Embracing Uncertainty Helps Bring Order to Quantum Chaos

In physics, chaos is something unpredictable. A butterfly flapping its wings somewhere in Guatemala might seem insignificant, but those flits and flutters might be the ultimate cause of a hurricane over the Indian Ocean. The butterfly effect captures what it means for something to behave chaotically: Two very similar starting points—a butterfly that either flaps its wings or doesn’t—could lead to two drastically different results, like a hurricane or calm winds.

But there's also a tamer, more subtle form of chaos in which similar starting points don’t cause drastically different results—at least not right away. This tamer chaos, known as ergodicity, is what allows a coffee cup to slowly cool down to room temperature or a piece of steak to heat up on a frying pan. It forms the basis of the field of statistical mechanics, which describes large collections of particles and how they exchange energy to arrive at a shared temperature. Chaos almost always grows out of ergodicity, forming its most eccentric variant.A system is ergodic if a particle traveling through it will eventually visit every possible point. In quantum mechanics, you never know exactly what point a particle is at, making ergodicity hard to track. In this schematic, the available space is divided into quantum-friendly cells, and an ergodic particle (left) winds through each of the cells, while a non-ergodic one (right) only visits a few. (Credit: Amit Vikram/JQI)A system is ergodic if a particle traveling through it will eventually visit every possible point. In quantum mechanics, you never know exactly what point a particle is at, making ergodicity hard to track. In this schematic, the available space is divided into quantum-friendly cells, and an ergodic particle (left) winds through each of the cells, while a non-ergodic one (right) only visits a few. (Credit: Amit Vikram/JQI)

Where classical, 19th-century physics is concerned, ergodicity is pretty well understood. But we know that the world is fundamentally quantum at the smallest scales, and the quantum origins of ergodicity have remained murky to this day—the uncertainty inherent in the quantum world makes classical notions of ergodicity fail. Now, Victor Galitski and colleagues in the Joint Quantum Institute (JQI) have found a way to translate the concept of ergodicity into the quantum realm. They recently published their results in the journal Physical Review Research. This work was supported by the DOE Office of Science (Office of Basic Energy Sciences).

“Statistical mechanics is based on the assumption that systems are ergodic,” Galitski says. “It’s an assumption, a conjecture, and nobody knows why. And our work sheds light on this conjecture.”

In the classical world, ergodicity is all about trajectories. Imagine an air hockey puck bouncing around a table. If you set it in motion, it will start bouncing off the walls, changing direction with each collision. If you wait long enough, that puck will eventually visit every point on the table's surface. This is what it means to be ergodic—to visit every nook and cranny available, given enough time. If you paint the puck’s path as you go, you will eventually color in the whole table. If lots of pucks are unleashed onto the table, they will bump into each other and eventually spread out evenly over the table.

To translate this idea of ergodicity into the quantum world of individual particles is tough. For one, the very notion of a trajectory doesn't quite make sense. The uncertainty principle dictates that you cannot know the precise position and momentum of a particle at the same time, so the exact path it follows ends up being a little bit fuzzy, making the normal definitions of chaos and ergodicity challenging to apply. 

Physicists have thought up several alternate ways to look for ergodicity or chaos in quantum mechanics. One is to study the particle’s quantum energy levels, especially how they space out and bunch up. If the way they bunch up has a particular kind of randomness, the theory goes, this is a type of quantum chaos. This might be a nice theoretical tool, but it’s difficult to connect to the actual motion of a quantum particle. Without such a connection to dynamics, the authors say there’s no fundamental reason to use this energy level signature as the ultimate definition of quantum chaos. “We don't really know what quantum chaos [or ergodicity] is in the first place,” says Amit Vikram, a graduate student in physics at JQI and lead author of the paper. “Chaos is a classical notion. And so what people really have are different diagnostics, essentially different things that they intuitively associate with chaos.”

Galitski and Vikram have found a way to define quantum ergodicity that closely mimics the classical definition. Just as an air hockey puck traverses the surface of the table, quantum particles traverse a space of quantum states—a surface like the air hockey table that lives in a more abstract world. But to capture the uncertainty inherent to the quantum world, the researchers break the space up into small cells rather than treating it as individual points. It's as if they divided the abstract air hockey table into cleverly chosen chunks and then checked to see if the uncertainty-widened particle has a decent probability of visiting each of the chunks.

“Quantum mechanically you have this uncertainty principle that says that your resolution in trajectories is a little bit fuzzy. These cells kind of capture that fuzziness,” Vikram says. “It's not the most intuitive thing to expect that some classical notion would just carry over to quantum mechanics. But here it does, which is rather strange, actually.”

Picking the correct cells to partition the space into is no easy task—a random guess will almost always fail. Even if there is only one special choice of cells where the particle visits each one, the system is quantum ergodic according to the new definition. The team found that the key to finding that magic cell choice, or ruling that no such choice exists, lies in the particle’s quantum energy levels, the basis of previous definitions of quantum chaos. This connection enabled them to calculate that special cell choice for particular cases, as well as connect to and expand the previous definition.

One advantage of this approach is that it's closer to something an experimentalist can see in the dynamics—it connects to the actual motion of the particle. This not only sheds light on quantum ergodicity, quantum chaos and the possible origins of thermalization, but it may also prove important for understanding why some quantum computing algorithms work while others do not.

As Galitski puts it, every quantum algorithm is just a quantum system trying to fight thermalization. The algorithm will only work if the thermalization is avoided, which would only happen if the particles are not ergodic. “This work not only relates to many body systems, such as materials and quantum devices, but that also relates to this effort on quantum algorithms and quantum computing,” Galitski says.

Original story by Dina Genkina: https://jqi.umd.edu/news/embracing-uncertainty-helps-bring-order-quantum-chaos

Reference Publications Dynamical quantum ergodicity from energy level statistics, A. Vikram Anand, and V. Galitski, Physical Review Research, 5, (2023)

Thomas Antonsen Honored by the American Physical Society

Distinguished University Professor Thomas M. Antonsen will receive the American Physical Society’s (APS) 2023 James Clerk Maxwell Prize for Plasma Physics for “pioneering contributions in the theory of magnetized plasma stability, RF, current drive, laser-plasma interactions, and charged particle beam dynamics”.  He will be honored at the 65th Annual Meeting of the APS Division of Plasma Physics in October.Thomas AntonsenThomas Antonsen

The James Clerk Maxwell Prize annually recognizes outstanding contributions to the field of plasma physics.  The prize is named after a nineteenth century Scottish physicist known for his work with electricity, magnetism and light.

Antonsen joined the department, then known as the Department of Electrical Engineering and Physics, in 1984.  He is highly recognized in his esearch fields of plasma theory, nonlinear dynamics and chaos, and currently holds appointments in Electrical and Computer Engineering (ECE), the Institute for Research in Electronics and Applied Physics (IREAP), Physics, and the Maryland Energy Innovation Institute.

In 2017, he was appointed University of Maryland Distinguished University Professor, the highest recognition for faculty members.  Other awards include the Clark School of Engineering Outstanding Research Award, the IEEE Plasma Science and Applications Award, the John R. Pierce Award for Excellence in Vacuum Electronics, and the IEEE Marie Sklodowska-Curie Award for contributions to plasma science. He is a fellow of IEEE and APS.

Antonsen will receive $10,000 and recognition at the 65th Annual Meeting of the APS Division of Plasma Physics this fall in Denver, Colorado. 

Previous UMD physicists who have won the Maxwell Prize include Hans R. Griem, Roald Sagdeev, James Drake, Phillip A. Sprangle and Ronald C. Davidson.


Ph.D. Student’s Initiative Led to Numerous Research Collaborations and Accolades

A big part of research is working with other scientists. As an undergraduate and graduate student at the University of Maryland, Jacob Bringewatt (B.S. ’18, physics) put in the work knocking on doors and connecting with professors, which allowed him to explore a broad range of research projects and earned him accolades along the way.

Bringewatt was torn deciding between a small liberal arts college and a bigger state university for college. He came to UMD to interview for a Banner/Key Scholarship and during the visit he spoke with Physics Professor Tom Cohen. Cohen emphasized that a strong research program—like the one UMD has—is an important component of a high-quality physics education. That conversation—and receiving the scholarship—pushed UMD to the top of Bringewatt’s list, and he enrolled in 2014.

As an incoming freshman, Bringewatt was eager to dive into theoretical physics research. During the first couple weeks of classes, he sought out Cohen to ask about joining a theoretical research project.

“He told me that I shouldn't do theory, even though he's a theorist,” Bringewatt said. “One should only do theory if they're like really bad at experiments or can't imagine doing anything else. I’ve learned since this is his standard line for eager undergrads.”

Jacob Bringewatt  Jacob Bringewatt

Bringewatt took Cohen’s advice and sought out an experimentalist: Physics Professor Carter Hall. Bringewatt joined Hall’s team and initially crunched numbers—analyzing experimental data instead of getting his hands dirty with experimental equipment. He eventually handled equipment in the lab and quickly realized it wasn’t for him. He still felt drawn to the math and theory side of physics. So he returned to Cohen, who directed him to Physics Professor William Dorland who was on sabbatical at the time. 

The summer before his junior year, Bringewatt wrote some computer code for Dorland to use in an ongoing project investigating how plasmas move. Dorland, who is a computational physicist, was interested in quantum computing and decided to spend some of his time during his sabbatical exploring the basics of quantum computation with Bringewatt. Their discussions developed into a collaboration with Stephen Jordan, who was then an adjunct associate professor of physics at UMD. The group investigated adiabatic quantum computation—a version of quantum computing that involves gradually evolving one quantum state into another. Bringewatt was the first author of a paper the collaboration wrote comparing the adiabatic quantum computing approach to a classical alternative. The experience focused Bringewatt on theoretical physics.

“I haven't really looked back since then,” Bringewatt said. “Maryland is a really good place to be for quantum computing. And, as a highly interdisciplinary field, it really does bring out the things I like most about research.”

Having settled on studying quantum theory, Bringewatt still had to decide where to attend grad school. UMD’s many experts and diverse research opportunities once again moved it to the top of his list. But he wanted to experience working in another group. So, before he graduated in 2018, he started visiting with professors. He found a match that felt right with Alexey Gorshkov, an adjunct associate professor of physics at UMD, and his group, which works on a broad range of theoretical physics topics.

During graduate school, Bringewatt has continued investigating adiabatic quantum computation, including collaborating with Michael Jarret (Ph.D. ’16, physics), who is now an assistant professor in the Mathematical Sciences Department at George Mason University. Together, they wrote a paper comparing classical and quantum adiabatic techniques for simulating quantum physics

Bringewatt also took on other challenges. A significant portion of his graduate research focuses on using quantum physics to push the limits of measurement technologies. This research involves improving sensor precision by optimizing the use of quantum entanglement—a fundamental quantum phenomenon that connects quantum particles and allows them to ignore some constraints of classical physics. The work looks at the smallest parts that contribute to a sensor, how the pieces interact, and how they come together during a measurement. By understanding sensors at this fundamental level, future technologies might be able to operate at the limits of what is allowed by physics.

Bringewatt shared this part of his research during the 2022 Three-Minute Thesis (3MT) competition hosted by UMD. 3MT competitions are hosted by many universities around the world to encourage graduate students to practice communicating technical research clearly and succinctly. In these events, the competitors distill a research project into a three-minute presentation that is accessible to someone unfamiliar with their field. Bringewatt was one of the eight winners in the campuswide competition, earning him a $1,000 prize. 

Jacob Bringewatt  delivers his 3-minute thesis.Jacob Bringewatt delivers his 3-minute thesis.“It was a fun challenge to explain in three minutes the big ideas behind a line of research I've been pursuing for several years with a number of excellent collaborators in Alexey Gorshkov's group,” Bringewatt said. 

As part of one of his projects on quantum sensor networks, Bringewatt, Gorshkov and UMD physics graduate student Adam Ehrenberg investigated the peak performance that networks of quantum sensors can achieve. His project built on previous work that had already established the best performance that is physically possible. Crucially, those results had assumed the maximum amount of entanglement—all the sensors are always connected to all the other sensors. But practically achieving maximum entanglement is difficult work, so Bringewatt and colleagues flipped the problem on its head. They identified the minimum amount of entanglement needed to achieve an optimal measurement, which for some cases didn't require maximum entanglement. They then developed protocols that achieve the theoretical target they had set. The team’s efforts earned them a place among the 12 groups of finalists for the 2022 UMD Invention of the Year Award.

"I'm honored to have gotten a chance to collaborate with Jake on many projects,” Gorshkov said. “I learned a lot from him and am very proud of his numerous achievements and well-deserved awards."

Even while juggling classes and research into both quantum sensors and adiabatic quantum computing, Bringewatt sought out new challenges. For his first four years as a graduate student, he was a Department of Energy (DOE) Computational Science Graduate Fellow. The program requires fellows to spend a summer working at a DOE laboratory, and it encourages them to explore new topics. 

Bringewatt was eager to try something completely new. He knew Zohreh Davoudi, associate professor of physics at UMD, from his undergraduate math methods course. And he was aware she studied nuclear theory and was interested in branching into quantum simulations. He thought a summer of nuclear theory might be interesting and have the additional benefit of providing a foundation to work with Davoudi. So, the first summer after starting graduate school, he requested to spend his summer at Jefferson Lab, which is home to a particle accelerator used for nuclear physics experiments. 

He spent his summer there as part of a team investigating the internal structure of protons. This small sample of nuclear physics research left Bringewatt eager for more, so he reached out to Davoudi. The timing worked out: She was looking for colleagues to collaborate with on developing quantum simulations of nuclear physics

He began attending Davoudi’s group meetings, and they eventually began pooling their skills on a project. Earlier this year, they published a paper on finding the best way to represent fermions—particles like electrons that can’t share their quantum state—and their interactions within quantum computer simulations. 

The topics of nuclear theory, quantum sensor research and adiabatic quantum computing have given Bringewatt diverse challenges and experiences throughout graduate school. As a result of his prodigious work ethic, he has been first author on ten research papers—an unusually high count for a graduate student.

“Being able to pursue these three distinct topics has been a real advantage of being here where there's a lot of experts on a wide array of things,” Bringewatt said. “I've gotten the chance to work with a lot of talented people with different areas of expertise, which has been really nice.”

Earlier this year, the College of Computer, Mathematical and Natural Sciences acknowledged his hard work and gave him the 2023 Board of Visitors Outstanding Graduate Student Award and a $5,000 prize. 

“I feel very honored to have received this recognition,” Bringewatt said. “Scientific research is never an individual effort, and having pursued both my undergraduate and graduate degree at the University of Maryland, I am extremely grateful to the university and all my mentors here who have enabled me to grow and excel as a young scientist.”

Bringewatt is wrapping up his research at UMD and looking for new collaborations and challenges as a postdoctoral researcher. He plans to graduate in the spring of 2024.

“I've been very happy to be at UMD,” Bringewatt said. “It's a great community, and, I think, the best of both worlds: It has a bunch of resources and world-class research, but people are also very approachable, friendly, and helpful. I feel extremely lucky for the years I’ve gotten to spend here.”

Written by Bailey Bedford


Related news stories:https://umdphysics.umd.edu/about-us/news/department-news/1639-davoudi-f20.html



From Particle Physics to Artificial Intelligence

Brian Calvert (Ph.D. '15, physics) grew up in southern Colorado in a rural community where “big world” opportunities were few and far between.

Brian CalvertBrian Calvert

“Right before you hit New Mexico there’s a tiny little town called Trinidad and we moved 40 miles northeast of there to the total boonies,” he recalled. “Our closest neighbors were a quarter of a mile away, we had no running water and no central heat. It was pretty wild.”

Calvert’s surroundings back then may have been simple, but his dreams were definitely not. As a teenager inspired by the problem-solving power of science and mathematics, he knew he wanted to take on challenges that impact people’s daily lives. But even he couldn’t have imagined that 20 years later he’d be blazing a trail on the cutting edge of artificial intelligence (AI) as co-founder of the San Francisco tech startup Graft.

“I had heard about robots and AI in the context of science fiction stories as a kid, but I had no exposure to what it meant to work on AI as it was back then,” Calvert said. “And AI has gone through such a massive renaissance that I'm not sure I could have imagined I'd work on it in the capacity that I have. But it’s exactly where I want to be.”

At Graft, Calvert is on a mission to make a difference by making AI more accessible.

"A lot of companies like nonprofits would love to be able to capitalize on the power of AI for their data, often for very clear social good, but it’s just really hard for them to do it—there are a lot of barriers to entry,” Calvert explained. “The core idea here is to help democratize access to the state-of-the-art infrastructure and techniques that are powering the AI giants of the world; let’s bring that to everybody else. That’s our mission: the AI of the 1%, for the 99%.”

Starting with physics

Calvert’s interests began with physics, first as an undergraduate at Princeton and then as a Ph.D. student at the University of Maryland. At UMD, Calvert quickly connected with Physics Professor Emeritus Nicholas Hadley. Intrigued by Hadley’s work in experimental particle physics, Calvert joined the CMS experiment at CERN, working in an inspiring collaboration with thousands of other scientists around the world to search for new physics at the world’s highest energy accelerator. Contributing to the 2012 discovery of the Higgs boson—the fundamental particle that enabled matter to form after the Big Bang created the universe billions of years ago—helped to focus the trajectory of Calvert’s Ph.D. dissertation research from 2013 through 2015.

“After the Higgs boson discovery, there were still more unanswered questions. One really elegant way to address a bunch of these questions is to introduce this notion of supersymmetry, where every fundamental particle has a mirror version of itself. If supersymmetry is correct, then we should find signatures of these supersymmetric partners,” Calvert explained. “Specifically, I was looking for the top squark, the supersymmetric partner to the heaviest fundamental particle, the top quark. For context, the two lightest quarks, the up- and down-quarks, are the primary building blocks of protons and neutrons, and the top quark can be thought of as the big brother of the up quark. If I could just find the top squark it would answer many other questions about the building blocks of the universe.”

Through his research in particle physics, Calvert saw the cross-disciplinary problem-solving power of science and mathematics in a whole new light.

“These particle physicists were working on algebraic stuff and math like I’d never seen and a bunch of computer science, too,” Calvert said. “We were analyzing petabytes and petabytes of data and there was a lot to the software part of it, like how do you analyze that much data at scale, particularly in the context of some problem you’re trying to solve. It’s like climbing a mountain. But it’s a mountain you want to climb.”

Wafers, hearing aids and self-driving cars

After earning his Ph.D. in 2015, Calvert landed a job as a senior imaging scientist at Intel’s wafer fabrication and manufacturing facility in Hillsboro, Oregon, working on the design of lithography photomasks used to print computer chips and performing large-scale analysis of electron microscope wafer images. At the time, concepts like machine learning (ML) and deep learning and the overall idea of AI were beginning to gain momentum and Calvert realized his skill set was a good fit.

He moved from Oregon to San Francisco to pursue opportunities in the space starting with some contract work building deep learning models for an audio detection system designed to enhance the function of hearing aids. In 2017, he went all in on ML and AI as a data scientist at Cruise Automation, a self-driving car company.

“That was a transformative experience,” Calvert recalled. "I initially worked on assessing the safety of the cars with a combination of ML and statistical models using data collected across the entire fleet of cars, then focused more on scalable data and machine learning infrastructure, as I knew from my Ph.D. experiences how important that was. That work got the attention of engineering leadership, and I was chosen to lead the whole overall machine learning infrastructure team. This included the AI models running on the car making real-time, safety-critical decisions and models running in the cloud analyzing data from the entire fleet. My team was building the structure to support that at scale and the work really energized me.”

After four years at Cruise, Calvert met Adam Oliner, CEO of Graft. Excited about the possibilities ahead, Calvert joined the company as a co-founder in 2021.

“I definitely think AI is the future,” Calvert said. “Humans keep generating data at larger and larger rates, so AI has to be the future. There’s no way you can manually process that much data at scale, nor should you.”

Graft’s aim is to create AI technology that can quickly perform large-scale analysis of unstructured data—including text, images, and graphs—to meet the needs of any client, whether it’s a customer-driven sales business or a search-and-rescue team trying to locate a missing hiker.

“Whether it’s a lost hiker and there are miles and miles worth of images to search through or it’s a business that wants a real-time customer churn prediction, Graft provides a platform,” Calvert explained. “You connect us to your data, we have ML science modeling experts and ML infrastructure experts on staff, and our system provides an automated workflow to help you get to the goal.”

The company—and venture capital support for its mission—have already come a long way.

“We did a pre-seed round of $4.5 million a few years ago in early 2021 and then we just closed a seed round of $10 million, so we’re at $14.5 million in venture capital funding so far,” Calvert said.

Though Graft’s AI platform is still in beta testing, Calvert is optimistic about the future.

“We ran a private beta starting in fall 2022. After the feedback from this beta, we've now expanded to a wider, controlled rollout,” he said. “We definitely think we have a product that people would pay money for.”

A strong foundation

For Calvert, Graft’s mission of bringing the capabilities of the world’s biggest AI companies to every business is as demanding as it is inspiring. He’s quick to point out he never would have gotten here without physics and his time at UMD, which provided a strong foundation for the challenges he faced on every step of his journey.

“150,000%—UMD helped me grow in so many ways,” Calvert noted. “My Ph.D., which focused on experimental particle physics, was effectively a data science Ph.D. It gave me higher-order systems-level thinking that I draw upon all the time, as well as statistics and large-scale data analysis and AI/ML skills. I’m really grateful for that.”

Twenty years ago, Calvert never could have envisioned a future in AI—now he can’t imagine being anywhere else.

“I couldn’t really see myself doing anything else right now,” Calvert reflected. “Will it be that way forever? Maybe, maybe not. Either way, right now this is a really good place for me to be.”

Written by Leslie Miller