2023 Fall – Advanced Quantum Computing

Hello! Welcome to my site for quantum computing.

Please note that I am not the instructor for this semester’s advanced quantum computing course. The course is being taught by Prof. Wenchao Ge from the University of Rhode Island. UMass Dartmouth students should access the lectures via a link that will be provided soon.

You can find the syllabus here.

You can also click on the syllabus link in the site panel.

I will be providing some support on the UMass Dartmouth side, including an office hour which is TBA.

 

 

More High Energy News

Results released yesterday from Fermilab confirm measurements from about 20 years ago that are in tension with the Standard Model’s prediction about the instrinsic magnetic properties of muons.

Have we discovered anything yet? No, not yet. Updates to these Standard Model-based calculations appear to bring them into closer alignment with these new experiments. But these new calculations are not completely vetted yet and if there is a problem, then it would seem we’re very close to a discovery. So, much like the recent LHCb results, we’re in a situation where tentative or cautious excitement is warranted, but it’s important not to get ahead of ourselves!

Here’s a really nice video from the Fermilab team that details aspects of this measurement:

https://www.youtube.com/watch?v=ZjnK5exNhZ0

And an excellent article that takes into account some key caveats:

https://www.quantamagazine.org/muon-g-2-experiment-at-fermilab-finds-hint-of-new-particles-20210407/

If you want more background about intrinsic spin, magnetic moments, and why mismatches could indicate new particles read on!

The muon is a heavier cousin of electrons. Both of them feature an intrinsic spin of half-hbar, where hbar is the reduced Planck constant. (Planck’s constant has dimensions of angular momentum.) The charge and spin properties of these particles mean that they act like microscopic bar-magnets, and hence, have a magnetic moment. (If you set an electrically charged object spinning, you create a rotating current that generates a magnetic field. There’s a quantum version of this happening with these particles.)

In a pristine world where particles never interact, the ratio between the intrinsic spin of electrons or muons and their magnetic moments would be 2. But that world is silly because magnetism is an interaction, so what does it matter if particles don’t interact?

In the real world, there’s a sense in which particles are really only approximate entities. The underlying description of particles comes from quantum field theory (QFT). In QFT, particles arise as states of a quantum field that carry definite amounts of momentum and are very well separated from each other. The assumption that these particle-like things are well-separated is essential because it means that they barely interact and so we can think of them as approximately equivalent to their counterparts in the silly, non-interacting world.

But this is only a first-approximation, because even if these approximate particle states aren’t interacting significantly with anything, the very possibility that they could interact with other particle-like things has to be accounted for in the definition of these states. Again, to a first approximation, we don’t take these possible interactions into account, but we then iteratively redefine the physical particle states by adding contributions that deform them away from the pristine, free particle approximation. Oftentimes such additions are described using the language of “virtual particles”. The idea is that even a muon left by itself in a vacuum is somehow affected by the existence of other particles because they may “fluctuate” out of the vacuum, interact, and then go away again, altering the muon’s physical behavior.

This is a very appealing picture but it’s important to understand that it’s not literal. There are no literal particles fluctuating into and out of existence. There is merely the fact that our free particle version of the muon and the actual, physical version are not identical because a theory with interactions is different from a theory without them. The virtual particles give us a convenient way to organize calculations that layer on corrections to the free particle theory, bringing its results closer to the physically, more realistic theory.

Anyway, it turns out that the muon’s magnetic moment is sensitive to the possibility of interacting with other particles in a way that causes the physical magnetic moment to diverge ever-so-slightly from the theoretical prediction with no interactions included. This divergence is called g – 2, also known as the “anomalous magnetic moment.”

These anomalies have been calculated and tested for both electrons and muons and the calculations and experiments agree to amazing levels of accuracy. However, measurements from around the year 2000 at Brookhaven National Labs and the more recent results from Fermilab indicate that the muon is more anomalous than what we’d expect from including interactions with just Standard Model particles. The most straightforward reading of this, assuming the anomaly is confirmed in future experiments, is that there is more for the muon to interact with than just the Standard Model particles, and thus, this would be very strong evidence for existence of particles beyond what we currently know.

But…(there’s always a “but”)…it could be that the experiments are fine and it’s the calculations that are messing up. The Standard Model is pretty tough to calculate with precisely because the contributions from all the possible interactions begin to get very intricate. So, magnetic moment calculations involve approximations and there are errors associated with these approximations. A recent calculation based on new techniques brings the theoretical prediction much closer to the new experimental results. If it turns out that these new techniques are valid, then it would mean that we *don’t* need new particles to explain the result.

So as I said early in the post, these new experimental results are exciting. They could indeed mean that there are new particles out there, just on the verge of discovery. But they could also mean that we’ve just got to find a better way to do our approximations using just the plain, vanilla Standard Model. So we can’t get too excited just yet.

Here’s a nice discussion of the situation from a more technical perspective:

http://resonaances.blogspot.com/2021/04/why-is-it-when-something-happens-it-is.html

Developments in HEP Worth Tentative Excitement

See the update at the end of the post!

During one of our recent QC classes I was discussing the problem of epicycles in approaches to interpretations of quantum theory. The basic idea here is that we have an interpretation that looks really nice in a specific context, but when you go to more general settings (for something like de Broglie-Bohm) or test against reality (for something like GRW) you find that to save the interpretation you need to modify in ways you wouldn’t have thought to originally (dBB) or push some parameters back (GRW) to bring things in line with observation again.

During a small digression I mentioned that issues with supersymmetry are rather like what happens with GRW: You predict that a class of supersymmetric models that have very strong theoretical motivation should be seen at LHC-accessible levels of energy. Then you fail to see them and you go, well, there are these other models that only really show up at higher energy. Less compelling, but next in line…

And that’s fine in my opinion, but gradually one becomes increasingly unmoored from the strongest (empirically-based) motivations.

Anyway, I mentioned that the LHC has been rather heart-wrenching in this respect, at least for only partially-informed theorists like myself, due to its great success at finding something we were extremely confident it would find (the Higgs) and basically nothing else at the fundamental level.

Well, maybe there are some glimmers of hope? Check out this article:

https://theconversation.com/evidence-of-brand-new-physics-at-cern-why-were-cautiously-optimistic-about-our-new-findings-157464

These glimmers have been around for a while, but as the article describes, the imbalances in the decay of beauty quarks to electrons versus muons are becoming increasingly statistically significant. It’s way too early to be confident that we’re finding new physics, but a little bit of tentative excitement and interest seems justified!

Note however that even if there is an eventual discovery, it likely won’t be clear which of several beyond-standard model scenarios are the right one. And my read on this is that it would by no means be definitive evidence for supersymmetry. Still, discovering a new particle that hints at a new type of force, and the potential unification of quarks and leptons (electrons, muons, taus, and neutrinos) would be huge. For people interested in these sorts of things, these are developments worth keeping an eye on.

Update: Tommaso Dorigo posted a very detailed explanation of why folks shouldn’t get overly excited about the results mentioned in the post above. The statistical significance level supports further careful study (which the research team plans to carry out!), but could easily be explained as a fluke in the data at this stage. Here’s Tommaso’s post:

https://www.science20.com/tommaso_dorigo/another_3_sigma_fluke_from_lhcb-253707

Are Quantum Computers Supreme Yet?

We’ve had a few discussions during class about whether or not quantum computational systems have clearly demonstrated superiority to their classical counterparts. Google is widely acknowledged to have achieved “quantum advantage” in 2019 with its 53 qubit system called Sycamore. There is still some debate about it because IBM claimed to be able to perform the same computation over a period of a few days on its most powerful supercomputer. Nature has a nice piece on this:

https://www.nature.com/articles/d41586-019-03213-z

A little over a year ago a group in China built a photonics-based system that carried out a type of quantum computation (called boson sampling) in 200 seconds. Classical algorithms are much slower, clocking in at 2.5 billion years. Nevertheless, there are some caveats, the most important being is that the photonics system is especially suited to the task of boson sampling and is not a basis for general quantum computing. Furthermore, boson sampling itself is not known to have any useful applications other than allowing quantum computer systems to demonstrate “quantum advantage” over classical systems. Despite these somewhat deflationary notes, I think it’s an impressive feat!

More recently, a researchers were able to construct a programmable photonics chip. The idea behind such an approach is that photons can be used as quantum information carriers. My understanding (which is limited!) is that there have been problems with controlling and scaling up such systems, but that this recent work marks an important step forward in developing this approach. You can take a look at the “News and Views” article about this work in Nature:

https://www.nature.com/articles/d41586-021-00488-z

There’s also a nice description of this in Ars Technica:

https://arstechnica.com/science/2021/03/programmable-optical-quantum-computer-arrives-late-steals-the-show/

I’m not an expert in these matters, but it seems like the progress has been amazing.

 

Due Dates Reminders

After our meeting today I remembered that I got rid of the class schedule! So I’ll post some due dates here:

Homeworks: These are due every week on Friday unless I announce otherwise.

Project outline: Due the week before spring break. Friday (3/5) of that week at the latest.

Project outline presentation: The week after spring break. Details TBD.

Project report: Due last week of finals.

Project report presentation: Last week of finals. Details TBD.

Spring 2021 Quantum Computing – Fun Reads

We were recently talking about Claude Shannon’s information theory, and I recalled reading a nice overview of Shannon and his work in quanta magazine:

https://www.quantamagazine.org/how-claude-shannons-information-theory-invented-the-future-20201222/

When it comes to controlling qubits, we still need classical processors. The trouble is that they heat up the environment and many qubit implementations require extremely low temperatures. This leads to limitations in the number of qubits you can actually work with. Some intriguing news out of Microsoft came out recently about chips that can function at ridiculously low temperatures. Personally, I don’t know enough (for now) about how much of this is realistic versus hyped, but it’s interesting nonetheless:

https://www.microsoft.com/en-us/research/blog/full-stack-ahead-pioneering-quantum-hardware-allows-for-controlling-up-to-thousands-of-qubits-at-cryogenic-temperatures/

Welcome to the Spring 2021 Quantum Information and Computing Class!

Hello and welcome to my course on quantum information and computing (phy 410/510) for the 2021 spring semester. This site will serve as a central hub from which you can access my basic info (name, email, and whatnot), notes, videos, the lecture schedule, and assignments. If I’m feeling inspired, I may occasionally post links to interesting quantum-related things I’ve come across and given the time and energy, write some posts exploring issues related to our class discussions.

I’m really excited about this course, and why not? It’s an amazing subject in so many different ways. Here are a few:

  1. The technological side of quantum computing and communication is very real and huge advances are being made year-by-year if not month-by-month!
  2. Quantum information and computing most likely establish a completely new basis for computing in general, dramatically impacting our abilities to solve certain types of problems that are (likely) intractable using only classical computing. (Why do I write “likely”? Something worth thinking about!)
  3. The quantum computing/information approach to quantum theory has helped to illuminate some of the famously murky conceptual underpinnings of the theory. New modes of conceptualizing quantum theory lead to interesting new ways to teach the subject that are in many ways much more accessible than the traditional approach you would learn in a standard quantum physics course.

There are many more reasons that this area is fun and exciting and I’m looking forward to sharing them with you. I’m also quite interested in the ideas that the subject sparks among you as we explore it this semester.