ago I excitedly posted my thoughts on Lubos Motl’s blog, but didn’t get much feedback, same as on Scott’s blog about 5 years ago. To confirm, Alice’s qubit in the example is the second one, right? Nice! But that would lead to a drastically different world than the one we observe, a world where the double-slit experiment and other basic quantum phenomena (which happen over MUCH longer timescales than a Planck time) wouldn’t work. No enrollment or registration. There are also dozens of books—including Mermin’s, which we used in this course. Ubuntu might be easier to deal with for running Python code. We don’t really know how to describe quantum gravity and what its m.w.i. Are worlds “branching” in some “emergent time”? Is this a flaw that’s specific to QC? Anyway, there have been only a finite number of events in our light cone since the Big Bang with a finite number of quantum possibilities each. They do seem like they get on a lot of tangents though. Scott: Quick note, the Watrous link is currently broken due to smart quotes. Basically, time is the energy that prevents the Universe from evolving in a wavefunction immediately from the Big Bang to a statistical distribution of the various quantum fields in space. If nothing else, no one can complain about a dearth of basic quantum algorithms here. would look like. So I appreciate your comments. This is one of the reasons why some lectures are much longer than others. The only way I could reconcile the (apparent?) Scott #13: “pip install PyPDF2” should hopefully make it work. Maybe you could use the ket notation in the classical equation too? Rand #3: Indeed, looking again at Watrous’s notes just now reminded me of how awesome they are! Rather, the top- and bottom-levels of abstraction seem to rely on each other in some sort of peculiar fashion , which refutes methodological reductionism! using Google Scholar), you can probably find most of the relevant literature. At least in my (silly?) So how does each branch remember/record that the probabilities were 2/3 and 1/3? But those two branches aren’t exactly created “equal” (because of the difference in probability). The proposal is flat-out wrong. From the path, it looks like you are using Windows. Minor typo, I think. Download files for later. So shouldn’t it be interpreted that it maps |0> to |0> and |1> to i|1> ? So the example of the flawed coin flip using a single qubit is enough! model we have a speed limit, due to the finite time it takes for a random jump, in deterministic models the universe all happens at once, which is a shame really. But unfortunately, doing nice equations in Google Docs turns out to be difficult. ie if we have the evolution rule U(t+dt) = ( exp(h x Anti_Symmetric_Matrix) – I ) x U(t), where h is a real number and I is the Identity matrix, then there exists an h which gives you a stable period-3 global oscillation which is an attractor for measure 1 of initial states, (this is actually an easy undergraduate (or advanced high school) level result, but not something I had seen before). We then view this as an ‘abstract duality’, with “Probability&Stats”/”Computational Logic” being the two poles, such that one could construct ‘Complexity Classes” *both* from the top-down (starting from formal languages) *and* from the bottom-up (starting from probabilities). I will now celebrate with a wild bout of uninformed speculation: 1.) To provide some context regarding the “1 collapse per Planck time” discussion: In the original GRW theory, the mean localization frequency is f=10^-16 s^-1 and a localization accuracy of 10^-5 cm. The total energy released by the Big Bang is thus ZPE + Cosmological constant, and the difference between the two is in essence the amount of energy “locked up” by this imposition of time. Zooming out again and looking at the 3 main areas of CS a whole, I propose this global ordering: Probability&Stats (bottom) – Computational Complexity (middle ) -Computational Logic (top). If space and energy are continuum, by the action==reaction principle, it’s impossible to measure anything without disturbance. I often see you refer to the maximum amount of info that can be stored in a given region of space (related to the study of blackholes, etc). Today, with […]. Note: If you’re taking the course in 2018 or a later year, these sets should be considered outdated and for study purposes only. In real events such as a partially-silvered glass pane which reflects 75% of photons in a beam-splitter experiment and transmits 25%, there are many branches, one for each possible photon trajectory. If it predicted electron distributions which were kinematically stable, but which ought to be very lossy according to classical electromagnetic theory, then there would be a contradiction, just as there is for the Bohr-Sommerfeld model. oh come on, Nature just does the random choices at Planck timescales, so several trillion trillion trillion random choices every second, each one followed by the entire universe updating via a unitary evolution. When I found tutorials, alongside this people kept discussing stuff that weren’t relevant algorithmically, using gross weird notation. Quantum information (lecture notes) Preskill. ), but also to Patrick Rall and Corey Ostrove for TA’ing the course, to Tom Wong and Supartha Podder for giving guest lectures, and of course, to all the students for making the course what it was. approximate any unitary transformation on any number of qubits to any desired precision.
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