## Self-correcting Fractals

A really exciting paper appeared on the arxiv today: A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less), by Courtney Brell. It gives the strongest evidence yet that self-correcting quantum memories are possible in “physically realistic” three-dimensional lattice models. In particular, Courtney has constructed families of local Hamiltonians in 3D whose terms consist of X- and Z-type stabilizer generators and that show phase-transition behavior akin to the 2D Ising model for both the X- and Z-type error sectors. This result doesn’t achieve a complete theoretical solution to the question of whether self-correcting quantum memories can exist in principle, as I’ll explain below, but it makes impressive progress using a mix of rigorous analysis and physical argument.

First, what do I mean by “physically realistic”? Well, obviously I don’t mean physically realistic (without quotes)—that’s a much greater challenge. Rather, we want to abstractly characterize some features that should be shared by a physically realistic implementation, but with enough leeway that a theorist can get creative. To capture this, Courtney introduces the so-called Caltech Rules for a self-correcting quantum memory.

The phrase “the Caltech Rules” is (I believe) attributable to David Poulin. Quantum memory aficionados have been debating these rules in emails and private discussions for the last few years, but I think this is the first time someone has put them in print. As rules, they aren’t really set in stone. They consist of a list of criteria that are either necessary or seemingly necessary to avoid models that are self-correcting for trivial and unphysical reasons (e.g., scaling the coupling strengths as a function of $n$). In Courtney’s version of the rules, we require a model with finite-dimensional spins (so no bosonic or fermionic models allowed… this might be objectionable to some people), bounded-strength short-range interactions between the spins, a constant density of spins, a perturbatively stable degenerate ground space for the encoded states, an efficient decoding algorithm, and an exponential memory lifetime against low-temperature thermal noise. One might wish to add even more desiderata like translation-invariant couplings or a spectral gap (which is closely related to stability), but finding a self-correcting memory subject to these constraints is already a tall order. For some more discussion on these points, check out another awesome paper that came on the arxiv yesterday, an excellent review article on quantum memories at finite temperature by Ben Brown et al..

To motivate the construction, it helps to remember everyone’s favorite models, the Ising model and the Toric code. When the temperature $T$ is zero, it’s easy to store a classical bit using the 1D Ising model; this is just a repetition code. Similarly, the 2D toric code can store quantum information at $T=0$. Both of these codes become unstable as memories at $T\textgreater 0$ because of the presence of string-like logical operators. The physical process by which these strings are created costs some energy, but then the strings can stretch and grow without any energy cost, and thermal fluctuations alone will create enough strings in a short time to cause a decoding failure. By contrast, the 2D Ising model can store a classical bit reliably for an exponential amount of time if you encode in the total magnetization and you are below the Curie temperature. The logical operators are now membranes that cost energy to grow. Similarly, the 4D toric code has such a phase transition, and this is because the X- and Z-type errors both act analogously to 2D Ising models with membranous logical operators.

Sierpinski carpet, with edges placed to form a “Sierpinski graph”.

The codes that Courtney defines are called embeddable fractal product codes (EFPC). The idea is that, if a product of two 1D Ising models isn’t a 2D self-correcting model, but a product of two 2D Ising models is a self-correcting memory, then what happens if we take two 1.5D Ising models and try to make a 3D self-correcting memory? The backbone of the construction consists of fractals such as the Sierpinski carpet that have infinite ramification order, meaning that an infinite number of edges on an associated graph must be cut to split it into two infinite components. Defining an Ising model on the Sierpinski graph yields a finite-temperature phase transition for the same reason as the 2D Ising model, the Peierls argument, which is essentially a counting argument about the density of domain walls in equilibrium with fixed boundary conditions. This is exactly the kind of behavior needed for self-correction.

Splitting the Sierpinski graph into two infinite components necessarily cuts an infinite number of edges.

Using the adjacency of the Sierpinski graph, the next step is to use a toric code-like set of generators on this graph, paying careful attention to the boundary conditions (in particular, plaquette terms are placed in such a way that the stabilizer group contains all the cycles that bound areas of the fractal, at any length scale). Then using homological product codes gives a natural way to combine X-like and Z-like copies of this code into a new code that naturally lives in four dimensions. Although the natural way to embed this code requires all four spatial dimensions, it turns out that a low-distortion embedding is possible with distortion bounded by a small constant, so these codes can be compressed into three dimensions while retaining the crucial locality properties.

Remarkably, this construction gives a finite-temperature phase transition for both the X- and Z-type errors. It essentially inherits this from the fact that the Ising models on the Sierpinski graph have phase transitions, and it is a very strong indication of self-correcting behavior.

However, there are some caveats. There are many logical qubits in this code (in fact, the code has constant rate), and only the qubits associated to the coarsest features of the fractal have large distance. There are many logical qubits associated to small-scale features that have small distance and create an exponential degeneracy of the ground space. With such a large degeneracy, one worries about perturbative stability in the presence of a generic local perturbation. There are a few other caveats, for example the question of efficient decoding, but to me the issue of the degeneracy is the most interesting.

Overall, this is the most exciting progress since Haah’s cubic code. I think I’m actually becoming optimistic about the possibility of self-correction. It looks like Courtney will be speaking about his paper at QIP this year, so this is yet another reason to make it to Sydney this coming January.

## A Breakthrough Donation for Computer Science

Lance Fortnow has a post summarizing some of the news affecting the CS community over the past month, including updates on various prizes as well as the significant media attention focusing on physics- and math-related topics such as movies about Turing and Hawking as well as Terrence Tao on the Colbert Report.

From his post, I just learned that former Microsoft chief executive Steven Ballmer is making a donation to Harvard that will endow twelve—that’s right, 12—new tenured and tenure-track faculty positions in computer science. This is fantastic news and will have a huge positive impact on Harvard CS.

One thing missing from Lance’s list was news about the Breakthrough Prizes in mathematics and fundamental physics. In case you’ve been living under a rock, these prizes give a very hefty US \$3 million purse to the chosen recipients. The winners are all luminaries in their field, and it’s great to see them get recognition for their outstanding work.

On the other hand, juxtaposing Ballmer’s donation and the Breakthrough Prizes couldn’t offer a starker contrast. It costs the same amount—\$3 million—to endow a university full professor with appointments in more than one discipline at Duke University. My initial googling would suggest that this is a pretty typical figure at top-tier institutions.

What if, instead of a offering a cash prize to the Breakthrough Prize winners, the reward was an upgrade to an endowed chair at the current institution subject to the condition that the existing position would go to a new tenured or tenure-track hire in the same field? This seems to be a much better investment in science overall because it will help build a community of researchers around the prize winner, and the marginal benefit to this community from associating with the prize winner is likely far greater than any extra incentive the researchers might get within the current system to simply strive to win \$3M cash.

Posted in \$\$\$, Computer Science, Prize | 5 Comments

## Goodbye Professor Tombrello

This morning I awoke to the horrible news that Caltech Physics Professor Tom Tombrello had passed away. Professor Tombrello was my undergraduate advisor, my research advisor, a mentor, and, most importantly a friend. His impact on me, from my career to the way I try to live my life, was profound.

Because life is surreal, just a few days ago I wrote this post that describes the event that led Professor Tombrello and I down entwined paths, my enrollment in his class Physics 11. Physics 11 was a class about how to create value in the world, disguised as a class about how to do “physics” research as an undergraduate. Indeed, in my own life, Professor Tombrello’s roll was to make me think really really hard about what it meant to create. Sometimes this creation was in research, trying to figure out a new approach or even a new problem. Sometimes this creation was in a new career, moving to Google to be given the opportunity to build high impact creations. I might even say that this creation extends into the far reaches of Washington state, where we helped bring about the creation of a house most unusual.

There are many stories I remember about Professor Tombrello. From the slightly amusing like the time after the Northridge earthquake when an aftershock shook our class while he was practicing his own special brand of teach, and we all just sort of sat still until we heard this assistant, Michelle, shout out “That’s it! I’m outta here!” and go storming out. To the time I talked with him following the loss of one of his family members, and could see the profound sadness even in a man who push optimistically forward at full speed.

Some portraits:

After one visit to Professor Tombrello, I actually recorded my thoughts on our conversation:

This blog post is for me, not for you. Brought to you by a trip down memory lane visiting my adviser at Caltech.

Do something new. Do something exciting. Excel. Whether the path follows your momentum is not relevant.

Don’t dwell. Don’t get stuck. Don’t put blinders on.

Consider how the problem will be solved, not how you are going to solve it.

Remember Feynman: solve problems.

Nothing is not interesting, but some things are boring.

Dyson’s driving lesson: forced intense conversation to learn what the other has to say.

Avoid confirmatory sources of news, except as a reminder of the base. Keep your ear close to the brains: their hushed obsessions are the next big news.

Learn something new everyday but also remember to forget the things not worth knowing.

Technically they can do it or they can’t, but you can sure help them do it better when they can.

Create. Create. Create.

Write a book, listen to Sandra Tsing Loh, investigate Willow Garage, and watch Jeff Bezos to understand how to be a merchant.

Create. Create. Create.

So tonight, I’ll have a glass of red wine to remember my professor, think of his family, and the students to whom he meant so much. And tomorrow I’ll pick myself up, and try to figure out just what I can create next.

## Sailing Stones: Mystery No More

My first research project, my first research paper, was on a perplexing phenomenon: the sliding rocks of Death Valley’s Racetrack playa. Racetrack playa is a large desolate dry lake bed that has one distinguishing feature above and beyond its amazing flatness. At the south end of the playa are a large number of large rocks (one man size and smaller), and behind these rocks, if you visit in the summer, are long tracks caked into the dried earth of the playa. Apparently these rocks, during the winter months, move and leave these long tracks. I say apparently, because, for many many years, no one had ever seen these rocks move. Until now! The following video makes me extremely happy

This is a shot of one of the playa stones actually moving! This is the end result of a large study that sought to understand the mechanism behind the sliding stones, published recently in PloS one:

In 1993, fresh out of Yreka High School, I found myself surrounded by 200+ geniuses taking Caltech’s first year physics class, Physics 1 (med schools sometimes ask students at Caltech to verify that they know Calculus because the transcripts have just these low numerical course indicators on them, and of course Physics 1 couldn’t actually be physics with calculus, could it?) It would be a lie to say that this wasn’t intimidating: some of the TAs in the class where full physics professors! I remember a test where the average score was 0.5 out of 10 and perhaps it didn’t help that my roommate studied with a Nobel prize winner as a high school student. Or that another freshman in my class was just finishing a paper with his parents on black holes (or that his dad is one of the founders of the theory of inflation!) At times I considered transferring, because that is what all Caltech students do when they realized how hard Caltech is going to be, and also because it wasn’t clear to me what being a physics major got you.

One day in Physics 1 it was announced that there was a class that you could gain entrance to that was structured to teach you not physics, but how to do creative research. Creativity: now this was something I truly valued! It was called Physics 11 and it was run by one Professor Tom Tombrello (I’d later see his schedule on the whiteboard with the abbreviation T2). The only catch was that you had to get accepted into the class and to do this you had to do you best at solving a toy research problem, what the class termed a “hurdle”. The students from the previous class then helped select the new Physics 11 students based upon their performance on the hurdles. The first hurdle also caught my eye: it was a problem based upon the old song Mairzy Doats which my father had weekly sung while showering in the morning. So I set about working on the problem. I don’t remember much of my solution, except that it was long and involved lots of differential equations of increasing complexity. Did I mention that it was long? Really long. I handed in the hurdle, then promptly ran out of time to work on the second hurdle.

Because I’d not handed in the second hurdle, I sort of expected that I’d not get selected into the class. Plus I wasn’t even in the advanced section of physics 1 (the one TAed by the professors, now those kids were well prepared and smart!) But one late night I went to my mailbox, opened it, and found…nothing. I closed it, and then, for some strange reason, thought: hey maybe there is something stuck in there. So I returned and opened the box, dug deep, and pulled out an invitation to join physics 11! This story doesn’t mean much to you, but I can still smell, feel, and hear Caltech when I think of this event. Also I’ve always been under the impression that being accepted to this class was a mistake and really the invitation I got was meant for another student in a mailbox next to mine. But that’s a story for another session on the couch.

So I enrolled in Physics 11. It’s not much of a stretch to say that it was the inspiration for me to go to graduate school, to do a postdoc, and to become a pseudo-professor. Creative research is an amazing drug, and also, I believe, one of the great endeavors of humanity. My small contribution to the racetrack playa story was published in the Journal of Geology:

The basic mystery was what caused these rocks to move. Was it the wind? It seemed hard to get enough force to move the rocks. Was it ice? When you placed stakes around the rocks, some of the rocks moved out of the stakes and some did not. In the above paper we pointed out that a moving layer of water would mean that there was more wind down low that one would normally get because the boundary layer was moving. We also looked for the effect of said boundary layer on the rocks motion and found a small effect.

The answer, however, as to why the rocks moved, turned out to be even more wonderful. Ice sheets dislodged and bashing the rocks forward. A sort of combination of the two competing previous hypothesis! This short documentary explains it nicely

So, another mystery solved! We know more about how the world works, not on a level of fundamental physics, but on a level of, “because it is interesting”, and “because it is fun”, and isn’t that enough? Arthur C. Clarke, who famously gave airtime to these rocks, would, I think, have been very please with this turn of events

## QIP 2015

The website is up for QIP 2015, which will be held this year in beautiful Sydney, Australia. Here is a timeline of the relevant dates:

• Submission of talks deadline: Sep 12, 2014
• Submission of posters deadline: Oct 25, 2014
• Decision on talks and posters submitted before talk deadline: Oct 20, 2014
• Decision on posters submitted after talk deadline: Nov 15, 2014
• Tutorial Session: Jan 10-11, 2015
• Main Conference: Jan 12-16, 2015

And students, don’t worry, there are plans to include some student support scholarships, so we hope that many of you can attend. We’re looking forward to seeing you all here!

Posted in Announcement, Conferences, QIS Annoucements, Quantum | 3 Comments

## Elsevier again, and collective action

We all know about higher education being squeezed financially. Government support is falling and tuition is going up. We see academic jobs getting scarcer, and more temporary. The pressure for research to focus on the short term is going up. Some of these changes may be fair, since society always has to balance its immediate priorities against its long-term progress. At other times, like when comparing the NSF’s \$7.6 billion FY2014 budget request to the ongoing travesty that is military procurement, it does feel as though we are eating our seed corn for not very wise reasons.

Against this backdrop, the travesty that is scientific publishing may feel like small potatoes. But now we are starting to find out just how many potatoes. Tim Gowers has been doing an impressive job of digging up exactly how much various British universities pay for their Elsevier subscriptions. Here is his current list. Just to pick one random example, the University of Bristol (my former employer), currently pays Elsevier a little over 800,000 pounds (currently \$1.35M) for a year’s access to their journals. Presumably almost all research universities pay comparable amounts.

To put this number in perspective, let’s compare it not to the F-35, but to something that delivers similar value: arxiv.org. Its total budget for 2014 is about 750,000 US dollars (depending on how you count overhead), and of course this includes access for the entire world, not only the University of Bristol. To be fair, ScienceDirect has about 12 times as many articles and the median quality is probably higher. But overall it is clearly vastly more expensive for society to have its researchers communicate in this way.

Another way to view the £800,000 price tag is in terms of the salaries of about 40 lecturers ($\approx$ assistant professors), or some equivalent mix of administrators, lecturers and full professors. The problem is that these are not substitutes. If Bristol hired 40 lecturers, they would not each spend one month per year building nearly-free open-access platforms and convincing the world to use them; they would go about getting grants, recruiting grad students and publishing in the usual venues. There are problems of collective action, of the path dependence that comes with a reputation economy and of the diffuse costs and concentrated benefits of the current system.

I wish I could end with some more positive things to say. I think at least for now it is worth getting across the idea that there is a crisis, and that we should all do what we can to help with it, especially when we can do so without personal cost. In this way, we can hopefully create new social norms. For example, it is happily unconventional now to not post work on arxiv.org, and I hope that it comes to be seen also as unethical. In the past, it was common to debate whether QIP should have published proceedings. Now major CS conferences are cutting themselves loose from parasitic professional societies (see in particular the 3% vote in favor of the status quo) and QIP has begun debating whether to require all submissions be accompanied by arxiv posts (although this is of course not at all clear-cut). If we cannot have a revolution, hopefully we can at least figure out an evolutionary change towards a better scientific publishing system. And then we can try to improve military procurement.

Posted in \$\$\$, Science 2.0, Scientific Publishing | 19 Comments

## Quantum computers can work in principle

Gil Kalai has just posted on his blog a series of videos of his lectures entitled “why quantum computers cannot work.”  For those of us that have followed Gil’s position on this issue over the years, the content of the videos is not surprising. The surprising part is the superior production value relative to your typical videotaped lecture (at least for the first overview video).

I think the high gloss on these videos has the potential to sway low-information bystanders into thinking that there really is a debate about whether quantum computing is possible in principle. So let me be clear.

There is no debate! The expert consensus on the evidence is that large-scale quantum computation is possible in principle.

Quoting “expert consensus” like this is an appeal to authority, and my esteemed colleagues will rebuke me for not presenting the evidence. Aram has done an admirable job of presenting the evidence, but the unfortunate debate format distorts perception of the issue by creating the classic “two sides to a story” illusion. I think it’s best to be unequivocal to avoid misunderstanding.

The program that Gil lays forth is a speculative research agenda, devoid of any concrete microscopic physical predictions, and no physicist has investigated any of it because it is currently neither clear enough nor convincing enough. At the same time, it would be extremely interesting if it one day leads to a concrete conjectured model of physics in which quantum computers do not work. To make the ideas more credible, it would help to have a few-qubit model that is at least internally consistent, and even better, one that doesn’t contradict the dozens of on-going experiments. I genuinely hope that Gil or someone else can realize this thrilling possibility someday.

For now, though, the reality is that quantum computation continues to make exciting progress every year, both on theoretical and experimental levels, and we have every reason to believe that this steady progress will continue. Quantum theory firmly predicts (via the fault-tolerance threshold theorem) that large-scale quantum computation should be achievable if noise rates and correlations are low enough, and we are fast approaching the era where the experimentally achievable noise rates begin to touch the most optimistic threshold estimates. In parallel, the field continues to make contributions to other lines of research in high-energy physics, condensed matter, complexity theory, cryptography, signal processing, and many others. It’s an exciting time to be doing quantum physics.

And most importantly, we are open to being wrong. We all know what happens if you try to update your prior by conditioning on an outcome that had zero support. Gil and other quantum computing skeptics like Alicki play a vital role in helping us sharpen our arguments and remove any blind spots in our reasoning. But for now, the arguments against large-scale quantum computation are simply not convincing enough to draw more than an infinitesimal sliver of expert attention, and it’s likely to remain this way unless experimental progress starts to systematically falter or a concrete and consistent competing model of quantum noise is developed.

## TQC 2014!

While many of us are just recovering from QIP, I want to mention that the submission deadline is looming for the conference TQC, which perhaps should be called TQCCC because its full name is Theory of Quantum Computation, Communication and Cryptography. Perhaps this isn’t done because it would make the conference seem too classical? But TQQQC wouldn’t work so well either. I digress.

The key thing I want to mention is the imminent 15 Feb submission deadline.

I also want to mention that TQC is continuing to stay ahead of the curve with its open-access author-keeps-copyright proceedings, and this year with some limited open reviewing (details here). I recently spoke to a doctor who complained that despite even her Harvard Medical affiliation, she couldn’t access many relevant journals online. While results of taxpayer-funded research on drug efficacy, new treatments and risk factors remain locked up, at least our community is ensuring that anyone wanting to work on the PPT bound entanglement conjecture will be able to catch up to the research frontier without having to pay \$39.95 per article.

One nice feature about these proceedings is that if you later want to publish a longer version of your submission in a journal, then you will not face any barriers from TQC. I also want to explicitly address one concern that some have raised about TQC, which is that the published proceedings will prevent authors from publishing their work elsewhere. For many, the open access proceedings will be a welcome departure from the usual exploitative policies of not only commercial publishers like Elsevier, but also the academic societies like ACM and IEEE. But I know that others will say “I’m happy to sign your petitions, but at the end of the day, I still want to submit my result to PRL” and who am I to argue with this?

So I want to stress that submitting to TQC does not prevent submitting your results elsewhere, e.g. to PRL. If you publish one version in TQC and a substantially different version (i.e. with substantial new material) in PRL, then not only is TQC fine with it, but it is compatible with APS policy which I am quoting here:

Similar exceptions [to the prohibition against double publishing] are generally made for work disclosed earlier in abbreviated or preliminary form in published conference proceedings. In all such cases, however, authors should be certain that the paper submitted to the archival
journal does not contain verbatim text, identical figures or tables, or other copyrighted materials which were part of the earlier publications, without providing a copy of written permission from the copyright holder. [ed: TQC doesn’t require copyright transfer, because it’s not run by people who want to exploit you, so you’re all set here] The paper must also contain a substantial body of new material that was not included in the prior disclosure. Earlier relevant published material should, of course, always be clearly referenced in the new submission.

I cannot help but mention that even this document (the “APS Policy on Prior Disclosure”) is behind a paywall and will cost you \$25 if your library doesn’t subscribe. But if you really want to support this machine and submit to PRL or anywhere else (and enjoy another round of refereeing), TQC will not get in your way.

Part of what makes this easy is TQC’s civilized copyright policy (i.e. you keep it). By contrast, Thomas and Umesh had a more difficult, though eventually resolved, situation when combining STOC/FOCS with Nature.

## Two Cultures in One of the Cultures

A long time ago in a mental universe far far away I gave a talk to a theory seminar about quantum algorithms. An excerpt from the abstract:

Quantum computers can outperform their classical brethren at a variety of algorithmic tasks….[yadda yadda yadaa deleted]… This talk will assume no prior knowledge of quantum theory…

The other day I was looking at recent or forthcoming interesting quantum talks and I stumbled upon one by a living pontiff:

In this talk, I’ll describe connections between the unique games conjecture (or more precisely, the closely relatedly problem of small-set expansion) and the quantum separability problem… [amazing stuff deleted]…The talk will not assume any knowledge of quantum mechanics, or for that matter, of the unique games conjecture or the Lasserre hierarchy….

And another for a talk to kick off a program at the Simons institute on Hamiltonian complexity (looks totally fantastic, wish I could be a fly on the wall at that one!):

The title of this talk is the name of a program being hosted this semester at the Simons Institute for the Theory of Computing….[description of field of Hamiltonian complexity deleted…] No prior knowledge of quantum mechanics or quantum computation will be assumed.

Talks are tricky. Tailoring your talk to your audience is probably one of the trickier sub-trickinesses of giving a talk. But remind me again, why are we apologizing to theoretical computer scientists / mathematicians (which are likely the audiences for the three talks I linked to) for their ignorance of quantum theory? Imagine theoretical computer science talks coming along with a disclaimer, “no prior knowledge of the PCP theorem is assumed”, “no prior knowledge of polynomial-time approximation schemes is assumed”, etc. Why is it still considered necessary, decades after Shor’s algorithm and error correction showed that quantum computing is indeed a fascinating and important idea in computer science, to apologize to an audience for a large gap in their basic knowledge of the universe?

As a counter argument, I’d love to hear from a non-quantum computing person who was swayed to attend a talk because it said that no prior knowledge of quantum theory is assumed. Has that ever worked? (Or similar claims of a cross cultural prereq swaying you to bravely go where none of your kind has gone before.)

## Error correcting aliens

Happy New Year!  To celebrate let’s talk about error correcting codes and….aliens.

The universe, as many have noted, is kind of like a computer.  Or at least our best description of the universe is given by equations that prescribe how various quantities change in time, a lot like a computer program describes how data in a computer changes in time.  Of course, this ignores one of the fundamental differences between our universe and our computers: our computers tend to be able to persist information over long periods of time.  In contrast, the quantities describing our universe tend to have a hard time being recoverable after even a short amount of time: the location (wave function) of an atom, unless carefully controlled, is impacted by an environment that quickly makes it impossible to recover the initial bits (qubits) of the location of the atom.

Computers, then, are special objects in our universe, ones that persist and allow manipulation of long lived bits of information.  A lot like life.  The bits describing me, the structural stuff of my bones, skin, and muscles, the more concretely information theoretic bits of my grumbly personality and memories, the DNA describing how to build a new version of me, are all pieces of information that persist over what we call a lifetime, despite the constant gnaw of second law armed foes that would transform me into unliving goo.  Maintaining my bits in the face of phase transitions, viruses, bowel obstructions, cardiac arrest, car accidents, and bears is what human life is all about, and we increasingly do it well, with life expectancy now approaching 80 years in many parts of the world.

But 80 years is not that long.  Our universe is 13.8ish billion years old, or about 170ish million current lucky human’s life expectancies.  Most of us would, all things equal, like to live even longer.  We’re not big fans of death.  So what obstacles are there toward life extension?  Yadda yadda biology squishy stuff, yes.  Not qualified to go there so I won’t.  But since life is like a computer in regards to maintaining information, we can look toward our understanding of what allows computers to preserve information…and extrapolate!

Enter error correction.  If bits are subject to processes that flip the values of the bits, then you’ll lose information.  If, however, we give up storing information in each individual bit and instead store single bits across multiple individual noisy bits, we can make this spread out bit live much longer.  Instead of saying 0, and watching it decay to unknown value, say 000…00, 0 many times, and ask if the majority of these values remain 0.  Viola you’ve got an error correcting code.  Your smeared out information will be preserved longer, but, and here is the important point, at the cost of using more bits.

Formalizing this a bit, there are a class of beautiful theorems, due originally to von Neumann, classically, and a host of others, quantumly, called the threshold theorems for fault-tolerant computing which tell you, given an model for how errors occur, how fast they occur, and how fast you can compute, whether you can reliably compute. Roughly these theorems all say something like: if your error rate is below some threshold, then if you want to compute while failing at a particular better rate, then you can do this using a complicated larger construction that is larger proportional to a polynomial in the log of inverse of the error rate you wish to achieve. What I’d like to pull out of these theorems for talking about life are two things: 1) there is an overhead to reliably compute, this overhead is both larger, in size, and takes longer, in time, to compute and 2) the scaling of this overhead depends crucially on the error model assumed.

Which leads back to life. If it is a crucial part of life to preserve information, to keep your bits moving down the timeline, then it seems that the threshold theorems will have something, ultimately, to say about extending your lifespan. What are the error models and what are the fundamental error rates of current human life? Is there a threshold theorem for life? I’m not sure we understand biology well enough to pin this down yet, but I do believe we can use the above discussion to extrapolate about our future evolution.

Or, because witnessing evolution of humans out of their present state seemingly requires waiting a really long time, or technology we currently don’t have, let’s apply this to…aliens. 13.8 billion years is a long time. It now looks like there are lots of planets. If intelligent life arose on those planets billions of years ago, then it is likely that it has also had billions of years to evolve past the level of intelligence that infects our current human era. Which is to say it seems like any such hypothetical aliens would have had time to push the boundaries of the threshold theorem for life. They would have manipulated and technologically engineered themselves into beings that live for a long period of time. They would have applied the constructions of the threshold theorem for life to themselves, lengthening their life by apply principles of fault-tolerant computing.

As we’ve witnessed over the last century, intelligent life seems to hit a point in its life where rapid technological change occurs. Supposing that the period of time in which life spends going from reproducing, not intelligent stuff, to megalords of technological magic in which the life can modify itself and apply the constructions of the threshold theorem for life, is fast, then it seems that most life will be found at the two ends of the spectrum, unthinking goo, or creatures who have climbed the threshold theorem for life to extend their lifespans to extremely long lifetimes. Which lets us think about what alien intelligent life would look like: it will be pushing the boundaries of using the threshold theorem for life.

Which lets us make predictions about what this advanced alien life would look life. First, and probably most importantly, it would be slow. We know that our own biology operates at an error rate that ends up being about 80 years. If we want to extend this further, then taking our guidance from the threshold theorems of computation, we will have to use larger constructions and slower constructions in order to extend this lifetime. And, another important point, we have to do this for each new error model which comes to dominate our death rate. That is, today, cardiac arrest kills the highest percentage of people. This is one error model, so to speak. Once you’ve conquered it, you can go down the line, thinking about error models like earthquakes, falls off cliffs, etc. So, likely, if you want to live a long time, you won’t just be slightly slow compared to our current biological life, but instead extremely slow. And large.

And now you can see my resolution to the Fermi paradox. The Fermi paradox is a fancy way of saying “where are the (intelligent) aliens?” Perhaps we have not found intelligent life because the natural fixed point of intelligent evolution is to produce entities for which our 80 year lifespans is not even a fraction of one of their basic clock cycles. Perhaps we don’t see aliens because, unless you catch life in the short transition from unthinking goo to masters of the universe, the aliens are just operating on too slow a timescale. To discover aliens, we must correlate observations over a long timespan, something we have not yet had the tools and time to do. Even more interesting the threshold theorems also have you spread your information out across a large number of individually erring sub-systems. So not only do you have to look at longer time scales, you also need to make correlated observations over larger and larger systems. Individual bits in error correcting codes look as noisy as before, it is only in the aggregate that information is preserved over longer timespans. So not only do we have too look slower, we need to do so over larger chunks of space. We don’t see aliens, dear Fermi, because we are young and impatient.

And about those error models. Our medical technology is valiantly tackling a long list of human concerns. But those advanced aliens, what kind of error models are they most concerned with? Might I suggest that among those error models, on the long list of things that might not have been fixed by their current setup, the things that end up limiting their error rate, might not we be on that list? So quick, up the ladder of threshold theorems for life, before we end up an error model in some more advanced creatures slow intelligent mind!