In the rapidly evolving landscape of quantum technologies, ensuring the functionality and reliability of quantum devices is critical. The ability to characterize these devices with high accuracy and speed is essential for their efficient integration into quantum circuits and computers, impacting both fundamental studies and practical applications.

Characterization helps determine if a device operates as expected, which is necessary when devices exhibit anomalies or errors. Identifying and addressing these issues is crucial for advancing the development of future quantum technologies.

Traditionally, scientists have relied on Quantum Process Tomography (QPT), a method that requires a large number of “projective measurements” to reconstruct a device’s operations fully. However, the number of required measurements in QPT scales quadratically with the dimensionality of the operations, posing significant experimental and computational challenges, especially for high-dimensional quantum information processors.

The University of Ottawa research team has pioneered an optimized technique named Fourier Quantum Process Tomography (FQPT). This method allows for the complete characterization of quantum operations with a minimal number of measurements. Instead of performing a large number of projective measurements, FQPT utilises a well-known map, the Fourier transform, to perform a portion of the measurements in two different mathematical spaces. The physical relation between these spaces enhances the information extracted from single measurements, significantly reducing the number of measurements needed. For instance, for processes with dimensions 2d (where d can be arbitrarily high), only seven measurements are required.

To validate their technique, the researchers conducted a photonic experiment using optical polarisation to encode a qubit. The quantum process was realized as a complex space-dependent polarisation transformation, leveraging state-of-the-art liquid-crystal technology. This experiment demonstrated the flexibility and robustness of the method.

“The experimental validation is a fundamental step to probe the technique’s resilience to noise, ensuring robust and high-fidelity reconstructions in realistic experimental scenarios,” said Francesco Di Colandrea, a postdoctoral fellow at the University of Ottawa.

This novel technique represents a remarkable advancement in quantum computing. The research team is already actively working on extending FQPT to arbitrary quantum operations, including non-Hermitian and higher-dimensional implementations, and in implementing AI techniques to increase accuracy and reduce measurement. This new technique represents a promising avenue for further advancements in quantum technology.

Fortunately, space has dropped a few clues — fragments of objects that formed early in solar system history and plunged through Earth’s atmosphere, called meteorites. The composition of meteorites tells stories of the solar system’s birth, but these stories often raise more questions than answers.

In a paper published in Proceedings of the National Academy of Sciences, a team of planetary scientists from UCLA and Johns Hopkins University Applied Physics Laboratory reports that refractory metals, which condense at high temperatures, such as iridium and platinum, were more abundant in meteorites formed in the outer disk, which was cold and far away from the sun. These metals should have formed close to the sun, where the temperature was much higher. Was there a pathway that moved these metals from the inner disk to the outer?

Most meteorites formed within the first few million years of solar system history. Some meteorites, called chondrites, are unmelted conglomerations of grains and dust left over from planet formation. Other meteorites experienced enough heat to melt while their parent asteroids were forming. When these asteroids melted, the silicate part and the metallic part separated due to their difference in density, similar to how water and oil don’t mix.

Today, most asteroids are located in a thick belt between Mars and Jupiter. Scientists think that Jupiter’s gravity disrupted the course of these asteroids, causing many of them to smash into each other and break apart. When pieces of these asteroids fall to Earth and are recovered, they are called meteorites.

Iron meteorites are from the metallic cores of the earliest asteroids, older than any other rocks or celestial objects in our solar system. The irons contain molybdenum isotopes that point toward many different locations across the protoplanetary disk in which these meteorites formed. That allows scientists to learn what the chemical composition of the disk was like in its infancy.

Previous research using the Atacama Large Millimeter/submillimeter Array in Chile has found many disks around other stars that resemble concentric rings, like a dartboard. The rings of these planetary disks, such as HL Tau, are separated by physical gaps, so this kind of disk could not provide a route to transport these refractory metals from the inner disk to the outer.

The new paper holds that our solar disk likely didn’t have a ring structure at the very beginning. Instead, our planetary disk looked more like a doughnut, and asteroids with metal grains rich in iridium and platinum metals migrated to the outer disk as it rapidly expanded.

But that confronted the researchers with another puzzle. After the disk expansion, gravity should have pulled these metals back into the sun. But that did not happen.

“Once Jupiter formed, it very likely opened a physical gap that trapped the iridium and platinum metals in the outer disk and prevented them from falling into the sun,” said first author Bidong Zhang, a UCLA planetary scientist. “These metals were later incorporated into asteroids that formed in the outer disk. This explains why meteorites formed in the outer disk — carbonaceous chondrites and carbonaceous-type iron meteorites — have much higher iridium and platinum contents than their inner-disk peers.”

Zhang and his collaborators previously used iron meteorites to reconstruct how water was distributed in the protoplanetary disk.

“Iron meteorites are hidden gems. The more we learn about iron meteorites, the more they unravel the mystery of our solar system’s birth,” Zhang said.

A similar idea is at play in the scientific field of membrane separations, a key process central to industries that include everything from biotechnology to petrochemicals to water treatment to food and beverage.

“Separations lie at the heart of so many of the products we use in our everyday lives,” said Seth Darling, head of the Advanced Materials for Energy Water Systems (AMEWS) Center at the U.S. Department of Energy’s (DOE) Argonne National Laboratory. ​”Membranes are the key to achieving efficient separations.”

Many commercial processes use membranes to separate out different sizes of solutes, which are substances that are dissolved in water or other fluids. Nearly all commercial membranes are polydisperse, which means that their pore sizes are not consistent. For these membranes, it’s nearly impossible to do a sharp separation of materials as different sizes of solutes can fit through different pores. ​”Essentially all commercial membranes, all membranes that are actually used for anything, have a wide range of pore sizes — little pores, medium pores and big pores,” Darling said.

Darling and his colleagues at Argonne and the Pritzker School of Molecular Engineering at the University of Chicago have been interested in looking at the properties of isoporous membranes, which are membranes in which all the pores are the same size. Previously, scientists had believed there was a limit to the sharpness of the separations that they could achieve at the nanoscale, not only because of variations in pore size, but also a phenomenon called ​”hindered transport.”

Hindered transport refers to the internal resistance of the fluid medium as the solute attempts to go through the pore.

“The water in the pore will create drag on a molecule or particle that’s trying to get through, causing it to slow down,” Darling said. ​”Those slower solutes appear to be rejected by the membrane. Counterintuitively, objects even half the size of the pore will end up being rejected about half the time.” Overcoming rejection created by hindered transport would enable unprecedented selectivity in size-based separations, he explained.

“The regime we’re interested in involves pores approximately 10 nanometers in diameter. With a perfect membrane and proper process design, we believe we could separate solutes with as little as a five percent difference in size. Current membranes have no chance to pull that off,” Darling said.

In a new study, Darling and his colleagues uncovered a dynamic that could only be revealed by studying isoporous membranes, and that gives hope for surmounting hindered transport limitations. ​”Until now, scientists had implicitly assumed that each solute only gets one try to go through a pore, and that hindered transport would produce rejection of many solutes that were smaller than the pore size, causing them to remain in the feed stream rather than the output stream,” Darling added. ​”Although it might seem obvious to some, people never really considered a situation in which the solutes could make multiple attempts to get through a membrane.”

To give the solute molecules multiple chances to get through the pore required cycling the feed solution for multiple weeks. ​”Even with an extended period of experimentation, we’re still only seeing individual solutes trying to get through a pore a couple of times on average, but it makes a big difference in moving the separation curve towards a sharper step-like function,” Darling said. ​”Given longer time, or more likely an improved process design, we believe we will see a clear, sharp separation right where the pore size matched the solute size.”

The insights learned from isoporous membranes could be applicable to existing membrane materials engineered to increase the number of opportunities for solutes to pass through the pores. ​”If these fundamental studies can be successfully transferred to industrial membrane separations, it could have tremendous impact across numerous sectors of our economy,” he said.

The work was supported by DOE’s Office of Basic Energy Sciences.

The existence of Titan’s large seas and smaller lakes was confirmed in 2007, with images taken by NASA’s Cassini spacecraft. Since then, scientists have pored over those and other images for clues to the moon’s mysterious liquid environment.

Now, MIT geologists have studied Titan’s shorelines and shown through simulations that the moon’s large seas have likely been shaped by waves. Until now, scientists have found indirect and conflicting signs of wave activity, based on remote images of Titan’s surface.

The MIT team took a different approach to investigate the presence of waves on Titan, by first modeling the ways in which a lake can erode on Earth. They then applied their modeling to Titan’s seas to determine what form of erosion could have produced the shorelines in Cassini’s images. Waves, they found, were the most likely explanation.

The researchers emphasize that their results are not definitive; to confirm that there are waves on Titan will require direct observations of wave activity on the moon’s surface.

“We can say, based on our results, that if the coastlines of Titan’s seas have eroded, waves are the most likely culprit,” says Taylor Perron, the Cecil and Ida Green Professor of Earth, Atmospheric and Planetary Sciences at MIT. “If we could stand at the edge of one of Titan’s seas, we might see waves of liquid methane and ethane lapping on the shore and crashing on the coasts during storms. And they would be capable of eroding the material that the coast is made of.”

Perron and his colleagues, including first author Rose Palermo, a former MIT-WHOI Joint Program graduate student and a research geologist at the U.S. Geological Survey, will publish their study in a forthcoming issue of Science Advances. Their co-authors include MIT research scientist Jason Soderblom, former MIT postdoc Sam Birch, now an assistant professor at Brown University, Andrew Ashton at the Woods Hole Oceanographic Institution, and Alexander Hayes of Cornell University.

“Taking a different tack”

The presence of waves on Titan has been a somewhat controversial topic ever since Cassini spotted bodies of liquid on the moon’s surface.

“Some people who tried to see evidence for waves didn’t see any, and said, ‘These seas are mirror-smooth,'” Palermo says. “Others said they did see some roughness on the liquid surface but weren’t sure if waves caused it.”

Knowing whether Titan’s seas host wave activity could give scientists information about the moon’s climate, such as the strength of the winds that could whip up such waves. Wave information could also help scientists predict how the shape of Titan’s seas might evolve over time.

Rather than look for direct signs of wave-like features in images of Titan, Perron says the team had to “take a different tack, and see, just by looking at the shape of the shoreline, if we could tell what’s been eroding the coasts.”

Titan’s seas are thought to have formed as rising levels of liquid flooded a landscape crisscrossed by river valleys. The researchers zeroed in on three scenarios for what could have happened next: no coastal erosion; erosion driven by waves; and “uniform erosion,” driven either by “dissolution,” in which liquid passively dissolves a coast’s material, or a mechanism in which the coast gradually sloughs off under its own weight.

The researchers simulated how various shoreline shapes would evolve under each of the three scenarios. To simulate wave-driven erosion, they took into account a variable known as “fetch,” which describes the physical distance from one point on a shoreline to the opposite side of a lake or sea.

“Wave erosion is driven by the height and angle of the wave,” Palermo explains. “We used fetch to approximate wave height because the bigger the fetch, the longer the distance over which wind can blow and waves can grow.”

To test how shoreline shapes would differ between the three scenarios, the researchers started with a simulated sea with flooded river valleys around its edges. For wave-driven erosion, they calculated the fetch distance from every single point along the shoreline to every other point, and converted these distances to wave heights. Then, they ran their simulation to see how waves would erode the starting shoreline over time. They compared this to how the same shoreline would evolve under erosion driven by uniform erosion. The team repeated this comparative modeling for hundreds of different starting shoreline shapes.

They found that the end shapes were very different depending on the underlying mechanism. Most notably, uniform erosion produced inflated shorelines that widened evenly all around, even in the flooded river valleys, whereas wave erosion mainly smoothed the parts of the shorelines exposed to long fetch distances, leaving the flooded valleys narrow and rough.

“We had the same starting shorelines, and we saw that you get a really different final shape under uniform erosion versus wave erosion,” Perron says. “They all kind of look like the flying spaghetti monster because of the flooded river valleys, but the two types of erosion produce very different endpoints.”

The team checked their results by comparing their simulations to actual lakes on Earth. They found the same difference in shape between Earth lakes known to have been eroded by waves and lakes affected by uniform erosion, such as dissolving limestone.

A shore’s shape

Their modeling revealed clear, characteristic shoreline shapes, depending on the mechanism by which they evolved. The team then wondered: Where would Titan’s shorelines fit, within these characteristic shapes?

In particular, they focused on four of Titan’s largest, most well-mapped seas: Kraken Mare, which is comparable in size to the Caspian Sea; Ligeia Mare, which is larger than Lake Superior; Punga Mare, which is longer than Lake Victoria; and Ontario Lacus, which is about 20 percent the size of its terrestrial namesake.

The team mapped the shorelines of each Titan sea using Cassini’s radar images, and then applied their modeling to each of the sea’s shorelines to see which erosion mechanism best explained their shape. They found that all four seas fit solidly in the wave-driven erosion model, meaning that waves produced shorelines that most closely resembled Titan’s four seas.

“We found that if the coastlines have eroded, their shapes are more consistent with erosion by waves than by uniform erosion or no erosion at all,” Perron says.

The researchers are working to determine how strong Titan’s winds must be in order to stir up waves that could repeatedly chip away at the coasts. They also hope to decipher, from the shape of Titan’s shorelines, from which directions the wind is predominantly blowing.

“Titan presents this case of a completely untouched system,” Palermo says. “It could help us learn more fundamental things about how coasts erode without the influence of people, and maybe that can help us better manage our coastlines on Earth in the future.”

This work was supported in part by NASA, the National Science Foundation, the USGS, and the Heising-Simons Foundation.