Yoinked from the comments of my post laugh therapy, John Preskill weighs in with a wise remark:
…But actually it is nice, for those of us who may have come to take the theory of quantum fault tolerance for granted, to be reminded of how truly remarkable and marvelous it is. This paper does not lay a glove on the theory. Even so, let’s be careful not to be too smug. We sure have a long way to go toward turning the theory into practice.
Indeed! My first reaction is always to act like I’m a book critic, and to crank up my hyperbole meter to overdrive. But I certainly agree with John that we should not be too smug. To destroy a line from a baseball movie, “Until we build it, they won’t come.” Indeed to me the best critique of quantum error correction is simply “you haven’t done it yet” to which I can only nod my head in agreement and then run over to the experimentalists and cheer them along.
But John’s comment got me thinking (again) about the relationship quantum computing theory has with the physics community. Certainly I don’t think there has been much of a change in the hiring practices of U.S. physics departments when it comes to quantum computing theorists. In two words: “not good.” And I wonder if perhaps one of the reasons for this is that the central message of the threshold(s) theorem(s) has not penetrated into physics. Indeed, in my mind, the threshold theorem for quantum computation is essentially a statement about a new phase of many-body quantum systems. But to many physicists, I’ll bet that the result, if they’ve heard anything about it at all, sounds more like a strange engineering/computer science result, and the inclussion of the word “theorem” sets off their antimathematical radar detection system.
In some ways what I’m saying is that it feels like we’ve lost the public relations battle in publicizing the significance of the threshold theorem to physics departments. Perhaps part of this is because the language used to describe the theorem is more often devoid of terms physicist would like to see. Indeed when I talk about the threshold theorem I always always immediately transport myself into computer science speak. But that doesn’t mean that there isn’t a beautiful way to cast the result in terms of the physics of many-body quantum systems. Should we be making fault-tolerance more accessible to physicists? Maybe this is a PR battle we should be trying harder to overcome!
Okay this is strange. Just as I was about to post this, an email popped into my inbox about the APS March meeting:
TGQI is also organizing a tutorial on Quantum Error Correction and Fault-Tolerant Quantum Computation, which will be given on Sunday, March 4, with Daniel Gottesman of the Perimeter Institute as the instructor. To attend a tutorial, you must pre-register for the Meeting.
Sounds like a good way to convert some physics skeptics!
At the risk of sounding like a broken record, if QC theorists really want to help build real QCs you have to let go of the “theoretical computer scientist’s QC” (ie the gate model) and start thinking about realistic quantum computational models.
A very useful exercise would be to derive “threshold theorems” in other QC models. AQC for example is already written in everyday physics language — energy spectra, Landau-Zener transitions, realistic Hamiltonians that can actually be constructed, no requirement for particles that don’t exist, all-DC control.
A related point is that most condensed matter physicists think of environments as terms in a Hamiltonian (eg. spin-boson models or spin bath models). While I get the fact that other ways to represent errors are equally legitimate, if you want to communicate with physicists I think you have to recast in their language. J(w) baby.
A good approach to communicating the threshold theorem to the physics community is to rederive it using a real AQC Hamiltonian + explicit environments in the Hamiltonian (that actually correspond to whatever the environment really is in practice) IMHO.
Note that the threshold you’ll get by doing this isn’t “errors per gate” for at least two reasons: (1) the parameters of the problem are actual terms in a Hamiltonian so errors –> physical parameters like coupling to a bath and temperature and (2) there are no gates in AQC. What you’ll get is some restriction on actual real physical parameters (like temperature, etc.) which will be clear to physicists (and engineers).
“Are you reading my desktop latex files Geordie?!”
No, but if you want to send them over here we’d love to take a look! Also if you can think of some experiments you’d like to see performed it’s possible we could run some.
“A very useful exercise would be to derive “threshold theorems†in other QC models. AQC for example is already written in everyday physics language — energy spectra, Landau-Zener transitions, realistic Hamiltonians that can actually be constructed, no requirement for particles that don’t exist, all-DC control.”
Are you reading my desktop latex files Geordie?! Some of us are working on exactly that! And I’ve even resisted commenting on your blog about the lack of fault-tolerant results for adiabatic quantum computation 🙂 And while I agree that they can already be constructed, it isn’t clear whether they can be constructed fault-tolerantly with current coupling strengths and temperatures. Crap now I’ve got to work even faster on this (not easy for a slow theorist like me…I’ve got a brain the size of pea compared to the rest of these quantum computing hotshots.)
Yeah, something in Dyakonov’s paper that I feel sympathetic with is the suggestion in Sec. 4 that we should consider the decoherence model in which each spin couples to a fluctuating magnetic field. In the Hamiltonian model, the known theorems (quant-ph/0402104, quant-ph/0504218, and quant-ph/0510231) express the threshold condition as an upper bound on the operator norm of terms in the system-bath coupling. It is interesting and useful (and also possible, I think) to reformulate this requirement as a condition on the correlation functions of the bath (or in Dyakonov’s example, the correlators of the magnetic field). I have worked on this problem, too, but I don’t have a nice solution yet.
Reading Dyakonov’s paper it really looks as though he’s failed to grasp that the FT theorem is a really big deal. I also get the impression that part of the problem is a language issue, part of it is also historical. The FT results were cast in terms of the gate model, and even a lot of QC theorists have a real issue in translating between the gate model and actual physical systems.
I think it would help the QC community in a big way if we could translate more of these results in terms of “normal” physics language. We also need to get out there and talk more about the implications of FTQC in terms of physics.
“Sounds like a good way to convert some physics skeptics!”
Um, probably not, even assuming the skeptics bother to attend. It’s all very well to talk about making fault-tolerance accessible to all kinds of physicists, but it’s already a big job making it accessible to quantum information specialists (e.g., experimentalists or theory grad students), which will be my goal.
It’s perhaps worth recalling that there’s a reason we use the gate model, which is that it’s a lot better for thinking about problems like this. Fault-tolerant protocols must look pretty bizarre if you write them in terms of control Hamiltonians. I don’t think it’s at all an accident that quantum error correction was discovered in the context of quantum computation, and not long before.
In fact, we do have a proof of the threshold when the errors are due to a Hamiltonian coupling to a very general spin bath model — but the way to prove that is to do almost everything in the gate model. It would be pretty hard, I suspect, to prove any reasonable threshold theorem without translating at some point to the gate model. Maybe with non-abelian anyons in four dimensions — but somehow I doubt most physicists would be happy with that.
Dave, your remarks are cogent, and you might consider adding a “global” aspect to them.
Globally speaking, enrollment of North American young people in physics graduate programs has been in decline for almost forty years, such that enrollment is presently down 40% from its peak in 1970.
Sloshing resources from one physics program to the other is like rearranging the deck chairs on a ship that, while not sinking catastrophically, has been slowly settling lower and lower in the water for a long time.
Resource-sloshing as a primary strategic activity DOES makes sense if you are convinced that the ship of physics is not going anywhere soon. This seems to be the unspoken consensus.
I do not embrace this consensus, but that’s another essay! And I would be interested to see posts from other people (students especially) who do not share this consensus.
Hi Dave,
Does QC really have a significantly worse relationship with physics departments than, say, any other subfield? It always strikes me that physics has a tendency to want to become smaller by excluding interesting new areas, or pushing them into math or chemistry or biology, but does QC suffer from this more than biophysics or soft matter or fluids?
Cheer up! It’s an exciting subject – our colleagues in physics are smart, they’ll get it. In the mean time we can have all the fun.
Just think, in ten years time we might be where string theory is now.
Peter
I agree Peter. Just having fun is much much more important! Somedays I just wake up on the grumpy side of the bed (that’s the right side of the bed, for those of you interested…thi sentence brought to you by the subliminal message policital action campaign and our secret desire to associate the word “right” with negative connotations 🙂 )
“but does QC suffer from this more than biophysics or soft matter or fluids?”
More than biophysics, yes. More than soft matter, maybe. More than fluids, no. Clicking on the research page for most physics departments will lead you to a “biophysics” group. But you’re right that crossdiscplinary work causes the academic system to go haywire. It’s interesting to see that the place I associate most with having low borders between departments, Caltech, is a big quantum computing center. I don’t think this is an accident.