Tech
New design tackles integer factorization problems through digital probabilistic computing
Probabilistic Ising machines (PIMs) are advanced and specialized computing systems that could tackle computationally hard problems, such as optimization or integer factorization tasks, more efficiently than classical systems. To solve problems, PIMs rely on interacting probabilistic bits (p-bits), networks of interacting units of digital information with values that randomly fluctuate between 0 and 1, but that can be biased to converge to yield desired solutions.
A class of PIMs that are intensively investigated use magnetic devices to inject randomness into a digital transistor-based circuit. While these systems have been found to be promising for the rapid resolution of various domain-specific and advanced problems, their large-scale design and reliable fabrication have so far proved challenging. This is primarily because their upscaling requires the precise control of small magnetic moments and often also entails the use of large circuits that convert digital signals into analog voltages and other additional components.
Researchers at Northwestern University and other institutes recently developed a new application-specific integrated circuit (ASIC) that could be used to create better performing probabilistic computers. In a paper published in Nature Electronics, they presented a probabilistic computer based on the new circuit and showed that it could perform integer factorization tasks.
“We were interested in exploring how one could build a scalable probabilistic computer by custom-designing an ASIC using foundry CMOS technology,” Pedram Khalili Amiri, senior author of the paper, told Tech Xplore.
“Our intuition was that by taking advantage of the digital CMOS platform and the high transistor densities available in today’s semiconductor technology, one could eventually build very large-scale probabilistic computers that can tackle problems related to, for example, combinatorial optimization. As a first step, we decided to try out these ideas, and develop the computing architecture and design approach, using a less advanced (130 nm) foundry node.”
When reviewing previous literature in the field and experimenting with probabilistic computing architectures, Amiri and his colleagues realized that, despite its numerous advantages, CMOS technology does not appear to be well-suited for creating random bit sequences. Notably, the creation of these random sequences is central to the functioning of probabilistic computers.
To overcome this limitation of CMOS technology, the researchers adapted voltage-controlled magnetic tunnel junctions (V-MTJs), hardware components that they introduced in their earlier work and had previously applied to the creation of magnetic random-access memory (MRAM) devices. They changed some elements of these devices so that they would serve as high-throughput and compact sources of randomness (i.e., entropy).
“Our probabilistic computer consists of an array of bistable probabilistic elements (called probabilistic bits or p-bits),” explained Amiri. “The interactions between these p-bits can be programmed so that the p-bit network (called a probabilistic Ising machine or PIM) collectively searches through the solution space of a problem. Our p-bits are implemented using digital CMOS circuitry on our ASIC and use bit sequences read from an adjacent V-MTJ chip to provide the required randomness. The energy minimum of the PIM is designed to correspond to the solution of the computing problem of interest.”

The new probabilistic architecture developed by Amiri and his colleagues could theoretically be used to efficiently tackle many real-world problems, including various optimization tasks. As part of their study, however, the team specifically applied their architecture to integer factorization tasks, which are known to be very challenging to solve computationally.
“This was a good place to start, mainly because there is only one correct solution to be found in the entire energy landscape, and because it is easy to check whether we found the right factors or not,” said Amiri. “The same approach, however, can be applied to many other computing problems.”
Two central advantages of the architecture developed by this research team are that it is digital and synchronous. This is in contrast with most other PIMs introduced in earlier works.
“This means that the probabilistic computer works with a clock that determines a well-defined time interval upon which p-bits can update and does not require area-consuming circuits such as digital-to-analog converters,” said Amiri. “In addition, the use of V-MTJs, which are currently implemented in a separate chip from the ASIC but can eventually be integrated within it, saves area and can provide high-throughput random bit sequences to the p-bits.”
V-MTJs, the components that Amiri and his colleagues used to create their architecture, were found to be inherently more robust against device-to-device variations when used to generate random bits compared to other spintronic random bit generators used in the past. The team’s initial findings were highly promising, highlighting the promise of their approach for creating probabilistic computers.
Notably, although it relies on VMTJs, the new approach is also compatible with established CMOS manufacturing processes and digital design strategies. In the future, it could contribute to the large-scale fabrication of PIMs that could solve a wide range of real-world optimization problems faster and more efficiently.
“Our next step will be to adapt this design to implement problems other than factorization,” added Amiri. “For example, we have a chip in the works that is tailored to other optimization problems with real-world significance. In addition, we plan to integrate the V-MTJs directly on the CMOS in a more advanced foundry node, which would allow us to make the probabilistic computer even more compact.”
Written for you by our author Ingrid Fadelli, edited by Gaby Clark, and fact-checked and reviewed by Robert Egan—this article is the result of careful human work. We rely on readers like you to keep independent science journalism alive.
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More information:
Christian Duffee et al, An integrated-circuit-based probabilistic computer that uses voltage-controlled magnetic tunnel junctions as its entropy source, Nature Electronics (2025). DOI: 10.1038/s41928-025-01439-6. On arXiv: DOI: 10.48550/arxiv.2412.08017
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The Best Presidents’ Day Deals on Gear We’ve Actually Tested
Presidents’ Day Deals have officially landed, and there’s a lot of stuff to sift through. We cross-referenced our myriad buying guides and reviews to find the products we’d recommend that are actually on sale for a truly good price. We know because we checked! Find highlights below, and keep in mind that most of these deals end on February 17.
Be sure to check out our roundup of the Best Presidents’ Day Mattress Sales for discounts on beds, bedding, bed frames, and other sleep accessories. We have even more deals here for your browsing pleasure.
WIRED Featured Deals
Branch Ergonomic Chair Pro for $449 ($50 off)
The Branch Ergonomic Chair Pro is our very favorite office chair, and this price matches the lowest we tend to see outside of major shopping events like Black Friday and Cyber Monday. It’s accessibly priced compared to other chairs, and it checks all the boxes for quality, comfort, and ergonomics. Nearly every element is adjustable, so you can dial in the perfect fit, and the seven-year warranty is solid. There are 14 finishes to choose from.
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Zillow Has Gone Wild—for AI
This will not be a banner year for the real estate app Zillow. “We describe the home market as bouncing along the bottom,” CEO Jeremy Wacksman said in our conversation this week. Last year was dismal for the real estate market, and he expects things to improve only marginally in 2026. (If January’s historic drop in home sales is indicative, that even is overoptimistic.) “The way to think about it is that there were 4.1 million existing homes sold last year—a normal market is 5.5 to 6 million,” Wacksman says. He hastens to add that Zillow itself is doing better than the real estate industry overall. Still, its valuation is a quarter of its high-water mark in 2021. A few hours after we spoke, Wacksman announced that Zillow’s earnings had increased last quarter. Nonetheless, Zillow’s stock price fell nearly 5 percent the next day.
Wacksman does see a bright spot—AI. Like every other company in the world, generative AI presents both an opportunity and a risk to Zillow’s business. Wacksman much prefers to dwell on the upside. “We think AI is actually an ingredient rather than a threat,” he said on the earnings call. “In the last couple years, the LLM revolution has really opened all of our eyes to what’s possible,” he tells me. Zillow is integrating AI into every aspect of its business, from the way it showcases houses to having agents automate its workflow. Wacksman marvels that with Gen AI, you can search for “homes near my kid’s new school, with a fenced-in yard, under $3,000 a month.” On the other hand, his customers might wind up making those same queries on chatbots operated by OpenAI and Google, and Wacksman must figure out how to make their next step a jump to Zillow.
In its 20-year history—Zillow celebrated the anniversary this week—the company has always used AI. Wacksman, who joined in 2009 and became CEO in 2024, notes that machine learning is the engine behind those “Zestimates” that gauge a home’s worth at any given moment. Zestimates became a viral sensation that helped make the app irresistible, and sites like Zillow Gone Wild—which is also a TV show on the HGTV network—have built a business around highlighting the most intriguing or bizarre listings.
More recently, Zillow has spent billions aggressively pursuing new technology. One ongoing effort is upleveling the presentation of homes for sale. A feature called SkyTour uses an AI technology called Gaussian Splatting to turn drone footage into a 3D rendering of the property. (I love typing the words “Gassian Splatting” and can’t believe an indie band hasn’t adopted it yet.) AI also powers a feature inside Zillow’s Showcase component called Virtual Staging, which supplies homes with furniture that doesn’t really exist. There is risky ground here: Once you abandon the authenticity of an actual photo, the question arises whether you’re actually seeing a trustworthy representation of the property. “It’s important that both buyer and seller understand the line between Virtual Staging and the reality of a photo,” says Wacksman. “A virtually staged image has to be clearly watermarked and disclosed.” He says he’s confident that licensed professionals will abide by rules, but as AI becomes dominant, “we have to evolve those rules,” he says.
Right now, Zillow estimates that only a single-digit percentage of its users take advantage of these exotic display features. Particularly disappointing is a foray called Zillow Immerse, which runs on the Apple Vision Pro. Upon rollout in February 2024, Zillow called it “the future of home tours.” Note that it doesn’t claim to be the near-future. “That platform hasn’t yet come to broad consumer prominence,” says Wacksman of Apple’s underperforming innovation. “I do think that VR and AR are going to come.”
Zillow is on more solid ground using AI to make its own workforce more productive. “It’s helping us do our job better,” says Wacksman, who adds that programmers are churning out more code, customer support tasks have been automated, and design teams have shortened timelines for implementing new products. As a result, he says, Zillow has been able to keep its headcount “relatively flat.” (Zillow did cut some jobs recently, but Wacksman says that involved “a handful of folks that were not meeting a performance bar.”)
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Do Waterproof Sneakers Keep the Slosh In or Out? Let WIRED Explain
Running with wet feet, in wet socks, in wet shoes is the perfect recipe for blisters. It’s also a fast track to low morale. Nothing dampens spirits quicker than soaked socks. On ultra runs, I always carry spares. And when faced with wet, or even snowy, mid-winter miles, the lure of weatherproof shoes is strong. Anything that can stem the soggy tide is worth a go, right?
This isn’t as simple an answer as it sounds. In the past, a lot of runners—that includes me—felt waterproof shoes came with too many trade-offs, like thicker, heavier uppers that change the feel of your shoes or a tendency to run hot and sweaty. In general, weatherproof shoes are less comfortable.
But waterproofing technology has evolved, and it might be time for a rethink. Winterized shoes can now be as light as the regular models, breathability is better, and the comfort levels have improved. Brands are also starting to add extra puddle protection to some of the most popular shoes. So it’s time to ask the questions again: Just how much difference does a bit of Gore-Tex really make? Are there still trade-offs for that extra protection? And is it really worth paying the premium?
I spoke to the waterproofing pros, an elite ultra runner who has braved brutal conditions, and some expert running shoe testers. Here’s everything you need to know about waterproof running shoes in 2026. Need more information? Check out our guide to the Best Running Shoes, our guide to weatherproof fabrics, and our guide to the Best Rain Jackets.
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How Do Waterproof Running Shoes Work?
On a basic level, waterproof shoes add extra barriers between your nice dry socks and the wet world outside. If you’re running through puddles deep enough to breach your heel collars, you’re still going to get wet feet. But waterproof shoes can protect against rain, wet grass, snow, and smaller puddles.
Gore-Tex is probably the most common waterproofing tech in footwear, but it’s not the only solution in town. Some brands have proprietary tech, or you might come across alternative systems like eVent and Sympatex. That GTX stamp is definitely the one you’re most likely to encounter, so here’s how GTX works.
The water resistance comes from a layered system that is composed of a durable water repellent (DWR) coating to the uppers with an internal membrane, along with other details like taped seams, more sealed uppers with tighter woven mesh, gusseted tongues, and higher, gaiter-style heel collars.
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