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  • richardmitnick 7:53 pm on March 17, 2022 Permalink | Reply
    Tags: "Toward a Quantum Computer That Calculates Molecular Energy", , , , Classical Computing, , Hybrid classical-quantum computing systems developed., Quantum computers are getting bigger and better but there are still few practical ways to take advantage of their extra computing power., , Quantum Monte Carlo algorithm: a system of methods for calculating probabilities when there are a large number of random unknown variables at play like in a game of roulette., Qubits however are fragile and error-prone: the more qubits used the less accurate the final answer., Researchers unveil an algorithm that reduces the statistical errors-or noise-produced by quantum bits- qubits-in crunching chemistry equations., Unlike binary digits-bits-made up of ones and zeros qubits can exist in two states simultaneously.   

    From Columbia University: “Toward a Quantum Computer That Calculates Molecular Energy” 

    Columbia U bloc

    From Columbia University

    March 16, 2022
    Ellen Neff

    Researchers at Columbia and Google Quantum AI have developed an algorithm that uses the most quantum bits to date to calculate ground state energy, the lowest-energy state in a quantum mechanical system. The discovery could help make it easier to design new materials.

    1
    An algorithm co-designed for classic and quantum computers may help research design materials for sustainability goals. Credit: Nicoletta Barolini.

    Quantum computers are getting bigger and better but there are still few practical ways to take advantage of their extra computing power. To get over this hurdle, researchers are designing algorithms to ease the transition from classical to quantum computers. In a new study in Nature, researchers unveil an algorithm that reduces the statistical errors, or noise, produced by quantum bits, or qubits, in crunching chemistry equations.

    Developed by Columbia chemistry professor David Reichman and postdoc Joonho Lee, with researchers at Google Quantum AI, the algorithm uses up to 16 qubits on Sycamore, Google’s 53-qubit computer, to calculate ground state energy, the lowest energy state of a molecule.

    “These are the largest quantum chemistry calculations that have ever been done on a real quantum device,” Reichman said.

    The ability to accurately calculate ground state energy, will enable chemists to develop new materials, said Lee, who is also a visiting researcher at Google Quantum AI. The algorithm could be used to design materials to speed up both nitrogen fixation for farming and hydrolysis for making clean energy, among other sustainability goals, he said.

    The algorithm uses a quantum Monte Carlo, a system of methods for calculating probabilities when there are a large number of random, unknown variables at play, like in a game of roulette. Here, the researchers used their algorithm to determine the ground state energy of three molecules: heliocide (H4), using eight qubits for the calculation; molecular nitrogen (N2), using 12 qubits; and solid diamond, using 16 qubits.

    Ground state energy is influenced by variables such as the number of electrons in a molecule, the direction in which they spin, and the paths they take as they orbit a nucleus. This electronic energy is encoded in the Schrodinger equation. Solving the equation on a classical computer becomes exponentially harder as molecules get bigger, although methods for estimating the solution have made the process easier. How quantum computers might circumvent the exponential scaling problem has been an open question in the field.

    In principle, quantum computers should be able to handle exponentially larger and more complex calculations, like those needed to solve the Schrodinger equation, because the qubits that make them up take advantage of quantum states. Unlike binary digits, or bits, made up of ones and zeros, qubits can exist in two states simultaneously. Qubits, however, are fragile and error-prone: the more qubits used, the less accurate the final answer. Lee’s algorithm harnesses the combined power of classical and quantum computers to solve chemistry equations more efficiently while minimizing the quantum computer’s mistakes.

    “It’s the best of both worlds,” Lee said. “We leveraged tools that we already had as well as tools that are considered state-of-the-art in quantum information science to refine quantum computational chemistry.”

    A classical computer can handle most of Lee’s quantum Monte Carlo simulation. Sycamore jumps in for the last, most computationally complex step: the calculation of the overlap between a trial wave function—a guess at the mathematical description of the ground state energy that can be implemented by the quantum computer—and a sample wave function, which is part of the Monte Carlo’s statistical process. This overlap provides a set of constraints, known as the boundary condition, to the Monte Carlo sampling, which ensures the statistical efficiency of the calculation (for more details on the math, see Lee’s webinar).

    The prior record for solving ground state energy used 12 qubits and a method called the variational quantum eigensolver, or VQE. But VQE ignored the effects of interacting electrons, an important variable in calculating ground state energy that Lee’s quantum Monte Carlo algorithm now includes. Adding virtual correlation techniques from classic computers could help chemists tackle even larger molecules, Lee said.

    The hybrid classical-quantum calculations in this new work were found to be as accurate as some of the best classical methods. This suggests that problems could be solved more accurately and/or quickly with a quantum computer than without—a key milestone for quantum computing. Lee and his colleagues will continue to tweak their algorithm to make it more efficient, while engineers work to build better quantum hardware.

    “The feasibility of solving larger and more challenging chemical problems will only increase with time,” Lee said. “This gives us hope that quantum technologies that are being developed will be practically useful.”

    See the full article here .

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    Columbia U Campus
    Columbia University was founded in 1754 as King’s College by royal charter of King George II of England. It is the oldest institution of higher learning in the state of New York and the fifth oldest in the United States.

    University Mission Statement

    Columbia University is one of the world’s most important centers of research and at the same time a distinctive and distinguished learning environment for undergraduates and graduate students in many scholarly and professional fields. The University recognizes the importance of its location in New York City and seeks to link its research and teaching to the vast resources of a great metropolis. It seeks to attract a diverse and international faculty and student body, to support research and teaching on global issues, and to create academic relationships with many countries and regions. It expects all areas of the University to advance knowledge and learning at the highest level and to convey the products of its efforts to the world.

    Columbia University is a private Ivy League research university in New York City. Established in 1754 on the grounds of Trinity Church in Manhattan Columbia is the oldest institution of higher education in New York and the fifth-oldest institution of higher learning in the United States. It is one of nine colonial colleges founded prior to the Declaration of Independence, seven of which belong to the Ivy League. Columbia is ranked among the top universities in the world by major education publications.

    Columbia was established as King’s College by royal charter from King George II of Great Britain in reaction to the founding of Princeton College. It was renamed Columbia College in 1784 following the American Revolution, and in 1787 was placed under a private board of trustees headed by former students Alexander Hamilton and John Jay. In 1896, the campus was moved to its current location in Morningside Heights and renamed Columbia University.

    Columbia scientists and scholars have played an important role in scientific breakthroughs including brain-computer interface; the laser and maser; nuclear magnetic resonance; the first nuclear pile; the first nuclear fission reaction in the Americas; the first evidence for plate tectonics and continental drift; and much of the initial research and planning for the Manhattan Project during World War II. Columbia is organized into twenty schools, including four undergraduate schools and 15 graduate schools. The university’s research efforts include the Lamont–Doherty Earth Observatory, the Goddard Institute for Space Studies, and accelerator laboratories with major technology firms such as IBM. Columbia is a founding member of the Association of American Universities and was the first school in the United States to grant the M.D. degree. With over 14 million volumes, Columbia University Library is the third largest private research library in the United States.

    The university’s endowment stands at $11.26 billion in 2020, among the largest of any academic institution. As of October 2020, Columbia’s alumni, faculty, and staff have included: five Founding Fathers of the United States—among them a co-author of the United States Constitution and a co-author of the Declaration of Independence; three U.S. presidents; 29 foreign heads of state; ten justices of the United States Supreme Court, one of whom currently serves; 96 Nobel laureates; five Fields Medalists; 122 National Academy of Sciences members; 53 living billionaires; eleven Olympic medalists; 33 Academy Award winners; and 125 Pulitzer Prize recipients.

     
  • richardmitnick 12:15 pm on February 15, 2022 Permalink | Reply
    Tags: "Race Not Over Between Classical and Quantum Computers", , Classical Computing, Gaussian boson sampling, ,   

    From Physics (US): “Race Not Over Between Classical and Quantum Computers” 

    About Physics

    From Physics (US)

    February 10, 2022
    Katie McCormick

    A new classical algorithm reduces—by a factor of one billion—a recent claim of so-called quantum advantage.

    1
    Researchers have significantly slashed the advantage of a recently demonstrated quantum-computing algorithm over its classical counterpart. Credit: Shuo/stock.adobe.com

    In the race to achieve the coveted “advantage” of a quantum computer, those developing quantum algorithms are pitted against each other and against those working on classical algorithms. With each potential claim of such an advantage—the successful calculation on a quantum computer of something that is infeasible on a classical one—scientists have designed more efficient classical algorithms against which the quantum algorithms must then be compared. Now, by exactly that route, Jacob Bulmer of the University of Bristol (UK), Bryn Bell of Imperial College London, and colleagues have knocked down a peg a recent claim of quantum advantage using a method called Gaussian boson sampling. The team behind that advantage claim had asserted that a classical computation of Gaussian boson sampling would take 600 million years on the world’s fastest supercomputer. But Bulmer, Bell, and colleagues show that their classical algorithm can do it in just 73 days. This result, along with other recent improvements to classical algorithms, helps build the case that the quantum-advantage race is far from over.

    Gaussian boson sampling is an adaptation of a 2011 idea from Scott Aaronson of the University of Texas-Austin and Alex Arkhipov, who, at the time, was at the Massachusetts Institute of Technology. The idea, known as boson sampling, proposed sending a beam of single photons through a network of beam splitters to create a complex web of correlations between the paths of the photons.

    To imagine the resulting photon-path web, Aaronson and Arkhipov compared their system to a quantum version of a Galton board, a vertical board with pegs fastened to its surface in a two-dimensional pattern. Drop a ball from the top of the board, and it will bounce off the pegs, tracing a random path, until it reaches the ground. If repeated many times, the horizontal distribution of the balls approaches a Gaussian shape. In the case of photons, this distribution should be much more complicated because of the ability of photons to entangle. Aaronson and Arkhipov argued that this distribution likely couldn’t be calculated efficiently with a classical computer. The simplicity of the problem made it a good candidate for a near-term demonstration of a quantum advantage.

    In 2020, a group of researchers led by Jian-Wei Pan at The University of Science and Technology of China [电子科技大学](CN) did just that using Gaussian boson sampling. This method uses a boson sampler to perform the calculation using squeezed states of light. Photodetectors stationed at the endpoints of all possible paths counted the number of photons that took each path. The team used the sampler to calculate—in 200 seconds—the distribution of the photons through a network of beam splitters with 100 possible paths, something that calculations at the time indicated would take 600 million years on the world’s fastest supercomputer, Fugaku.

    Fugaku is a claimed exascale supercomputer (while only at petascale for mainstream benchmark), at The RIKEN Center for Computational Science in Kobe, Japan. It started development in 2014 as the successor to the K computer, and is officially scheduled to start operating in 2021. Fugaku made its debut in 2020, and became the fastest supercomputer in the world in the June 2020 TOP500 list, the first ever supercomputer that achieved 1 exaFLOPS. As of April 2021, Fugaku is currently the fastest supercomputer in the world.

    Bulmer, Bell, and their colleagues decide to see if they could reduce that classical calculation time.

    Bulmer says that the team knew that one of the main bottlenecks in the classical calculation was determining the “loop Hafnian,” a matrix function that is at the heart of simulating Gaussian-boson-sampling experiments. This function gives the probability of measuring a particular distribution of photons at the end of the experiment. The function is inherently difficult to calculate classically, which gives Gaussian boson samplers their advantage over classical computers. Bulmer, Bell, and their colleagues found that they could improve the calculation time by taking advantage of patterns in the structure of the matrix that mathematically describe how photons travel through the maze of beam splitters. This change, along with some other improvements and simplifications, allowed the team to reduce the estimated simulation time of the USTC experiment to just 73 days.

    “I think it’s great that they’ve managed to improve the [classical] runtime,” Aaronson says. But he adds that the new algorithm developed by Bulmer, Bell, and colleagues “still isn’t able to simulate classically, in any reasonable amount of time, the most recent quantum [advantage] experiments” (see Viewpoint: Quantum Leap for Quantum Primacy).

    While the USTC team’s Gaussian-boson-sampling algorithm is still about 4 orders of magnitude faster than that of Bulmer, Bell, and colleagues, some researchers see the factor-of-a-billion drop in classical simulation time as a sign that determining a quantum advantage is a murky problem. “The reality is that this line is not actually well defined,” says Alex Moylett, a scientist at Riverlane, UK, a quantum engineering company.

    In the distant future, most researchers expect that quantum computers will outperform classical ones by such a large margin that nobody could possibly doubt that they are better. Aaronson has the same hope, but in the meantime, he thinks that classical computers “can, at least for a while, fight back.” He says, “developments like these send a message that the experimenters need to up their game if they want [a] quantum [advantage]…to be maintained and improved into the future.”

    See the full article here .

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    Physicists are drowning in a flood of research papers in their own fields and coping with an even larger deluge in other areas of physics. How can an active researcher stay informed about the most important developments in physics? Physics (US) highlights a selection of papers from the Physical Review journals. In consultation with expert scientists, the editors choose these papers for their importance and/or intrinsic interest. To highlight these papers, Physics features three kinds of articles: Viewpoints are commentaries written by active researchers, who are asked to explain the results to physicists in other subfields. Focus stories are written by professional science writers in a journalistic style and are intended to be accessible to students and non-experts. Synopses are brief editor-written summaries. Physics provides a much-needed guide to the best in physics, and we welcome your comments.

     
  • richardmitnick 12:07 pm on January 15, 2022 Permalink | Reply
    Tags: "From bits to qubits", , , Classical Computing, , , , , ,   

    From Symmetry: “From bits to qubits” 

    Symmetry Mag

    From Symmetry

    01/13/22
    Sarah Charley

    1
    Illustration by Sandbox Studio, Chicago with Ana Kova.

    Quantum computers go beyond the binary.

    The first desktop computer was invented in the 1960s. But computing technology has been around for centuries, says Irfan Siddiqi, director of the Quantum Nanoelectronics Laboratory at The University of California- Berkeley (US).

    “An abacus is an ancient computer,” he says. “The materials science revolution made bits smaller, but the fundamental architecture hasn’t changed.”

    Both modern computers and abaci use basic units of information that have two possible states. In a classical computer, a binary digit (called a bit) is a 1 or a 0, represented by on-off switches in the hardware. On an abacus, a sliding bead can also be thought of as being “on” or “off,” based on its position (left or right on an abacus with horizontal rods, or up or down on an abacus with vertical ones). Bits and beads can form patterns that represent other numbers and, in the case of computers, letters and symbols.

    But what if there were even more possibilities? What if the beads of an abacus could sit in between two positions? What if the switches in a computer could consult each other before outputting a calculation?

    This is the fundamental idea behind quantum computers, which embrace the oddities of quantum mechanics to encode and process information.

    “Information in quantum mechanics is stored in very different ways than in classical mechanics, and that’s where the power comes from,” says Heather Gray, an assistant professor and particle physicist at UC Berkeley.

    Classical computer; classical mechanics

    Computing devices break down numbers into discrete components. A simple abacus could be made up of three rows: one with beads representing 100s, one with beads representing 10s, and one with beads representing 1s. In this case, the number 514 could be indicated by sliding to the right 5 beads in the 100s row, 1 bead in the 10s row, and 4 beads in the 1s row.

    The computer you may be using to read this article does something similar, counting by powers of two instead of 10s. In binary, the number 514 becomes 1000000010.

    The more complex the task, the more bits or time a computer needs to perform the calculation. To speed things up, scientists have over the years found ways to fit more and more bits into a computer. “You can now have one trillion transistors on a small silicon chip, which is a far cry from the ancient Chinese abacus,” Siddiqi says.

    But as engineers make transistors smaller and smaller, they’ve started to notice some funny effects.

    The quantum twist on computing

    Bits that behave classically are determinate: A 1 is a 1. But at very small scales, an entirely new set of physical rules comes into play.

    “We are hitting the quantum limits,” says Alberto Di Meglio, the head of CERN’s Quantum Technology Initiative. “As the scale of classic computing technology becomes smaller and smaller, quantum mechanics’ effects are not negligible anymore, and we do not want this in classic computers.”

    But quantum computers use quantum mechanics to their benefit. Rather than offering decisive answers, quantum bits, called qubits, behave like a distribution of probable values.

    Di Meglio likens qubits to undecided voters in an election. “You might know how a particular person is likely to vote, but until you actually ask them to vote, you won’t have a definite answer,” Di Meglio says.

    Qubits can be made from subatomic particles, such as electrons. Like other, similar particles, electrons have a property called spin that can exist in one of two possible states (spin-up or spin-down).

    If we think of these electrons as undecided voters, the question they are voting on is their direction of spin. Quantum computers process information while the qubits are still undecided—somewhere in between spin-up and spin-down.

    The situation becomes even more complicated when the “voters” can influence one another. This happens when two qubits are entangled. “For example, if one person votes yes, then an entangled ‘undecided’ voter will automatically vote no,” Di Meglio says. “The relationships become important, and the more voters you put together, the more chaotic it becomes.”

    When the qubits start talking to each other, each qubit can find itself in many different configurations, Siddiqi says. “An entangled array of qubits—with ‘n’ number of qubits—can exist in 2^n configurations. A quantum computer with 300 good qubits would have 2^300 possible configurations, which is more than the number of particles in the known universe.”

    With great power comes great… noise

    Entanglement allows a quantum computer to perform a complex task in a fraction of the time it would take a classical computer. But entanglement is also the quantum computer’s greatest weakness.

    “A qubit can get entangled with something else that you don’t have access to,” Siddiqi says. “Information can leave the system.”

    An electron from the computer’s power supply or a stray photon can entangle with a qubit and make it go rogue.

    “Quantum computing is not just about the number of qubits,” Di Meglio says. “You might have a quantum computer with thousands of qubits, but only a fraction are reliable.”

    Because of the problem of rogue qubits, today’s quantum computers are classified as noisy intermediate-scale quantum, or NISQ, devices. “Most quantum computers look like a physics experiment,” Gray says. “We’re very far from having one you could use at home.”

    But scientists are trying. In the future, scientists hope that they can use quantum computers to quickly search through large databases and calculate complex mathematical matrices.

    Today, physicists are already experimenting with quantum computers to simulate quantum processes, such as how particles interact with each other inside the detectors at the Large Hadron Collider. “You can do all sorts of cool things with entangled qubits,” Gray says.

    See the full article here .


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    Symmetry is a joint Fermilab/SLAC publication.


     
  • richardmitnick 10:37 pm on June 11, 2021 Permalink | Reply
    Tags: "People of PI- Women in STEM Christine Muschik enjoys the best of both worlds", Classical Computing, Hybrid computing systems offer new approaches to simulation and analysis that can move fields from cosmology to particle physics forward., Muschik has developed new computational approaches that squeeze more power out of existing quantum technologies and flow the results into a feedback loop with classical processors., Perimeter Institute (CA), , , Quantum-classical hybrid computers, Reconciling quantum mechanics and classical physics, We want to have quantum simulations that work not only on paper but that also lead to proof-of-concept demonstrations.   

    From Perimeter Institute for Theoretical Physics (CA): “People of PI- Women in STEM Christine Muschik enjoys the best of both worlds” 

    Perimeter Institute

    From Perimeter Institute for Theoretical Physics (CA)

    Jun 02, 2021
    Patchen Barss

    1
    Christine Muschik. Credit: Perimeter Institute.

    When Christine Muschik was completing her PhD in the 2010s, the privilege of running an experiment on a quantum computer required the kind of money, fame, or insider connections few early-career researchers could muster.

    “If you had an idea, it was very difficult to get it implemented on hardware. Hardware development was just crazy expensive,” says Muschik, who is now an associate faculty member at Perimeter Institute, cross-appointed with the University of Waterloo (CA).

    As a theorist with great interest in moving from the whiteboard to real-world experiments, Muschik continually strained against technological and logistical restrictions. At every opportunity, she pushed to advance both the science and the technology.

    “We want to have quantum simulations that work not only on paper but that also lead to proof-of-concept demonstrations. This is why we work with experimental teams: To make it real. To bring it to life in the lab,” she says.

    A decade later, quantum hardware has advanced more quickly than anyone could have imagined. Quantum tech is still in its early, fragile, somewhat experimental stages, but it has become much more accessible, freeing Muschik’s curiosity and intellect.

    “We’re all surprised by the rapid acceleration of hardware development,” she says. “It’s happening because industry – the Googles and the IBMs – are getting on board and pumping a lot of money into it. Everybody is hunting after the ‘quantum advantage.’ For our last publication, we just ran the program we needed on an IBM cloud-based quantum computer.”

    A 2019 report in Nature estimated that private investors in North America and Europe had poured at least $450 million (USD) into quantum technology start-up companies in the preceding two years. (Similar information was not available for China, which has become a powerhouse of quantum technology.)

    Many of these start-ups are racing with each other, and with established tech giants, to achieve “quantum supremacy,” an industry term for the milestone of a quantum computer solving a useful or interesting problem that is impossible for classical computers. The term is ambiguous (Google claimed they had achieved quantum supremacy in 2019, but critics disputed it) and also deceptive: Quantum supremacy does not mean that quantum computers take over from conventional computers. Each is suited for different types of computational challenges.

    Muschik has been working to combine the best of both.

    “She understands both the intricacies of complex theories and the subtleties of experimental implementation,” says Raymond Laflamme, the Mike and Ophelia Lazaridis John von Neumann Chair in Quantum Information at Waterloo’s Institute for Quantum Computing. “She is very hands on in both areas, which makes her stand out.”

    Muschik has developed new computational approaches that squeeze more power out of existing quantum technologies and flow the results into a feedback loop with classical processors, creating increasingly capable hybrid systems. While this work will inevitably make waves in the commercial tech sector, she is more interested in using these tools to create new knowledge.

    “The whole guiding theme of my group involves one question: What if quantum computers could help us to make new scientific discoveries?” she says. She’s interested in questions about matter and antimatter, the inner workings of neutron stars, and other mysteries that conventional computers haven’t been able to solve.

    Hybrid computing systems offer new approaches to simulation and analysis that can move fields from cosmology to particle physics forward. But even before she begins exploring questions from other fields, Muschik’s core work in developing such systems already helps advance a central challenge that has confounded theoretical physicists for decades: reconciling quantum mechanics and classical physics.

    Each of these powerful theoretical frameworks does a great job of describing the universe from a specific perspective: Quantum mechanics covers the subatomic world of protons and quarks. Classical physics describes the macroscopic world of people and planets. Each provides an accurate and precise description of the same physical reality, as seen from a different point of view.

    But each is inconsistent and incompatible with the other.

    Quantum-classical hybrid computers send information back and forth between these contradictory frameworks, using both to solve problems and run simulations with implications for the aerospace industry, drug discovery, financial services, and many areas of scientific research.

    Muschik makes the technology sound easy.

    “It’s all about how you formulate the problem,” she says. “You take a question like ‘Why is there more matter than antimatter?’ You reformulate your question in the form of an optimization problem. I teach my quantum core processor to analyze this problem and spit out numbers. And classical computers know how to deal with numbers.”

    Muschik works on applications for existing “noisy intermediate-sized quantum computers,” but also plans projects that benefit – and benefit from – continuing technological developments.

    “We play a dual role, not only simulating the physics now, but also focusing on method development for future quantum computers,” she says. “This is how you pave the way to scale it up for future generations.”

    Muschik oversees the Quantum Simulations of Fundamental Interactions initiative, a joint venture of Perimeter Institute and the Institute for Quantum Computing at the University of Waterloo. Among other things, her lab is developing the technology to simulate forces and particles that extend beyond the Standard Model of particle physics. The rapid advance of quantum computers over the past decades has made it much more possible to simulate quantum fields and fundamental forces that the Standard Model can’t explain.

    “Where our understanding fails is the most interesting part. It is a hint about where we can find new physics. The models beyond the Standard Model are freaking difficult. Standard methods cannot tackle them. My personal computer cannot tackle them. The biggest supercomputer cannot. Even future supercomputer centres that are only planned – even those will not be able to tackle these questions,” she says.

    “And you can say, ‘Ok, we should give up.’ But this is a tremendous opportunity. Quantum computers right now are too small, but they have tremendous promise to answer these big, deep, open questions.”

    See the full article here .

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    Perimeter Institute for Theoretical Physics (CA) is a leading centre for scientific research, training and educational outreach in foundational theoretical physics. Founded in 1999 in Waterloo, Ontario, Canada, its mission is to advance our understanding of the universe at the most fundamental level, stimulating the breakthroughs that could transform our future. Perimeter also trains the next generation of physicists through innovative programs, and shares the excitement and wonder of science with students, teachers and the general public.

    The Institute’s founding and major benefactor is Canadian entrepreneur and philanthropist Mike Lazaridis.

    The original building, designed by Saucier + Perrotte, opened in 2004 and was awarded a Governor General’s Medal for Architecture in 2006. The Stephen Hawking Centre, designed by Teeple Architects, was opened in 2011 and was LEED Silver certified in 2015.

    In addition to research, Perimeter also provides scientific training and educational outreach activities to the general public. This is done in part through Perimeter’s Educational Outreach team.

    Research

    Perimeter’s research encompasses nine fields:

    Cosmology
    Mathematical physics
    Particle Physics
    Quantum fields and strings
    Quantum foundations
    Quantum gravity
    Quantum information
    Quantum matter
    Strong gravity

     
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