In the spring of 2017, Urmila Mahadev found herself in what most graduate students would consider a pretty sweet position. She had just solved a major problem in quantum computation, the study of computers that derive their power from the strange laws of quantum physics. Combined with her earlier papers, Mahadev’s new result, on what is called blind computation, made it “clear she was a rising star,” said Scott Aaronson, a computer scientist at the University of Texas, Austin.

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Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

Mahadev, who was 28 at the time, was already in her seventh year of graduate school at the University of California, Berkeley — long past the stage when most students become impatient to graduate. Now, finally, she had the makings of a “very beautiful Ph.D. dissertation,” said Umesh Vazirani, her doctoral adviser at Berkeley.

But Mahadev did not graduate that year. She didn’t even consider graduating. She wasn’t finished.

For more than five years, she’d had a different research problem in her sights, one that Aaronson called “one of the most basic questions you can ask in quantum computation.” Namely: If you ask a quantum computer to perform a computation for you, how can you know whether it has really followed your instructions, or even done anything quantum at all?

This question may soon be far from academic. Before too many years have elapsed, researchers hope, quantum computers may be able to offer exponential speedups on a host of problems, from modeling the behavior around a black hole to simulating how a large protein folds up.

But once a quantum computer can perform computations a classical computer can’t, how will we know if it has done them correctly? If you distrust an ordinary computer, you can, in theory, scrutinize every step of its computations for yourself. But quantum systems are fundamentally resistant to this kind of checking. For one thing, their inner workings are incredibly complex: Writing down a description of the internal state of a computer with just a few hundred quantum bits (or “qubits”) would require a hard drive larger than the entire visible universe.

And even if you somehow had enough space to write down this description, there would be no way to get at it. The inner state of a quantum computer is generally a superposition of many different non-quantum, “classical” states (like Schrödinger’s cat, which is simultaneously dead and alive). But as soon as you measure a quantum state, it collapses into just one of these classical states. Peer inside a 300-qubit quantum computer, and essentially all you will see is 300 classical bits — zeros and ones — smiling blandly up at you.

“A quantum computer is very powerful, but it’s also very secretive,” Vazirani said.

Given these constraints, computer scientists have long wondered whether it is possible for a quantum computer to provide any ironclad guarantee that it really has done what it claimed. “Is the interaction between the quantum and the classical worlds strong enough so that a dialogue is possible?” asked Dorit Aharonov, a computer scientist at the Hebrew University of Jerusalem.

During her second year of graduate school, Mahadev became captivated by this problem, for reasons even she doesn’t fully understand. In the years that followed, she tried one approach after another. “I’ve had a lot of moments where I think I’m doing things right, and then they break, either very quickly or after a year,” she said.

But she refused to give up. Mahadev displayed a level of sustained determination that Vazirani has never seen matched. “Urmila is just absolutely extraordinary in this sense,” he said.

Now, after eight years of graduate school, Mahadev has succeeded. She has come up with an interactive protocol by which users with no quantum powers of their own can nevertheless employ cryptography to put a harness on a quantum computer and drive it wherever they want, with the certainty that the quantum computer is following their orders. Mahadev’s approach, Vazirani said, gives the user “leverage that the computer just can’t shake off.”

For a graduate student to achieve such a result as a solo effort is “pretty astounding,” Aaronson said.

Mahadev, who is now a postdoctoral researcher at Berkeley, presented her protocol recently at the annual Symposium on Foundations of Computer Science, one of theoretical computer science’s biggest conferences, held this year in Paris. Her work has been awarded the meeting’s “best paper” and “best student paper” prizes, a rare honor for a theoretical computer scientist.

In a blog post, Thomas Vidick, a computer scientist at the California Institute of Technology who has collaborated with Mahadev in the past, called her result “one of the most outstanding ideas to have emerged at the interface of quantum computing and theoretical computer science in recent years.”

Quantum computation researchers are excited not just about what Mahadev’s protocol achieves, but also about the radically new approach she has brought to bear on the problem. Using classical cryptography in the quantum realm is a “truly novel idea,” Vidick wrote. “I expect many more results to continue building on these ideas.”

A Long Road

Raised in Los Angeles in a family of doctors, Mahadev attended the University of Southern California, where she wandered from one area of study to another, at first convinced only that she did not want to become a doctor herself. Then a class taught by the computer scientist Leonard Adleman, one of the creators of the famous RSA encryption algorithm, got her excited about theoretical computer science. She applied to graduate school at Berkeley, explaining in her application that she was interested in all aspects of theoretical computer science — except for quantum computation.

“It sounded like the most foreign thing, the thing I knew least about,” she said.

But once she was at Berkeley, Vazirani’s accessible explanations soon changed her mind. He introduced her to the question of finding a protocol for verifying a quantum computation, and the problem “really fired up her imagination,” Vazirani said.

“Protocols are like puzzles,” Mahadev explained. “To me, they seem easier to get into than other questions, because you can immediately start thinking of protocols yourself and then breaking them, and that lets you see how they work.” She chose the problem for her doctoral research, launching herself on what Vazirani called “a very long road.”

If a quantum computer can solve a problem that a classical computer cannot, that doesn’t automatically mean the solution will be hard to check. Take, for example, the problem of factoring large numbers, a task that a big quantum computer could solve efficiently, but which is thought to be beyond the reach of any classical computer. Even if a classical computer can’t factor a number, it can easily check whether a quantum computer’s factorization is correct — it just needs to multiply the factors together and see if they produce the right answer.

Yet computer scientists believe (and have recently taken a step toward proving) that many of the problems a quantum computer could solve do not have this feature. In other words, a classical computer not only cannot solve them, but cannot even recognize whether a proposed solution is correct. In light of this, around 2004, Daniel Gottesman — a physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario — posed the question of whether it is possible to come up with any protocol by which a quantum computer can prove to a non-quantum observer that it really has done what it claimed.

Within four years, quantum computation researchers had achieved a partial answer. It is possible, two different teams showed, for a quantum computer to prove its computations, not to a purely classical verifier, but to a verifier who has access to a very small quantum computer of her own. Researchers later refined this approach to show that all the verifier needs is the capacity to measure a single qubit at a time.

And in 2012, a team of researchers including Vazirani showed that a completely classical verifier could check quantum computations if they were carried out by a pair of quantum computers that can’t communicate with each other. But that paper’s approach was tailored to this specific scenario, and the problem seemed to hit a dead end there, Gottesman said. “I think there were probably people who thought you couldn’t go further.”

It was around this time that Mahadev encountered the verification problem. At first, she tried to come up with an “unconditional” result, one that makes no assumptions about what a quantum computer can or cannot do. But after she had worked on the problem for a while with no progress, Vazirani proposed instead the possibility of using “post-quantum” cryptography — that is, cryptography that researchers believe is beyond the capability of even a quantum computer to break, although they don’t know for sure. (Methods such as the RSA algorithm that are used to encrypt things like online transactions are not post-quantum — a large quantum computer could break them, because their security depends on the hardness of factoring large numbers.)

In 2016, while working on a different problem, Mahadev and Vazirani made an advance that would later prove crucial. In collaboration with Paul Christiano, a computer scientist now at OpenAI, a company in San Francisco, they developed a way to use cryptography to get a quantum computer to build what we’ll call a “secret state” — one whose description is known to the classical verifier, but not to the quantum computer itself.

Their procedure relies on what’s called a “trapdoor” function — one that is easy to carry out, but hard to reverse unless you possess a secret cryptographic key. (The researchers didn’t know how to actually build a suitable trapdoor function yet — that would come later.) The function is also required to be “two-to-one,” meaning that every output corresponds to two different inputs. Think, for example of the function that squares numbers — apart from the number 0, each output (such as 9) has two corresponding inputs (3 and −3).

Armed with such a function, you can get a quantum computer to create a secret state as follows: First, you ask the computer to build a superposition of all the possible inputs to the function (this might sound complicated for the computer to carry out, but it’s actually easy). Then, you tell the computer to apply the function to this giant superposition, creating a new state that is a superposition of all the possible outputs of the function. The input and output superpositions will be entangled, which means that a measurement on one of them will instantly affect the other.

Next, you ask the computer to measure the output state and tell you the result. This measurement collapses the output state down to just one of the possible outputs, and the input state instantly collapses to match it, since they are entangled — for instance, if you use the squaring function, then if the output is the 9 state, the input will collapse down to a superposition of the 3 and −3 states.

But remember that you’re using a trapdoor function. You have the trapdoor’s secret key, so you can easily figure out the two states that make up the input superposition. But the quantum computer cannot. And it can’t simply measure the input superposition to figure out what it is made of, because that measurement would collapse it further, leaving the computer with one of the two inputs but no way to figure out the other.

In 2017, Mahadev figured out how to build the trapdoor functions at the core of the secret-state method by using a type of cryptography called Learning With Errors (LWE). Using these trapdoor functions, she was able to create a quantum version of “blind” computation, by which cloud-computing users can mask their data so the cloud computer can’t read it, even while it is computing on it. And shortly after that, Mahadev, Vazirani and Christiano teamed up with Vidick and Zvika Brakerski (of the Weizmann Institute of Science in Israel) to refine these trapdoor functions still further, using the secret-state method to develop a foolproof way for a quantum computer to generate provably random numbers.

Mahadev could have graduated on the strength of these results, but she was determined to keep working until she had solved the verification problem. “I was never thinking of graduation, because my goal was never graduation,” she said.

Not knowing whether she would be able to solve it was stressful at times. But, she said, “I was spending time learning about things that I was interested in, so it couldn’t really be a waste of time.”

Set in Stone

Mahadev tried various ways of getting from the secret-state method to a verification protocol, but for a while she got nowhere. Then she had a thought: Researchers had already shown that a verifier can check a quantum computer if the verifier is capable of measuring quantum bits. A classical verifier lacks this capability, by definition. But what if the classical verifier could somehow force the quantum computer to perform the measurements itself and report them honestly?

The tricky part, Mahadev realized, would be to get the quantum computer to commit to which state it was going to measure before it knew which kind of measurement the verifier would ask for — otherwise, it would be easy for the computer to fool the verifier. That’s where the secret-state method comes into play: Mahadev’s protocol requires the quantum computer to first create a secret state and then entangle it with the state it is supposed to measure. Only then does the computer find out what kind of measurement to perform.

Since the computer doesn’t know the makeup of the secret state but the verifier does, Mahadev showed that it’s impossible for the quantum computer to cheat significantly without leaving unmistakable traces of its duplicity. Essentially, Vidick wrote, the qubits the computer is to measure have been “set in cryptographic stone.” Because of this, if the measurement results look like a correct proof, the verifier can feel confident that they really are.

“It is such a wonderful idea!” Vidick wrote. “It stuns me every time Urmila explains it.”

Mahadev’s verification protocol — along with the random-number generator and the blind encryption method — depends on the assumption that quantum computers cannot crack LWE. At present, LWE is widely regarded as a leading candidate for post-quantum cryptography, and it may soon be adopted by the National Institute of Standards and Technology as its new cryptographic standard, to replace the ones a quantum computer could break. That doesn’t guarantee that it really is secure against quantum computers, Gottesman cautioned. “But so far it’s solid,” he said. “No one has found evidence that it’s likely to be breakable.”

In any case, the protocol’s reliance on LWE gives Mahadev’s work a win-win flavor, Vidick wrote. The only way that a quantum computer could fool the protocol is if someone in the quantum computing world figured out how to break LWE, which would itself be a remarkable achievement.

Mahadev’s protocol is unlikely to be implemented in a real quantum computer in the immediate future. For the time being, the protocol requires too much computing power to be practical. But that could change in the coming years, as quantum computers get larger and researchers streamline the protocol.

Mahadev’s protocol probably won’t be feasible within, say, the next five years, but “it is not completely off in fantasyland either,” Aaronson said. “It is something you could start thinking about, if all goes well, at the next stage of the evolution of quantum computers.”

And given how quickly the field is now moving, that stage could arrive sooner rather than later. After all, just five years ago, Vidick said, researchers thought that it would be many years before a quantum computer could solve any problem that a classical computer cannot. “Now,” he said, “people think it’s going to happen in a year or two.”

As for Mahadev, solving her favorite problem has left her feeling a bit at sea. She wishes she could understand just what it was about that problem that made it right for her, she said. “I have to find a new question now, so it would be nice to know.”

But theoretical computer scientists see Mahadev’s unification of quantum computation and cryptography not so much as the end of a story, but as the initial exploration of what will hopefully prove a rich vein of ideas.

“My feeling is that there are going to be lots of follow-ups,” Aharonov said. “I’m looking forward to more results from Urmila.”

Original story reprinted with permission from Quanta Magazine, an editorially independent division of whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

You Can Power a Calculator With Some LEDs

March 20, 2019 | Story | No Comments

Suppose you are getting ready to take a physics test. Everything is set—but wait! Your calculator battery died. What do you do? If you're extra crafty, you could grab an LED (light-emitting diode) and use it to get your calculator to function again. I know this seems crazy, but it's true. In fact, I did indeed run a calculator using some LEDs, which I will show you below.

Of course, to really understand how this works we need to look at what an LED actually is. I'm sure you have a few in the smartphone in your pocket. Many video displays use LEDs. It's very possible you've got one screwed into your ceiling light. They are everywhere.

Let's start off with just a diode. A diode is a device that is made from two types of semiconductors that are connected together. In one of the semiconductors, there are extra electrons (negative charges) that can move around to make the material a conductor. We call this an n-type semiconductor (the n stands for negative). The other type of material is called a p-type semiconductor. I bet you can guess what the p stands for—yup, positive charges. In the p-type there are actually atoms with missing electrons. These are called positive holes because an electron should be there. But these holes essentially behave like a positive charge.

When you put a p-type together with an n-type, you get a diode. If a current of negative electrons (which is the way most electrical currents work) enters the n-type side of the diode, everything works fine. The negative electrons can move through the n-type part of the diode with no problems. When these charges get to the p-type side, they combine with a positive hole (they fill in the holes). This makes it look as if a positive hole is moving in the opposite direction as the negative charge, such that there is a constant current across the diode.

If you switch the direction of the electric current, something different happens. To do that, you have to change the direction of the electric field inside the diode. This field then pushes the negative charges in the n-type and the positive holes in the p-type farther apart. Now it is much harder for the n's and p's to combine, so you essentially get no current.

That's the essence of a diode. Current can go one way through it, but not the other way. But wait! What about the light part? It turns out that a negative charge in the n-type side has a greater energy than the positive holes in the p-type side. So when a negative charge combines with a hole, there is a decrease in energy for the charge. Since energy has to be conserved, that energy has to go somewhere. It does. It makes light.

It's actually even crazier that that. It turns out that the frequency of the light produced is proportional to the change in energy. Yes, this is from quantum mechanics, but it is still real. Here is that relationship:

In this expression, ΔE is the change in energy of the electron and f is the frequency of light. The h is Planck's constant—it's kind of a big deal in quantum mechanics. But that is your LED, the light-emitting diode. I use them. You use them. Everyone uses them. They are great for lights because they mostly just create light and don't get very hot like incandescent or fluorescent bulbs.

Now let's get super crazy. What if you take an LED and you don't connect it to a battery? Instead you connect the LED to a voltmeter and measure the electric potential across the leads of the LED? Check this out.

Notice that by connecting the LED to the voltmeter, you get a voltage right away. This LED comes from an overhead light. When I cover up the LED, the voltage drops. Shining a bright light increases the voltage quite a bit. But why? Essentially, the diode is acting like a solar panel. OK, it IS a solar panel. The light gives energy to the electrons in the n-type material so that it has enough energy to move to the p-type side. This movement of charges builds up a potential difference (it's essentially acting like a capacitor here) so that you get voltage.

In case you can't tell, I think this is awesome. The LED is a two-way device. Run a current through and you get light. Shine light on it and you can get an electric current (if you connect it to something). OK. Game on. Can I use some LEDs to power something? In fact, YES. Check this out. Here are a bunch of LEDs connected in parallel such that the current from each LED adds to the total current. This LED bank is connected to a solar power calculator with the solar cell removed.

It works. OK, I had plans for something bigger. I wanted to have this run some tiny electric motor, but I couldn't get it to work. The calculator is pretty low power so it's perfect for this job.

But wait. If an LED can be both a light and a solar panel, can a solar panel also be a light? Apparently, yes. I didn't get this to work, but I've been told that if you connect a solar panel to a power supply, it will glow. Oh, you can't see it—it glows in the near infrared (like your TV remote). This means you will need a camera without an infrared filter to see it. I'm going to keep trying with this.

Let me tell you my real plan (since it didn't work). I was going to connect a motor to an LED and shine a light on the LED to run the motor. Then I was going to turn the motor really fast so that it acts like a generator and lights up the LED. That would be pretty cool.

Yes, an electric motor and an electric generator are the same thing. If you run current through it, it spins. If you spin it, you can get a current. Boom. Double duty. There are other devices that go both ways. What about the speaker? If you connect a speaker to the audio input on your computer, it acts as a microphone. Also, there is the TEG (thermoelectric generator). This is a device that is essentially just two different metals connected together. If you heat up one of the metals you can create an electric current. This sort of device is used with spacecraft (and a radioactive source for heat) to provide deep-space power. However, if you take this same device and run current through it, one side gets hot and one side gets cold. It's an electric cooler with zero moving parts.

So, now I'm adding the LED to this list of dual-purpose devices. Now I just need to figure out how to build an LED solar panel from scratch. That will be fun.

Cannabis strain names can get a bit … quirky (Lamb’s Bread, anyone?). But without them, patients that rely on marijuana to treat ailments like pain would be lost. If you want to treat seizures, you might want ACDC—a strain that expresses almost zero THC and very high CBD, a non-psychoactive cannabinoid—and stay away from the potentially panic-inducing Ghost OG, which verges on 25 percent THC.

Unfortunately, there isn’t an official federal database with information about cannabis strains, for obvious reasons. After all, this hasn’t been a regulated industry—you’re not allowed to call a Gala apple a Red Delicious, but no one is stopping you from calling your crop ACDC when it is in fact Ghost OG. It’s a big problem examined in a new study, posted to the preprint site BioRxiv, from the University of Northern Colorado. Researchers there bought samples of 30 separate cannabis strains, several for each, from dispensaries and compared them genetically.

Almost every strain, they found, had at least one sample that was a genetic mismatch (aka an imposter). And while strains did fall generally into one of two genetic groups, they didn’t fall neatly into the well-popularized dichotomy of indica and sativa.

The researchers looked at commonly used genetic markers called microsatellites, which have a high rate of mutation. Those mutations make it easier for scientists to identify differences between individuals. The researchers got their hands on as many as nine and as few as two samples of each strain, and compared them genetically in this way.

Cannabis strains are genetically unique because for decades, growers—particularly in Northern California’s famous Emerald Triangle, which provides perhaps three quarters of the marijuana in the US—have developed varieties of the cannabis plant by selecting for desirable traits. If you’ve got an individual plant that produces more THC, or grows faster, or produces bigger buds, you can take a cutting of that individual and grow a new plant from it. That’d make it a clone, genetically identical to its mother.

That results in unique strains that the researchers could sample genetically. “Out of the 30 strains, there were only four that were genetically consistent,” says geneticist Anna Schwabe, lead author on the paper. Something was awry. It could be that the grower sincerely believed they were growing Durban Poison, but in fact had a slightly different strain—or that somewhere in the process the product was mislabeled.

“It's not necessarily that somebody is doing anything malicious,” Schwabe says. Growers typically identifying their strains by smell, or color of their buds. “But because there are so many strains, it starts to get really hard to correctly identify plants based on their morphological characteristics.”

Then the answer is cloning, right? Get what you know is Purple Kush and just take cuttings of your mother plant to clone it. Not so fast. Sure, you’d get the right genetics, but genes aren’t everything. Even if you know you have Purple Kush, it can express different traits depending on environmental factors like light. “When you hear these cultivators like, ‘Oh I've had the same mother plant for 10 years,’ well, you definitely weren't producing the same clones all the time,” says Jeff Raber, CEO of the Werc Shop, a lab that tests cannabis, “because it's a different mother the second time you go back because you stressed the daylights out of her taking the first round of clones.”

Really, this variability isn’t unique to cannabis. Depending on where and how it’s grown, a particular variety of apple will vary as well. We still call a Red Delicious apple a Red Delicious, even if it isn’t as red or delicious as we expect.

So this is not a call to abolish cannabis strain naming conventions. “We need names,” says Jonathan Page, CEO of Anandia Labs, who coauthored a previous study showing genetic inconsistencies in cannabis strains. “In every other thing we consume—whether it's wine and merlot, Red Delicious apples, or cherry tomatoes—we name things.”

This new study also found problems with the famous indica-sativa cannabis divide—indica strains are supposedly more for sleepy times while sativa is supposedly more uplifting. You’d expect, then, for strains to map neatly to one of the two groups. While the study did find two genetic groups, they didn’t correspond well to known indica or sativa strains. For example, the researchers found that Grape Ape, an indica strain, didn’t assign particularly well to either of these novel genetic groups. “There's not very much evidence to support the widespread use of indica, sativa, and hybrid in classifying cannabis,” says Page. “However, they did find in this paper a suggestion of certain genotypes to which strains can be more closely related.”

“The other issue to keep in mind is that these things have been crossed by humans for a long time,” says plant evolutionary biologist Mitchell McGlaughlin, coauthor on the new paper. One theory holds that sativa and indica are separate species that were once geographically isolated. “That very well could be true, but then when you have hundreds if not thousands of years of humans then modifying that plant and making crosses—and in the wild this would be a wind-pollinated plant with pollen traveling reasonable distances—you then end up with issues where that historic signal has been lost.”

There are some caveats to consider with this new study, though. Again, the cannabis sample sizes here were small—as few as two for some strains. Because it’s preprint, it hasn’t been peer reviewed, the gold standard in scientific publishing. And microsatellites aren’t the only way to go about genetically testing cannabis—Page’s study, for instance, looked more broadly at the genomes, while microsatellites are a more targeted approach on those mutation-prone regions.

“They might be right, but far too many people in this field are using shady sub-par genomic methods to make claims that they are the arbiter of cannabis truth without subjecting their methods to peer review before doing so,” says Kevin McKernan, chief science officer of cannabis lab Medicinal Genomics.

These are very early days for cannabis research. But this study also shows how research like this is finally getting easier. Historically, the University of Mississippi has been the sole provider of research cannabis, and the quality ain’t super. But because marijuana is legal in Colorado, these researchers could procure their own samples of unique strains. Better access means better research—and a better understanding of the genetics that code for what is still one of the most mysterious plants on Earth.

Friday morning began with delays at New York’s LaGuardia Airport. That’s not unusual—New York’s airports are famously balky. But this time, the cause wasn't something prosaic, like a blizzard. It was staffing. Because of the federal government shutdown, the airport didn’t have enough Transportation Security Administration agents and air traffic controllers; things slowed to a ground stop.

Then it started to spread—Newark, Philadelphia, even the key hub of Atlanta all began to wind down. And that’s terrifying. Airports are nodes on a global network, and the science that guides how that network behaves means that if one node has a problem, that problem will spread. The international air travel network exists on something of a knife-edge. It doesn’t take much to knock it out of optimal flow.

Basically, the delay problem is one of "connected resources"; planes land and have to get turned around to perform other flights, and some of the passengers on them are getting onto other flights, too. If you’ve ever flown, you know all that, but what it means in practice is that small mistakes or delays at one airport get magnified as they move down the line, propagating and sometimes intensifying. “The systems operating these queues are very close to capacity,” says Hamsa Balakrishnan, an aerospace engineer at MIT who studies the air transport network. “Both LaGuardia and Newark had wind-related delays today. With full staffing you might have been able to manage, but with a decrease in staffing as well you have delays, which then end up spreading to other airports as well, because of connectivity.”

Typically you might expect that the biggest airports in the world—the ones with the most flights in and out, say, or that move the most people—would have the biggest effect on overall movement across the network. But in fact, an airport’s “delay propagation multiplier” varies depending on all kinds of things, from how an airport is scheduled to its overall capacity, and even the weather. By one calculation, a minute of delay causes an average of 30 seconds of slowdown elsewhere in the network. But some airports are more resilient than others. The time it takes to get from one to the other has an effect. It’s so complicated that it daunts even the most intrepid network modelers.

Airlines try to account for all this by building slack into the schedule. They calculate the amount of time a given flight should take—the “scheduled block time”—and the amount of time the plane should have to spend on the ground, the “scheduled turnaround time.” But then they have a choice. “They insert buffer time in their schedules and ground operations,” says Bo Zou, a transportation engineer at the University of Illinois. “They still encounter delays, and a newly formed delay for one flight will propagate to the second and third flights. Part of it will be absorbed by the buffer, but not all of it.” Build too small a buffer, and the delays propagate further. Build too large a buffer and you’re not using your fleet efficiently, and losing money. “One side is efficiency, the other is robustness,” Zou says.

And it changes all the time, depending on changing conditions—some are predictable, like winter storms, and some are not, like government shutdowns and informal sick-outs. That’s called a “dynamical complex network.” It has to adapt, constantly.

Because if it doesn’t? According to one study, flight delays cost the US economy over $30 billion a year. It’s not just lost time or flight expenses; it’s whatever the people on those flights were planning on doing when they arrived. “A prolonged shutdown, or even slow down, would likely affect all kinds of unforeseen things,” says Luís Bettencourt, a network scientist at the University of Chicago. “The reliability of time­-sensitive logistics will degrade, and the hub character of some of these cities will have to be bypassed, at least temporarily. A prolonged slow down would be most disastrous to large cities, their influence, and their economies.”

Having shut down the shutdown, the government can now get its TSA agents and air traffic controllers back on station. That’ll build some resilience back into the airports just in time for a big-ass snowstorm due to hit the midwest next week. But the overall health of the air travel network will still be precarious.

That’s why researchers are working on accumulating more and more data on how it all works (or doesn’t). If humans can’t schedule all these flights in an efficient and robust way, maybe an algorithm can. Balakrishnan has even cofounded a startup that’s trying to make it happen. “There are so many moving pieces that it’s hard for a human being to come up with all possible solutions,” she says. “But that’s something we know how to get computers to do.” If you enjoy flying on an intractable and incomprehensible network now, wait until it’s run by an intractable, incomprehensible robot.