What are the prime factors, or multipliers, for the number 15? Most grade school students know the answer — 3 and 5 — by memory. A larger number, such as 91, may take some pen and paper. An even larger number, say with 232 digits, can (and has) taken scientists two years to factor, using hundreds of classical computers operating in parallel. Because factoring large numbers is so devilishly hard, this “factoring problem” is the basis for many encryption schemes for protecting credit cards, state secrets and other confidential data. It’s thought that a single quantum computer may easily crack this problem, by using hundreds of atoms, essentially in parallel, to quickly factor huge numbers. In 1994, Peter Shor, the Morss Professor of Applied Mathematics at MIT, came up with a quantum algorithm that calculates the prime factors of a large number, vastly more efficiently than a classical computer. However, the algorithm’s success depends on a computer with a large number of quantum bits. While others have attempted to implement Shor’s algorithm in various quantum systems, none have been able to do so with more than a few quantum bits, in a scalable way. Now, in a paper published March 3, 2016, in the journal Science, researchers from MIT and the University of Innsbruck in Austria report that they have designed and built a quantum computer from five atoms in an ion trap. The computer uses laser pulses to carry out Shor’s algorithm on each atom, to correctly factor the number 15. The system is designed in such a way that more atoms and lasers can be added to build a bigger and faster quantum computer, able to factor much larger numbers. The results, they say, represent the first scalable implementation of Shor’s algorithm. “We show that Shor’s algorithm, the most complex quantum algorithm known to date, is realizable in a way where, yes, all you have to do is go in the lab, apply more technology, and you should be able to make a bigger quantum computer,” says Isaac Chuang, professor of physics and professor of electrical engineering and computer science at MIT. “It might still cost an enormous amount of money to build — you won’t be building a quantum computer and putting it on your desktop anytime soon — but now it’s much more an engineering effort, and not a basic physics question.” Seeing through the quantum forest In classical computing, numbers are represented by either 0s or 1s, and calculations are carried out according to an algorithm’s “instructions,” which manipulate these 0s and 1s to transform an input to an output. In contrast, quantum computing relies on atomic-scale units, or “qubits,” that can be simultaneously 0 and 1 — a state known as a superposition. In this state, a single qubit can essentially carry out two separate streams of calculations in parallel, making computations far more efficient than a classical computer. In 2001, Chuang, a pioneer in the field of quantum computing, designed a quantum computer based on one molecule that could be held in superposition and manipulated with nuclear magnetic resonance to factor the number 15. The results, which were published in Nature, represented the first experimental realization of Shor’s algorithm. But the system wasn’t scalable; it became more difficult to control the system as more atoms were added. “Once you had too many atoms, it was like a big forest — it was very hard to control one atom from the next one,” Chuang says. “The difficulty is to implement [the algorithm] in a system that’s sufficiently isolated that it can stay quantum mechanical for long enough that you can actually have a chance to do the whole algorithm.” Chuang and his colleagues have now come up with a new, scalable quantum system for factoring numbers efficiently. While it typically takes about 12 qubits to factor the number 15, they found a way to shave the system down to five qubits, each represented by a single atom. Each atom can be held in a superposition of two different energy states simultaneously. The researchers use laser pulses to perform “logic gates,” or components of Shor’s algorithm, on four of the five atoms. The results are then stored, forwarded, extracted, and recycled via the fifth atom, thereby carrying out Shor’s algorithm in parallel, with fewer qubits than is typically required. The team was able to keep the quantum system stable by holding the atoms in an ion trap, where they removed an electron from each atom, thereby charging it. They then held each atom in place with an electric field. “That way, we know exactly where that atom is in space,” Chuang explains. “Then we do that with another atom, a few microns away — [a distance] about 100th the width of a human hair. By having a number of these atoms together, they can still interact with each other, because they’re charged. That interaction lets us perform logic gates, which allow us to realize the primitives of the Shor factoring algorithm. The gates we perform can work on any of these kinds of atoms, no matter how large we make the system.” Chuang’s team first worked out the quantum design in principle. His colleagues at the University of Innsbruck then built an experimental apparatus based on his methodology. They directed the quantum system to factor the number 15 — the smallest number that can meaningfully demonstrate Shor’s algorithm. Without any prior knowledge of the answers, the system returned the correct factors, with a confidence exceeding 99 percent. “In future generations, we foresee it being straightforwardly scalable, once the apparatus can trap more atoms and more laser beams can control the pulses,” Chuang says. “We see no physical reason why that is not going to be in the cards.” Mark Ritter, senior manager of physical sciences at IBM, says the group’s method of recycling qubits reduces the resources required in the system by a factor of 3 — a significant though small step towards scaling up quantum computing. “Improving the state-of-the-art by a factor of 3 is good,” says Ritter. But truly scaling the system “requires orders of magnitude more qubits, and these qubits must be shuttled around advanced traps with many thousands of simultaneous laser control pulses.” If the team can successfully add more quantum components to the system, Ritter says it will have accomplished a long-unrealized feat. “Shor's algorithm was the first non-trivial quantum algorithm showing a potential of ‘exponential’ speed-up over classical algorithms,” Ritter says. “It captured the imagination of many researchers who took notice of quantum computing because of its promise of truly remarkable algorithmic acceleration. Therefore, to implement Shor's algorithm is comparable to the ‘Hello, World’ of classical computing.” What will all this eventually mean for encryption schemes of the future? “Well, one thing is that if you are a nation state, you probably don’t want to publicly store your secrets using encryption that relies on factoring as a hard-to-invert problem,” Chuang says. “Because when these quantum computers start coming out, you’ll be able to go back and unencrypt all those old secrets.” This research was supported, in part, by the Intelligence Advanced Research Project Activity (IARPA), and the MIT-Harvard Center for Ultracold Atoms, a National Science Foundation Physics Frontier Center.
Why the brain is folded can be rationalized easily from an evolutionary perspective; folded brains likely evolved to fit a large cortex into a small volume with the benefit of reducing neuronal wiring length and improving cognitive function. Less understood is how the brain folds. Several hypotheses have been proposed but none have been directly used to make testable predictions. Now, researchers at the Harvard John A. Paulson School of Engineering and Applied Sciences collaborating with scientists in Finland and France have shown that while many molecular processes are important in determining cellular events, what ultimately causes the brain to fold is a simple mechanical instability associated with buckling. The research is published in Nature Physics. Understanding how the brain folds could help unlock the inner workings of the brain and unravel brain-related disorders, as function often follows form. "We found that we could mimic cortical folding using a very simple physical principle and get results qualitatively similar to what we see in real fetal brains," said L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, Organismic and Evolutionary Biology, and Physics. The number, size, shape and position of neuronal cells during brain growth all lead to the expansion of the gray matter, known as the cortex, relative to the underlying white matter. This puts the cortex under compression, leading to a mechanical instability that causes it to crease locally. "This simple evolutionary innovation, with iterations and variations, allows for a large cortex to be packed into a small volume, and is likely the dominant cause behind brain folding, known as gyrification," said Mahadevan, who is also a core faculty member of the Wyss Institute for Biologically Inspired Engineering, and member of the Kavli Institute for Bionano Science and Technology, at Harvard University. Mahadevan's previous research found that the growth differential between the brain's outer cortex and the soft tissue underneath explains the variations in the folding patterns across organisms in terms of just two parameters, the relative size of the brain, and the relative expansion of the cortex. Building on this, the team collaborated with neuroanatomists and radiologists in France and directly tested this theory using data from human fetuses. The team made a three-dimensional, gel model of a smooth fetal brain based on MRI images. The model's surface was coated with a thin layer of elastomer gel, as an analog of the cortex. To mimic cortical expansion, the gel brain was immersed in a solvent that is absorbed by the outer layer causing it to swell relative to the deeper regions. Within minutes of being immersed in liquid solvent, the resulting compression led to the formation of folds similar in size and shape to real brains. The extent of the similarities surprised even the researchers. "When I put the model into the solvent, I knew there should be folding but I never expected that kind of close pattern compared to human brain," said Jun Young Chung, post doctoral fellow and co-first author of the paper. "It looks like a real brain." The key to those similarities lies in the unique shape of the human brain. "The geometry of the brain is really important because it serves to orient the folds in certain directions," said Chung. "Our model, which has the same large scale geometry and curvature as a human brain, leads to the formation of folds that matches those seen in real fetal brains quite well." The largest folds seen in the model gel brain are similar in shape, size and orientation to what is seen in the fetal brain, and can be replicated in multiple gel experiments. The smallest folds are not conserved, mirroring similar variations across human brains. "Brains are not exactly the same from one human to another, but we should all have the same major folds in order to be healthy," said Chung. "Our research shows that if a part of the brain does not grow properly, or if the global geometry is disrupted, we may not have the major folds in the right place, which may cause dysfunction in the brain. " Explore further: Simple origami fold may hold the key to designing pop-up furniture, medical devices and scientific tools
Home > Press > Designing a pop-up future: Simple origami fold may hold the key to designing pop-up furniture, medical devices and scientific tools Abstract: What if you could make any object out of a flat sheet of paper? That future is on the horizon thanks to new research by L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, Organismic and Evolutionary Biology, and Physics at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS). He is also a core faculty member of the Wyss Institute for Biologically Inspired Engineering, and member of the Kavli Institute for Bionano Science and Technology, at Harvard University. Mahadevan and his team have characterized a fundamental origami fold, or tessellation, that could be used as a building block to create almost any three-dimensional shape, from nanostructures to buildings. The research is published in Nature Materials. The folding pattern, known as the Miura-ori, is a periodic way to tile the plane using the simplest mountain-valley fold in origami. It was used as a decorative item in clothing at least as long ago as the 15th century. A folded Miura can be packed into a flat, compact shape and unfolded in one continuous motion, making it ideal for packing rigid structures like solar panels. It also occurs in nature in a variety of situations, such as in insect wings and certain leaves. "Could this simple folding pattern serve as a template for more complicated shapes, such as saddles, spheres, cylinders, and helices?" asked Mahadevan. "We found an incredible amount of flexibility hidden inside the geometry of the Miura-ori," said Levi Dudte, graduate student in the Mahadevan lab and first author of the paper. "As it turns out, this fold is capable of creating many more shapes than we imagined." Think surgical stents that can be packed flat and pop-up into three-dimensional structures once inside the body or dining room tables that can lean flat against the wall until they are ready to be used. "The collapsibility, transportability and deployability of Miura-ori folded objects makes it a potentially attractive design for everything from space-bound payloads to small-space living to laparoscopic surgery and soft robotics," said Dudte. To explore the potential of the tessellation, the team developed an algorithm that can create certain shapes using the Miura-ori fold, repeated with small variations. Given the specifications of the target shape, the program lays out the folds needed to create the design, which can then be laser printed for folding. The program takes into account several factors, including the stiffness of the folded material and the trade-off between the accuracy of the pattern and the effort associated with creating finer folds - an important characterization because, as of now, these shapes are all folded by hand. "Essentially, we would like to be able to tailor any shape by using an appropriate folding pattern," said Mahadevan. "Starting with the basic mountain-valley fold, our algorithm determines how to vary it by gently tweaking it from one location to the other to make a vase, a hat, a saddle, or to stitch them together to make more and more complex structures." "This is a step in the direction of being able to solve the inverse problem - given a functional shape, how can we design the folds on a sheet to achieve it," Dudte said. "The really exciting thing about this fold is it is completely scalable," said Mahadevan. "You can do this with graphene, which is one atom thick, or you can do it on the architectural scale." ### Co-authors on the study include Etienne Vouga, currently at the University of Texas at Austin, and Tomohiro Tachi from the University of Tokyo. The work was funded by the Wyss Institute for Bioinspired Engineering, the Kavli Institute for Bionano Science and Technology, and the Harvard MRSEC. For more information, please click If you have a comment, please us. Issuers of news releases, not 7th Wave, Inc. or Nanotechnology Now, are solely responsible for the accuracy of the content.
Music functions as a universal connector that pervades most cultures. More specifically, rhythm and synchronization — both within and beyond the realm of music — are forms of communication that stimulate brain activity. In a recently-published paper in the SIAM Journal on Applied Mathematics, authors Donald Drew, Kevin Dolch and Maury Castro propose a stochastic differential equation model that simulates how musical performers in a large ensemble sustain tempo and phase while responding to a conductor, other musicians and additional distractions modeled as “noise.” In an ideal situation, musicians would be able to perfectly coordinate the rate of change at which pitch and relative loudness occur while simultaneously ignoring noise and the distractions of the other musicians. However, the authors recognize that the aforementioned stimuli cause execution errors from each individual. The authors assume that individual performers preserve an internal tempo when responding to the conductor, who offers the correct rhythm sequence. Their phase correction model assumes that the correction of a rate of error is contingent on the ratio of tempo variation to a performer’s ability to resist noise distraction and concentrate solely on the conductor. The correction model is based on deliberate responses of the human brain when determining tempo and phase, rather than assuming error correction based on biochemical oscillators, as in other models. The authors acknowledge that musical performances involve a certain amount of individual tempo variations to achieve a sense of artistry. But their proposed models offer a means by which to manage tempo discrepancies, improve synchronization, and thus enhance the overall quality of performed music. Citation: Donald Drew, Kevin Dolch, Maury Castro. A Model for Tempo Synchronization in Music Performance. SIAM Journal on Applied Mathematics, 2015; 75 (6): 2540 DOI: 10.1137/140992357 Read the full article Donald Drew is now retired; before retiring he was the Chair of Mathematical Sciences and Professor of Mechanical, Aerospace, and Nuclear Engineering at Rensselaer Polytechnic Institute; Kevin Dolch studied at Rensselaer Polytechnic Institute; Maury Castro is the Organist & Choirmaster and Director of Communications at St. Christopher’s Episcopal Church. About SIAM The Society for Industrial and Applied Mathematics (SIAM), headquartered in Philadelphia, PA, is an international society of more than 14,000 individual, academic and corporate members from 85 countries. SIAM helps build cooperation between mathematics and the worlds of science and technology to solve real-world problems through publications, conferences and communities like chapters, sections and activity groups.
News Article | August 31, 2016
A team led by Nanfang Yu, assistant professor of applied physics at Columbia Engineering, has discovered a new phase-transition optical material and demonstrated novel devices that dynamically control light over a much broader wavelength range and with larger modulation amplitude than what has currently been possible. The team, including researchers from Purdue, Harvard, Drexel, and Brookhaven National Laboratory, found that samarium nickelate (SmNiO3) can be electrically tuned continuously between a transparent and an opaque state over an unprecedented broad range of spectrum from the blue in the visible (wavelength of 400 nm) to the thermal radiation spectrum in the mid-infrared (wavelength of a few tens of micrometers). The study, which is the first investigation of the optical properties of SmNiO and the first demonstration of the material in photonic device applications, is published online in Advanced Materials. “The performance of SmNiO is record-breaking in terms of the magnitude and wavelength range of optical tuning,” Yu says. “There is hardly any other material that offers such a combination of properties that are highly desirable for optoelectronic devices. The reversible tuning between the transparent and opaque states is based on electron doping at room temperature, and potentially very fast, which opens up a wide range of exciting applications, such as ‘smart windows’ for dynamic and complete control of sunlight, variable thermal emissivity coatings for infrared camouflage and radiative temperature control, optical modulators, and optical memory devices.” Some of the potential new functions include using SmNiO ‘s capability in controlling thermal radiation to build “intelligent” coatings for infrared camouflage and thermoregulation. These coatings could make people and vehicles, for example, appear much colder than they actually are and thus indiscernible under a thermal camera at night. The coating could help reduce the large temperature gradients on a satellite by adjusting the relative thermal radiation from its bright and dark side with respect to the sun and thereby prolong the lifetime of the satellite. Because this phase-transition material can potentially switch between the transparent and opaque states with high speed, it may be used in modulators for free-space optical communication and optical radar and in optical memory devices. Researchers have long been trying to build active optical devices that can dynamically control light. These include Boeing 787 Dreamliner’s “smart windows,” which control (but not completely) the transmission of sunlight, rewritable DVD discs on which we can use a laser beam to write and erase data, and high-data-rate, long-distance fiber optic communications systems where information is “written” into light beams by optical modulators. Active optical devices are not more common in everyday life, however, because it has been so difficult to find advanced actively tunable optical materials, and to design proper device architectures that amplify the effects of such tunable materials. When Shriram Ramanathan, associate professor of materials science at Harvard, discovered SmNiO ‘s giant tunable electric resistivity at room temperature, Yu took note. The two met at the IEEE Photonics Conference in 2013 and decided to collaborate. Yu and his students, working with Ramanathan, who is a co-author of this paper, conducted initial optical studies of the phase-transition material, integrated the material into nanostructured designer optical interfaces — “metasurfaces” — and created prototype active optoelectronic devices, including optical modulators that control a beam of light, and variable emissivity coatings that control the efficiency of thermal radiation. “SmNiO is really an unusual material,” says Zhaoyi Li, the paper’s lead author and Yu’s PhD student, “because it becomes electrically more insulating and optically more transparent as it is doped with more electrons — this is just the opposite of common materials such as semiconductors.” It turns out that doped electrons “lock” into pairs with the electrons initially in the material, a quantum mechanical phenomenon called “strong electron correlation,” and this effect makes these electrons unavailable to conduct electric current and absorbing light. So, after electron doping, SmNiO3 thin films that were originally opaque suddenly allow more than 70 percent of visible light and infrared radiation to transmit through. “One of our biggest challenges,” Zhaoyi adds, “was to integrate SmNiO into optical devices. To address this challenge, we developed special nanofabrication techniques to pattern metasurface structures on SmNiO thin films. In addition, we carefully chose the device architecture and materials to ensure that the devices can sustain high temperature and pressure that are required in the fabrication process to activate SmNiO .” Yu and his collaborators plan next to run a systematic study to understand the basic science of the phase transition of SmNiO and to explore its technological applications. The team will investigate the intrinsic speed of phase transition and the number of phase-transition cycles the material can endure before it breaks down. They will also work on addressing technological problems, including synthesizing ultra-thin and smooth films of the material and developing nanofabrication techniques to integrate the material into novel flat optical devices. “This work is one crucial step towards realizing the major goal of my research lab, which is to make an optical interface a functional optical device,” Yu notes. “We envision replacing bulky optical devices and components with ‘flat optics’ by utilizing strong interactions between light and two-dimensional structured materials to control light at will. The discovery of this phase-transition material and the successful integration of it into a flat device architecture are a major leap forward to realizing active flat optical devices not only with enhanced performance from the devices we are using today, but with completely new functionalities.” Yu’s team included Ramanathan, his Harvard PhD student You Zhou, and his Purdue postdoctoral fellow Zhen Zhang, who synthesized the phase-transition material and did some of the phase transition experiments (this work began at Harvard and continued when Ramanathan moved to Purdue); Drexel University Materials Science Professor Christopher Li, PhD student Hao Qi, and research scientist Qiwei Pan, who helped make solid-state devices by integrating SmNiO with novel solid polymer electrolytes; and Brookhaven National Laboratory staff scientists Ming Lu and Aaron Stein, who helped device nanofabrication. Yuan Yang, Assistant Professor of Materials Science and Engineering in the Department of Applied Physics and Applied Mathematics at Columbia Engineering, was consulted during the progress of this research. The study was funded by DARPA YFA (Defense Advanced Research Projects Agency Young Faculty Award), ONR YIP (Office of Naval Research Young Investigator Program), AFOSR MURI (Air Force Office of Scientific Research Multidisciplinary University Research Initiative) on metasurfaces, Army Research Office, and NSF EPMD (Electronics, Photonics, and Magnetic Devices) program.