Undergraduate

Bringing the Quantum to the Classical: A Hybrid Simulation of Supernova Neutrinos

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By Daniel Heimsoth, Physics PhD student

Simulating quantum systems on classical computers is currently a near-impossible task, as memory and computation time requirements scale exponentially with the size of the system. Quantum computers promise to solve this scalability issue, but there is just one problem: they can’t reliably do that right now because of exorbitant amounts of noise. 

So when UW–Madison physics postdoc Pooja Siwach, former undergrad Katie Harrison BS ‘23, and professor Baha Balantekin wanted to simulate neutrino evolution inside a supernova, they needed to get creative.  

profile photo of Pooja Siwach
Pooja Siwach

Their focus was on a phenomenon called collective neutrino oscillations, which describes a peculiar type of interaction between neutrinos. Neutrinos are unique among elementary particles in that they change type, or flavor, as they propagate through space. These oscillations between flavors are dictated by the density of neutrinos and other matter in the medium, both of which change from the core to the outer layers of a supernova. Physicists are interested in how the flavor composition of neutrinos evolve in time; this is calculated using a time evolution simulation, one of the most popular calculations currently done on quantum computers.  

Ideally, researchers could calculate each interaction between every possible pair of neutrinos in the system. However, supernovae produce around 10^58 neutrinos, a literally astronomical number. “It’s really complex, it’s very hard to solve on classical computers,” Siwach says. “That’s why we are interested in quantum computing because quantum computers are a natural way to map such problems.” 

profile photo of Katie Harrison
Katie Harrison

This naturalness is due to the “two-level” similarities between quantum computers and neutrino flavors. Qubits are composed of two-level states, and neutrino flavor states are approximated as two levels in most physical systems including supernovae.  

In a paper published in Physical Review D in October, Siwach, Harrison, and Balantekin studied the collective oscillation problem using a quantum-assisted simulator, or QAS, which combines the benefits of the natural mapping of the system onto qubits and classical computers’ strength in solving matrix equations. 

In QAS, the interactions between particles are broken down into a linear combination of products of Pauli matrices, which are the building blocks for quantum computing operations, while the state itself is split into a sum of simpler states. The quantum portion of the problem then boils down to computing products of basis states with each Pauli term in the interaction. These products are then inputted into the oscillation equations.

a graph with 4 neutrino traces in 4 colors
Flavor composition (y-axis) of four supernova neutrinos over time due to collective oscillations, calculated using the quantum-assisted simulator. The change in flavor for each neutrino over time shows the effect of neutrino-neutrino interactions.

“Then we get the linear-algebraic equations to solve, and solving such equations on a quantum computer requires a lot of resources,” explains Siwach. “That part we do on classical computers.”  

This approach allows researchers to use the quantum computers only once before the actual time evolution simulation is done on a classical computer, avoiding common pitfalls in quantum calculations such as error accumulation over the length of the simulation due to noisy gates. The authors showed that the QAS results for a four-neutrino system match with a pure classical calculation, showcasing the power of this approach, especially compared to a purely quantum simulation which quickly deviates from the exact solution due to accumulated errors from gates controlling two qubits at the same time. 

Still, as with any current application of quantum computers, there are limitations. “There’s only so much information that we can compute in a reasonable amount of time [on quantum computers],” says Siwach. She also laments the scalability of both the QAS and full quantum simulation. “One more hurdle is scaling to a larger number of neutrinos. If we scale to five or six neutrinos, it will require more qubits and more time, because we have to reduce the time step as well.” 

Harrison, who was an undergraduate physics student at UW–Madison during this project, was supported by a fellowship from the Open Quantum Initiative, a new program to expand undergrad research experiences in quantum computing and quantum information science. She enjoyed her time in the program and thinks that it benefits students looking to get involved in research in the field: “I think it’s really good for students to see what it really means to do research and to see if it’s something that you’re capable of doing or something that you’re interested in.” 

trace of neutrino flavor composition over time comparing a quantum simulation to a full classical one
Flavor composition of a neutrino over time using a full quantum simulation (red points) compared to exact solution (black line). The points start to drift from the exact solution after only a few oscillations, highlighting how noise in the quantum computer negatively affects the calculation.

 

Physics major Nathan Wagner awarded Goldwater Scholarship

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This story is modified from one published by University Communications

Physics and mathematics major Nathan Wagner is one of four UW–Madison students named as winners of 2024 Goldwater Scholarships, the premier undergraduate scholarship in mathematics, engineering and the natural sciences in the United States.

The scholarship program honors the late Sen. Barry Goldwater and is designed to foster and encourage outstanding students to pursue research careers.

“I’m so proud of these four immensely talented scholars and all they’ve accomplished,” says Julie Stubbs, director of UW’s Office of Undergraduate Academic Awards. “Their success also reflects well on a campus culture that prioritizes hands-on research experiences for our undergraduates and provides strong mentoring in mathematics, engineering and the natural sciences.”

The other UW–Madison students are juniors Katarina Aranguiz and Scott Chang and sophomore Max Khanov .

A Goldwater Scholarship provides as much as $7,500 each year for up to two years of undergraduate study. A total of 438 Goldwater Scholars were selected this year from a field of 1,353 students nominated by their academic institutions.

profile picture of Nathan Wagner
Nathan Wagner (Photo by Taylor Wolfram / UW–Madison)

Sophomore Nathan Wagner of Madison, Wisconsin

Wagner is majoring in physics and mathematics. Wagner began research in Professor Mark Saffman’s quantum computing lab in spring 2021 as a high school junior. His first-author manuscript, “Benchmarking a Neutral-Atom Quantum Computer” was recently accepted for publication in the International Journal of Quantum Information. In Summer 2023, Wagner started research with the Physics Department’s High Energy Physics Group, working alongside Professor Sridhara Dasu and others on future particle colliders design research. Wagner was invited to present his research at the Department of Physics Board of Visitors meeting in fall 2023. This summer, he will complete a research internship at Argonne National Laboratory near Chicago, focusing on computational physics. Wagner plans to pursue a PhD in physics and a career at a U.S. Department of Energy national laboratory researching novel carbon-neutral energy generation, quantum computing and networking, nuclear photonics and computational physics.

About the Goldwater Scholarship

Congress established the Barry Goldwater Scholarship and Excellence in Education Foundation in 1986. Goldwater served in the U.S. Senate for over 30 years and challenged Lyndon B. Johnson for the presidency in 1964. A list of past winners from UW–Madison can be found here.

Undergraduates named 2023 Hilldale Fellows

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Physics major Dhanvi Hiriyanna Bharadwaj has been named a 2023 Hilldale Fellow, working with Ramathasan Thevamaran in Mechanical Engineering. Astronomy-physics major Vicki Braianova, who is working with physics professor Peter Timbie, has also received the award.

The Hilldale Undergraduate/Faculty Research Fellowship provides research training and support to undergraduates at UW–Madison. Students have the opportunity to undertake their own research project in collaboration with UW–Madison faculty or research/instructional academic staff. Approximately 97 – 100 Hilldale awards are available each year.

Two students receive Sophomore Research Fellowships

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Two physics majors have received a UW–Madison Sophomore Research Fellowship as a fellow or honorable mention. The students are:

  • Erica Magee, Mathematics, Physics; working with Martin Zanni (Chemistry)
  • Elias Mettner, Physics; working with Abdollah Mohammadi (Physics)

The fellowships include a stipend to each student and to their faculty advisers. Fellowships are funded by grants from the Brittingham Wisconsin Trust and the Kemper K. Knapp Bequest, with additional support from UW-System, the Chancellor’s Office and the Provost’s Office.

Opening doors to quantum research experiences with the Open Quantum Initiative

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This past winter, Katie Harrison, then a junior physics major at UW–Madison, started thinking about which areas of physics she was interested in studying more in-depth.

“Physics is in general so broad, saying you want to research physics doesn’t really cut it,” Harrison says.

She thought about which classes she enjoyed the most and talked to other students and professors to help figure out what she might focus on. Quantum mechanics was high on her list. During her search for additional learning opportunities, she saw the email about the Open Quantum Initiative (OQI), a new fellowship program run by the Chicago Quantum Exchange (CQE).

“This could be something I’m interested in, right?” Harrison thought. “I’ll apply and see what happens.”

What happened was that Harrison was one of 12 undergraduate students accepted into the inaugural class of OQI Fellows. These students were paired with mentors at CQE member institutions, where they conducted research in quantum science information and engineering. OQI has a goal of connecting students with leaders in academia and industry and increasing their awareness of quantum career opportunities. The ten-week Fellowship ran through August 19.

11 students pose on a rock wall, all students are wearing the same Chicago Quantum Exchange hooded sweatshirt
OQI students attend a wrap-up at the University of Chicago on August 17. Each student presented at a research symposium that day, which also included a career panel from leaders across academia, government, and industry and an opportunity to network. | Photo provided by the Chicago Quantum Exchange

OQI also places an emphasis on establishing diversity, equity, and inclusion as priorities central to the development of the quantum ecosystem. Almost 70% of this year’s fellowship students are Hispanic, Latino, or Black, and half are the first in their family to go to college. In addition, while the field of quantum science and engineering is generally majority-male, the 2022 cohort is half female.

This summer, UW–Madison and the Wisconsin Quantum Institute hosted two students: Harrison with physics professor Baha Balantekin and postdoc Pooja Siwach; and MIT physics and electrical engineering major Kate Arutyunova with engineering physics professor Jennifer Choy, postdoc Maryam Zahedian and graduate student Ricardo Vidrio.

Harrison and Arutyunova met at OQI orientation at IBM’s quantum research lab in New York, and they hit it off immediately. (“We have the most matching energies (of the fellows),” Arutyunova says, with Harrison adding, “The synergy is real.”)

Four people stand in a lab in front of electronics equipment
OQI Fellow Kate Arutyunova with her research mentors. (L-R) Engineering Physics professor Jennifer Choy, graduate student Ricardo Vidrio, Kate Arutyunova, and postdoc Maryam Zahedian. | Photo provided by Kate Arutyunova

Despite their very different research projects — Harrison’s was theoretical and strongly focused on physics, whereas Arutyunova’s was experimental and with an engineering focus — they leaned on each other throughout the summer in Madison. They met at Union South nearly every morning at 7am to read and bounce ideas off each other. Then, after a full day with their respective research groups, they’d head back to Union South until it closed.

Modeling neutrino oscillations

Harrison’s research with Balantekin and Siwach investigated the neutrinos that escape collapsing supernovae cores. Neutrinos have a neutral charge and are relatively small particles, they make it out of cores without interacting with much — and therefore without changing much — so studying them helps physicists understand what is happening inside those stars. However, this is a difficult task because neutrinos oscillate between flavors, or different energy levels, and therefore require a lot of time and resources to calculate on a classical computer.

Harrison’s project, then, was to investigate two types of quantum computing methods, pulse vs circuit based, and determine if one might better fit their problem than the other. Previous studies suggest that pulsed based is likely to be better, but circuit based involves less complicated input calculations.

“I’ve been doing calibrations and calculating the frequencies of the pulses we’ll need to send to our qubits in order to get data that’s as accurate as a classical computer,” Harrison says. “I’m working with the circuit space, the mathematical versions of them, and then I’ll send my work to IBM’s quantum computers and they’ll calculate it and give results back.”

While she didn’t fully complete the project, she did make significant progress.

“(Katie) is very enthusiastic and she has gone a lot further than one would have expected an average undergraduate could have,” Balantekin says. “She started an interesting project, she started getting interesting results. But we are nowhere near the completion of the project, so she will continue working with us next academic year, and hopefully we’ll get interesting results.”

Developing better quantum sensors 

Over on the engineering side of campus, Arutyunova was studying different ways to introduce nitrogen vacancy (NV) centers in diamonds. These atomic-scale defects are useful in quantum sensing and have applications in magnetometry. Previous work in Choy’s group made the NV centers by a method known as nitrogen ion beam implantation. Arutyunova’s project was to compare how a different method, electron beam irradiation, formed the NV centers under different starting nitrogen concentrations in diamond.

Briefly, she would mark an edge of a very tiny (2 x 2 x 0.5 millimeter), nitrogen-containing diamond, and irradiate the sample with a scanning electron microscope. She used confocal microscopy to record the initial distribution of NV centers, then moved the sample to the annealing step, where the diamond is heated up to 1200 celsius in a vacuum annealing furnace. The diamonds are then acid washed and reexamined with the confocal microscope to see if additional NV centers are formed.

“It’s a challenging process as it requires precise coordinate-by-coordinate calculation for exposed areas and extensive knowledge of how to use the scanning electron microscope,” says Arutyunova, who will go back to MIT after the fellowship wraps. “I think I laid down a good foundation for future steps so that the work can be continued in my group.”

Choy adds:

Kate made significant strides in her project and her work has put us on a great path for our continued investigation into effective ways of generating color centers in diamond. In addition to her research contributions, our group has really enjoyed and benefited from her enthusiasm and collaborative spirit. It’s wonderful to see the relationships that Kate has forged with the rest of the group and in particular her mentors, Maryam and Ricardo. We look forward to keeping in touch with Kate on matters related to the project as well as her academic journey.

Beyond the summer fellowship

 Both Harrison and Arutyunova think that this experience has drawn them to the graduate school track, likely with a focus on quantum science. More importantly, it has helped them both to learn what they like about research.

“I would prefer to work on a problem and see the final output rather than a question where I do not have an idea of the application,” Arutyunova says. “And I realized how much I like to collaborate with people, exchange ideas, propose something, and listen to people and what they think about research.”

They also offer similar advice to other undergraduate students who are interested in research: do it, and start early.

“No matter when you start, you’re going to start knowing nothing,” Harrison says. “And if you start sooner, even though it’s scary and you feel like you know even less, you have more time to learn, which is amazing. And get in a research group where they really want you to learn.”

Physics undergraduates named 2022 Hilldale Fellows

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Three UW–Madison undergraduate physics majors have been named 2022 Hilldale Fellows, in addition to one engineering physics major who is conducting their research in the Physics Department.

The Hilldale Undergraduate/Faculty Research Fellowship provides research training and support to undergraduates at UW–Madison. Students have the opportunity to undertake their own research project in collaboration with UW–Madison faculty or research/instructional academic staff. Approximately 97 – 100 Hilldale awards are available each year.

The students are:

  • Astronomy-Physics and Physics major Elyse Incha, in Susanna Widicus Weaver’s group (Chemistry)
  • Mathematics and Physics major Haoyi Jia, in Sridhara Dasu’s group (Physics)
  • Music and Physics major Daniel Laws, in Mary Halloran’s group (Integrative Biology)
  • Engineering physics major Nico Ranabhat, in Shimon Kolkowitz’s group (Physics)

Lucy Steffes awarded 2022 Goldwater Scholarship

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This story was adapted from one first published by University Communications

Four University of Wisconsin–Madison students have been named winners of 2022 Barry Goldwater Scholarships, one of the most prestigious awards in the U.S. for undergraduates studying the sciences.

The UW–Madison winners are sophomore Lucy Steffes and juniors Sarah Fahlberg, Elias Kemna and Samuel Neuman.

Each university in the country may nominate up to four undergraduates for the annual award. To have all four candidates win is remarkable, says Julie Stubbs, director of UW’s Office of Undergraduate Academic Awards.

Lucy Steffes is a sophomore from Milwaukee, double-majoring in astronomy-physics and physics with a certificate in German. Her freshman year, Steffes began working with astronomy professor Snezana Stanimirovic on the ALMA-SPONGE project, for which she co-authored two papers recently published in the Astrophysical Journal. The project looks at molecular formation in the interstellar medium to describe potentially star-forming regions. At the end of her freshman year, Steffes earned a Hilldale Undergraduate Research Fellowship to calculate the upper limits of molecular detections in the Magellanic Stream. She spent last summer working at the Green Bank Observatory in West Virginia examining the chemical composition and evolution of two globules in the Helix Nebula. This summer, she will be returning to the observatory to examine neutral atomic carbon across the Helix Nebula. She plans to pursue a Ph.D. in astrophysics.

Physics & math senior Gage Siebert awarded NSF GRFP

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profile photo of gage siebert
Gage Siebert

Congratulations to Gage Siebert for being awarded a National Science Foundation Graduate Research Fellowship! Gage is a senior math and physics major who has been conducting research in radio astronomy and cosmology. He is working on the optics of NASA’s EXCLAIM mission and constructing a periodicity search using the Tianlai Radio Array. Gage is also a 2021 Hilldale Fellow and Goldwater Scholar, and has won the department’s Hagengruber Scholarship, Liebenberg Family Scholarship, and Henry & Eleanor Firminhac Scholarship. He plans to attend graduate school but has not decided where yet.

Peter Timbie, Gage’s research advisor, says:

Congratulations Gage on winning one of these exceedingly rare awards! We’re really proud of you,Best of luck with you proposal to search for periodic signals in cosmological survey data and your plans for graduate school.

21 UW–Madison students in total received the fellowship, a highly sought and competitive award. The Graduate Research Fellowship Program supports high-potential scientists and engineers in the early stages of their careers. Each year, more than 12,000 applicants compete for 2,000 fellowship awards.

Awardees from UW–Madison, including both undergraduate and graduate students, represent a variety of specializations across science, engineering, and technology. Another 23 UW–Madison students were recognized with honorable mentions.

The program provides awardees with three years of financial support consisting of a $34,000 annual stipend and a $12,000 education allowance. UW–Madison contributes toward fringe benefits.

Coral skeleton formation rate determines resilience to acidifying oceans

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A new University of Wisconsin–Madison study has implications for predicting coral reef survival and developing mitigation strategies against having their bony skeletons weakened by ocean acidification.

Though coral reefs make up less than one percent of the ocean floor, these ecosystems are among the most biodiverse on the planet — with over a million species estimated to be associated with reefs.

The coral species that make up these reefs are known to be differently sensitive or resilient to ocean acidification — the result of increasing atmospheric carbon dioxide levels. But scientists are not sure why.

In the study, researchers show that the crystallization rate of coral skeletons differs across species and is correlated with their resilience to acidification.

A woman holding two coral species stands in front of a body of water
“Finding solutions that are science-based is a priority,” says physics professor Pupa Gilbert, shown here with samples of scleractinian coral along the Lake Monona shoreline in Madison. | Photo: Jeff Miller

“Many agencies keep putting out reports in which they say, ‘Yes, coral reefs are threatened,’ with no idea what to do,” says Pupa Gilbert, a physics professor at UW–Madison and senior author of the study that was published Jan. 17 in the Journal of the American Chemical Society. “Finding solutions that are science-based is a priority, and having a quantitative idea of exactly what’s happening with climate change to coral reefs and skeletons is really important.”

Reef-forming corals are marine animals that produce a hard skeleton made up of the mostly insoluble crystalline material aragonite. Aragonite forms when precursors made up of a more soluble form, amorphous calcium carbonate, are deposited onto the growing skeleton and then crystallize.

The team studied three genera of coral and took an in-depth look at the components of their growing skeletons. They used a technique that Gilbert pioneered called PEEM spectromicroscopy, which detects the different forms of calcium carbonate with the greatest sensitivity to date.

When they used these spectromicroscopy images to compare the thickness of amorphous precursors to the crystalline form, they found that Acropora, which is more sensitive to acidification, had a much thicker band of amorphous calcium carbonate than Stylophora, which is less sensitive.

A third genus of unknown sensitivity, Turbinaria, had an even thinner amorphous precursor layer than Stylophora, suggesting it should be the most resilient of the three to ocean acidification.

two bright colored images assign a color to the form of calcium present in coral skeletons. On the left there is a thicker band of non-blue (blue is crystalline aragonite) compared to the image on the right where there is almost all blue, indicating the skeleton on the right crystallizes to aragonite more quickly
Coral skeletons were studied with PEEM spectromicroscopy, which identifies the calcium spectrum associated with each imaging pixel, then renders it in false color depending on the form of calcium. Blue is aragonite, the insoluble, crystalline form of calcium carbonate; the other colors represent one of the two amorphous precursor forms, a mix of the two, or a mix of aragonite and precursor form. Acropora spp. (left), has more non-blue pixels compared to Turbinaria spp. (right), indicating that Acropora has more of the soluble, non-crystalline form in its growing skeleton. | Pupa Gilbert and team in JACS

The thicker the band of uncrystallized minerals, the slower the crystallization process.

“If the surface of the coral skeleton, where all this amorphous calcium carbonate is being deposited by the living animal, crystallizes quickly, then that particular species is resilient to ocean acidification; if it crystallizes slowly, then it’s vulnerable,” Gilbert says. “For once, it’s a really simple mechanism.”

The mechanism may have worked out to be simple, but the data analysis required to process and interpret the PEEM images is anything but. Each pixel of imaging data acquired has a calcium spectrum that needs to be analyzed, which results in millions of data points. Processing the data includes many decision-making points, plus massive computing power.

The team has tried to automate the analysis or use machine-learning techniques, but those methods have not worked out. Instead, Gilbert has found that humans making decisions are the best data processors.

Gilbert did not want to base conclusions off the decision-making of just one or two people. So she hired a group of UW–Madison undergraduates, most of whom came from the Mercile J. Lee Scholars Program, which works to attract and retain talented students from underrepresented groups. This team provided a large and diverse group of decision makers.

a zoom screen showing several of the people who conducted the study
Gilbert and her research team met several times a week via Zoom, where students were assigned the same dataset to process in parallel and discuss at their next meeting. The Cnidarians — named after the phylum to which corals belong — include current and former UW–Madison undergraduates: Celeo Matute Diaz, Jorge Rivera Colon, Asiya Ahmed, Virginia Quach, Gabi Barreiro Pujol, Isabelle LeCloux, Sydney Davison, Connor Klaus, Jaden Sengkhamee, Evan Walch and Benjamin Fordyce; and graduate students Cayla Stifler, and Connor Schmidt. Schmidt was also the lead author of the study. | Provided by Pupa Gilbert

Dubbed the Cnidarians — from the phylum to which corals, anemones and jellyfish belong — this group of students became integral members of the team. They met several times a week via Zoom, when Gilbert would assign multiple students the same dataset to process in parallel and discuss at their next meeting.

“If multiple people come up with precisely the same solution even though they make different decisions, that means our analysis is robust and reliable,” Gilbert says. “The Cnidarians’ contributions were so useful that 13 of them are co-authors on this study.”

THIS STUDY WAS SUPPORTED BY THE DEPARTMENT OF ENERGY (DE-FG02-07ER15899 AND DE-AC02-05CHH11231), THE NATIONAL SCIENCE FOUNDATION (DMR-1603192) AND THE EUROPEAN RESEARCH COUNCIL (755876).

Several physics majors awarded Hilldale Fellowships

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Six UW–Madison undergraduate physics or AMEP majors have been named 2021 Hilldale Fellows, in addition to one computer science major who is conducting their research in the Physics Department.

The Hilldale Undergraduate/Faculty Research Fellowship provides research training and support to undergraduates at UW–Madison. Students have the opportunity to undertake their own research project in collaboration with UW–Madison faculty or research/instructional academic staff. Approximately 97 – 100 Hilldale awards are available each year.

Three students are conducting research in the Department of Physics, including:

  • Mathematics and Physics major Gage Siebert, in Prof. Peter Timbie’s group
  • Physics major Haley Stueber, in Prof. Dan McCammon’s group
  • Computer Sciences major Nikhilesh Venkatasubramanian, in Prof. Tulika Bose’s group

The physics or AMEP majors who have been named Hilldale Fellows and are conducting research outside the department are:

  • Mathematics and Physics major Sam Christianson, with Saverio Spagnolie (Mathematics)
  • Astronomy – Physics, Biochemistry, Chemistry, Mathematics, Molecular & Cell Biology, Neurobiology, Physics, Psychology, and Zoology major Renxi Li, with Catherine Gallagher (Neurology)
  • AMEP major Shenwei Yin, with Joseph Andrews (Mechanical Engineering)
  • Computer Sciences and Physics major Heqiao (Wonder) Zhu, with Kevin Eliceiri (LOCI)