Enhancing Simulations of Curved Space with Qubits

One of the mind-bending ideas that physicists and mathematicians have come up with is that space itself—not just objects in space—can be curved. When space curves (as happens dramatically near a black hole), sizes and directions defy normal intuition. Something as straightforward as defining a straight line requires careful consideration.

Understanding curved spaces is important to expanding our knowledge of the universe, but it is fiendishly difficult to study curved spaces in a lab setting (even using simulations). A previous collaboration between researchers at JQI explored using labyrinthine circuits made of superconducting resonators to simulate the physics of certain curved spaces (see the previous story for additional background information and motivation of this line of research). In particular, the team looked at hyperbolic lattices that represent spaces—called negatively curved spaces(link is external)—that have more space than can fit in our everyday “flat” space. Our three-dimensional world doesn’t even have enough space for a two-dimensional negatively curved space.

Now, in a paper published in the journal Physical Review Letters(link is external) on Jan. 3, 2022, the same collaboration between the groups of Alicia Kollár and Alexey Gorshkov expands the potential applications of the technique to include simulating more intricate physics. They’ve laid a theoretical framework for adding qubits—the basic building blocks of quantum computers—to serve as matter in a curved space made of a circuit full of flowing microwaves. Specifically, they considered the addition of qubits that change between two quantum states when they absorb or release a microwave photon—an individual quantum particle of the microwaves that course through the circuit.(Left image) Microwave photons that create an interaction between pairs of qubits (black dots on the edge) in a hyperbolic space are most likely to travel along the shortest path (dotted line). In both images, the darker colors show where photons are more likely to be found. (Right image) A quantum state formed by a qubit (grey dot containing parallel black lines) and an attached microwave photon that can be found at one of the intersections of the grid representing a curved space. (Credit: Przemyslaw Bienias/JQI)(Left image) Microwave photons that create an interaction between pairs of qubits (black dots on the edge) in a hyperbolic space are most likely to travel along the shortest path (dotted line). In both images, the darker colors show where photons are more likely to be found. (Right image) A quantum state formed by a qubit (grey dot containing parallel black lines) and an attached microwave photon that can be found at one of the intersections of the grid representing a curved space. (Credit: Przemyslaw Bienias/JQI)

“This is a new frontier in tabletop experiments studying effects of curvature on physical phenomena,” says first author Przemyslaw Bienias, a former Joint Quantum Institute (JQI) assistant research scientist who is now working for Amazon Web Services as a Quantum Research Scientist. “Here we have a system where this curvature is huge and it's very exciting to see how it influences the physics.”

For researchers to use these simulations they need a detailed understanding of how the simulations represent a curved space and even more importantly under what situations the simulation fails. In particular, the edges that must exist on the physical circuits used in the simulations must be carefully considered since scientists are often interested in an edgeless, infinite curved space. This is especially important for hyperbolic lattices because they have nearly the same number of sites on the edge of the lattice as inside. So the team identified situations where the circuits should reflect the reality of an infinite curved space despite the circuit’s edge and situations where future researchers will have to interpret results carefully.

The team found that certain properties, like how likely a qubit is to release a photon, shouldn’t be dramatically impacted by the circuit’s edge. But other aspects of the physics, like the proportion of states that photons occupy at a given shared total energy, will be strongly influenced by the edge.

With proper care, this type of simulation will provide a peek into how negatively curved spaces are a foundation for an entirely new world of physics.

“In this paper, we asked the question, ‘What happens when you add qubits to the photons living on those hyperbolic lattices?’” Bienias says. “We are asking, ‘What type of physics emerges there and what type of interactions are possible?’”

The researchers first looked at how the microwaves and a single qubit in the circuit can combine. The team predicts that the size of special quantum states in which a photon is attached to a particular qubit—a bound state—will be limited by the curved space in a way that doesn’t happen in flat space. The right-side image above shows such a state with the darker coloring showing where the photon is most likely to be found around the qubit represented by the grey dot.

They then investigated what happens when there are multiple qubits added to a circuit full of microwaves. The photons traveling between qubits serve as intermediaries and allow the qubits to interact. The team’s analysis suggests that the photons that are causing qubits to interact tend to travel along the shortest path between the two points in the circuit—corresponding to the shortest distance in the simulated curved space. One of these paths through the curved space is shown in the left-side image above. This result matches physicists’ current expectations of such a space and is a promising sign that the simulations will reveal useful results in more complex situations.

Additionally, the researchers predict that the curvature will limit the range of the interactions between qubits similar to the way it limits the size of the individual bound states. Simulations using this setup could allow scientists to explore the behaviors of many particles interacting in a curved space, which is impractical to study using brute numerical calculation.

These results build upon the previous research and provide additional tools for exploring new physics using superconducting circuits to simulate curved space. The inclusion of interactions explored in this paper could aid in using the simulations to investigate the topic called AdS/CFT correspondence that combines theories of quantum gravity and quantum field theories.

“Hyperbolic connectivity is immensely useful in classical computation, underlying, for example, some of the most efficient classical error correcting codes in use today,” Kollár says. “We now know that adding qubits to a hyperbolic resonator lattice will endow the qubits’ interactions with hyperbolic structure, rather than the native flat curvature of the lab. This opens the door to allow us to carry out direct experiments to examine the effect of hyperbolic connectivity on quantum bits and quantum information.”

Original story by Bailey Bedford: https://jqi.umd.edu/news/enhancing-simulations-curved-space-qubits

In addition to Kollár, Gorshkov and Bienias, other co-authors of the paper were Ron Belyansky, a JQI physics graduate student, and Igor Boettcher, a former JQI postdoctoral researcher and current assistant professor at the University of Alberta.

Sau Named UMD Co-Director of JQI

Associate Professor Jay Sau has been appointed the newest University of Maryland Co-Director of JQI. He assumed the role on January 1, 2022.

“JQI has been a key part of my research environment since I started as a postdoc at Maryland in 2009,” says Sau, who is also a member of the Condensed Matter Theory Center. “I am glad to have the opportunity to help preserve and strengthen our research environment.”Jay Sau is now the UMD co-director of JQI. (Credit: Moutusi Sau)Jay Sau is now the UMD co-director of JQI. (Credit: Moutusi Sau)

Sau followed his first position at UMD with a postdoctoral fellowship at Harvard University, before returning to UMD as an assistant professor in 2013. During his time at UMD, he has performed extensive theoretical research into the phenomena that arise when many quantum particles interact, particularly phenomena that can be understood through the mathematics of topology. Sau and his collaborators at UMD have developed tools that are laying a foundation for quantum technologies, hopefully including topological quantum computers.

Previously, Sau has been a co-organizer of both the JQI seminar series and the physics colloquium series, and he has been participating in expanding the quantum research group at UMD. He is taking over the role of UMD Co-Director from JQI Fellow Fred Wellstood, who has held the position since 2017.

“I’ve enjoyed working with Fred as Co-Directors over the past four years" says Gretchen Campbell, the current NIST Co-Director of JQI. "He has worked tirelessly to help keep the JQI running during these challenging times, including spearheading the recent renewal of the JQI grant.  Moving forward, I am looking forward to working with Jay. He is a great colleague, and I appreciate his willingness to take over the role of Co-Director.”

Original story by Bailey Bedford: https://jqi.umd.edu/news/sau-named-umd-co-director-jqi

In a Smooth Move, Ions Ditch Disorder and Keep Their Memories

A Persian adage, notably wielded by Abe Lincoln(link is external) and the band OK Go(link is external), expresses the ephemeral nature of the world: “This, too, shall pass.”

Physicists have their own version of this rule. It says that wiggles and wrinkles—really any small disturbances—tend to get ironed out over time. For instance, a couple drops of blue food coloring mixed into some cake batter will impart a blue tint to the whole batch; fresh water from a river funneled into the salty ocean will spread out and make a slightly less salty ocean; and a gush of cold wind entering your room will mingle with the air inside and reach a single, cooler temperature. The basic idea is that, given enough time, everything will reach equilibrium, regardless of where it started.

There are a few notable exceptions to this equanimous rule. In the quantum world of atoms and electrons, particles confined in a container made of electric and magnetic fields—akin to a bowl confining cake batter—can get stuck in place if the container isn’t smooth. When this “bowl” is rough, disorderly, and random, the particles can’t make up their minds about which way to go and instead stay put. Oddly, even when a bunch of these localized particles are allowed to influence each other, they can manage to stay localized, not exchanging energy and avoiding equilibrium. This effect, known as many-body localization (MBL), imparts particles with a kind of memory of where they started.

Now, scientists have found a new way to create disturbances that do not fade away. Instead of relying on disorder to freeze things in place, they tipped the quantum particles’ container to one side—a trick that is easier to conjure in the lab. A collaboration between the experimental group of College Park Professor Christopher Monroe and the theoretical group of Alexey Gorshkov, who is also a Fellow of the Joint Quantum Institute, and the Joint Center for Quantum Information and Computer Science and a physicist at the National Institute of Standards and Technology, has used trapped ions to implement this new technique, confirming that it prevents their quantum particles from reaching equilibrium. The team also measured the slowed spread of information with the new tipping technique for the first time. They published their results(link is external) recently in the journal Nature.

“One advantage of this method of many-body localization is that we don't need that disorder,” says Fangli Liu, former graduate student in physics at the University of Maryland (now a research scientist at QuEra Computing) and lead theorist on the work. “In the original system the disorder is realized in a random form. But with this method, each time you do a measurement you will have exactly the same result. It gives us the possibility to more efficiently use this many-body localization to do something interesting.”Researchers have demonstrated a new way for atomic ions to host disturbances that do not fade away. (credit: E. Edwards/JQI)Researchers have demonstrated a new way for atomic ions to host disturbances that do not fade away. (credit: E. Edwards/JQI)

Instead of color (as in the dough example) or temperature (in the case of air in your room), the disturbance in the JQI experiment was in the ions’ spins—their little internal magnets that can point up or down (or a bit of both at the same time, as in a quantum superposition). These ion spins sit in a container shaped not like a bowl but instead like a single row of an egg carton, with each ion residing in a different dimple of the container. Normally, after some time all spins would point in the same direction uniformly, with no memory of whether each spin pointed up or down to begin with.

By controlling the ions individually, the scientists can prepare one spin that points up while the rest point down. With an egg carton container that’s flat (like it’s sitting on a table), the single spin disturbance can hop between ions, chatting with neighbors and ultimately causing all the ions to agree on a uniform configuration. In traditional many-body localization, where randomness and disorder rule the Normally, ion spins that start out pointing in opposite directions will interact and reach an equilibrium, with no trace of where they started. But when the tilt in their container is large enough, they keep pointing in their original direction, creating a many-body localized state that remembers its initial configuration. (Credit: Adapted from article by the authors/JQI)Normally, ion spins that start out pointing in opposite directions will interact and reach an equilibrium, with no trace of where they started. But when the tilt in their container is large enough, they keep pointing in their original direction, creating a many-body localized state that remembers its initial configuration. (Credit: Adapted from article by the authors/JQI)day, the egg-carton dimples become offset up or down from each other in a random way, paralyzing each spin in its spot.

Instead of adding disorder, the team tilted the egg carton, offsetting each dimple a little higher than its neighbor to the left in a smooth, consistent way. This caused the spins to get localized as well, but for a very different reason. Quantum particles have wave-like properties, and once they start rolling down in the direction of a tilt, they can get reflected by the edges of the egg carton dimples. So instead of rolling downhill forever, they roll down and bounce back up over and over again, which confines them to their small region of the container.  

For a single particle, this pinning mechanism has been known since the 1930s. But whether it would persist in the face of interactions between many particles and halt equilibration has only recently been explored. Indeed, the idea that tilting the egg carton would result in a breakdown of equilibration was only proposed in 2019.

The JQI team confirmed this in their experiment. Using tightly focused lasers, they adjusted each ion individually and prepared them in a highly disturbed state, with spins pointing in alternating directions. At the same time, they had extra lasers shining on all the ions together, allowing them to talk to each other even while far apart. If the tilt was high enough, the team found, the ions’ spins remained in their original configuration for an extended period, refusing to succumb to equilibrium.

In addition to a conceptual leap, creating MBL without disorder may come with certain practical advantages. First, it is experimentally easier to implement a smooth tilt (in fact, a small tilt was present in the JQI experiment whether they wanted it or not). Second, it makes measurements much more straightforward. And third, this method is immune to an accidental break down of MBL. In regular disorder-based MBL, the random offsets of the dimples need to be large. If they aren’t, localization can break down in some spots and infect the whole batch. With a smooth tilt, there’s no such risk.

This opens the possibility of using many-body localization to create a robust memory. MBL might help maintain quantum information in future quantum computers or help preserve curiosities like time crystals or topological phases.

In the past year, two other experiments realizing this method were reported. The team of H. Wang in Hangzhou, China set it up using superconducting qubits(link is external), and Monika Aidelburger’s team in Munich, Germany made it happen(link is external) with ultracold atoms.

“There's a lot of shared themes between our three papers,” says William Morong, a postdoctoral researcher at JQI and lead author on the work, “and I would say all of them together give a more complete picture of the phenomenon then each individually.”

The JQI group was the only one, however, to demonstrate another key property of many-body localization: the slow spread of entanglement between their ions. The team used a technique adapted from nuclear magnetic resonance imaging to measure the crawling pace with which entanglement spread across their atoms, a hallmark of MBL.

“I think that our work shows the exciting progress that has been made in modern quantum simulation platforms,” Morong says, “We are reaching the point where we have enough control over collections of quantum particles in these platforms that we can read a theoretical paper describing some interesting effect that emerges in a specific system, program in the forces that we need to create this effect for ourselves, and measure subtle signatures in the quantum entanglement between the particles that are only revealed when you can observe each particle individually. "

Original story by Dina Genkina:  https://jqi.umd.edu/news/smooth-move-ions-ditch-disorder-and-keep-their-memories

In addition to Liu, Morong, Monroe and Gorshkov, authors on the paper included former graduate student in physics Patrick Becker (now a physicist at Booz Allen Hamilton), graduate student in physics Kate Collins, postdoctoral researcher at JQI Lei Feng, former graduate student in physics (now a postdoctoral fellow at Indiana University in Bloomington) Antonis Kyprianidis, former postdoctoral fellow at JQI (now assistant professor of physics at Rice University) Guido Pagano, and undergraduate researcher Tianyu You.

Research Contact
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Michael E. Fisher, 1931-2021

Michael Ellis Fisher, an eminent scientist whose interests spanned condensed matter theory, statistical mechanics, chemistry, mathematics and bioscience, died on November 26, 2021 at age 90.

Born in Trinidad, Fisher received his Ph.D. in 1957 at King’s College, London. He worked there as a lecturer, reader and professor until accepting an appointment at Cornell University.  He was the Horace White Professor of Chemistry, Physics and Mathematics at Cornell University until joining the University of Maryland in 1987. At UMD, he was jointly appointed in the Institute for Physical Sciences and Technology and the Department of Physics, and was a University System of Maryland Regents Professor, a Distinguished University Professor and Distinguished Scholar-Teacher.

Fisher was a Fellow of the Royal Society, the American Academy of Arts and Sciences, the American Association for the Advancement of Science and the American Physical Society. He was a Foreign Associate of the National Academy of Sciences. Among his many awards were the Irving Langmuir Prize in Chemical Physics, the Boltzmann Medal in Thermodynamics and Statistical Mechanics and the Hildebrand Award of the American Chemical Society. Fisher received the inaugural American Physical Society Lars Onsager Prize for statistical physics in 1995.

Known both for his attention to detail and for his broad approach to understanding the world, Fisher was commended by the Wolf Prize in Physics committee in 1980 “for bringing together, and teaching a common language to, chemists and physicists working on diverse problems of phase transitions.”   

Fisher retired in 2012, and a two-day UMD symposium honored his many achievements. In 2015, he was a special guest at the Conversations with Icons in Science conference in Port of Spain, Trinidad.


A memorial has not yet been announced.
The IPST remembrance is posted here: https://ipst.umd.edu/news/distinguished-university-professor-emeritus-michael-e-fisher-1931-2021