The Lindahl Letter

Thank you for tuning in to week 218 of the Lindahl Letter publication. A new edition arrives every Friday. This week the topic under consideration for the Lindahl Letter is, “Nested learning and the illusion of depth.”Just for fun with this nested learning paper we are evaluating today, I downloaded the 52 page PDF and uploaded it to my Google Drive to have Gemini create an audio overview of the paper. That is just a one button request these days. We have reached a point where we can easily listen to a paper recap with very little friction. It’s actually harder to get a complete reading of the PDF as an audio file. I had tried the Adobe Acrobat read aloud feature and I don’t really like the robotic output. Sometimes, I would rather listen to a paper than read it when I am trying to really think deeply about something. The 5 minutes of podcast audio Gemini spit out about the paper are embedded below. It’s interesting to say the least how quickly Gemini turned that paper into a short podcast. It’s entirely possible that my analysis might be less entertaining than the podcast Gemini created on the fly. You will be the judge of that one. This is a paper I actually printed out 2 pages per page using the double sided setting. That is how I used to read papers during graduate school. This paper had a few color elements that is something my graduate school papers never really had. They were all monochromatic. I had to put on my reading glasses and hold the paper a little closer than I used to with the 2 pages per page printing. I’ll have to remember to just print using single page spacing next time around. I really only print out papers I want to keep in my stack of stuff. This one certainly fits that criteria.Trying to make content that is accessible is one of the reasons that I have been recording audio for the Lindahl Letter. Sometimes listening to something is a great unlock. Other times due to complexity and the diagrams included you just have to read academic papers. I try to bring things forward without complex charts in a highly consumable way. My take on research notes is that they need to be generally understandable and communicate a clear take on whatever topic is being covered. The content has to be condensed into something that can be considered in 5-10 minutes. To that end I’m going to do my best to bring this paper on nested learning to life today.This paper matters, it really does, because the research presented undermines one of the core assumptions driving modern AI investment and the endless LLM building and training that has been occurring, namely that stacking more layers reliably produces qualitatively better intelligence [1]. The mantra to just keep scaling maybe will fade away. If many so-called deep models collapse into shallow equivalents during training, then reported gains attributed to architectural depth may instead be artifacts of data scale, regularization, or optimization heuristics rather than true representational progress.This has direct implications for benchmarking, since comparisons that reward parameter count or depth risk overstating advances that do not translate into more robust reasoning or generalization. It also affects hardware and infrastructure strategy, because enormous resources are being allocated to support depth that may not deliver proportional returns. At a deeper level, the result forces a reconsideration of what meaningful learning progress actually looks like, shifting attention from surface complexity toward mechanisms that introduce genuinely new inductive structure and adaptive behavior.Maybe the long term impact of this call out is likely to be gradual rather than abrupt, but it meaningfully shifts the intellectual ground beneath current AI narratives [1]. The paper in question provides a formal vocabulary for a concern many researchers have held intuitively, that architectural depth has become a proxy metric for progress rather than a principled design choice. Over time, this reframing may influence how serious research groups evaluate models, placing more weight on identifiably distinct learning mechanisms, training dynamics, and robustness properties instead of raw scale.It is unlikely to immediately change the minds of investors or vendors whose incentives favor larger systems, but it can shape academic norms, reviewer expectations, and eventually benchmark construction. Historically, results like this matter most not because they halt a paradigm, but because they constrain it, narrowing the space of credible claims and forcing future advances to justify themselves on grounds other than appearance and size.This argument intersects directly with my broader concerns about interpretability and generalization. I am still curious about creating a combiner model, but this might change the mechanics of how that might ultimately work. If performance gains arise primarily from optimization dynamics rather than architectural expressivity, then claims about learned representations should be treated with caution. Apparent abstraction may not correspond to stable semantic structure but to transient equilibria shaped by training order, learning rates, and implicit regularization. This aligns with growing skepticism about whether large models truly learn hierarchical concepts or merely approximate them through iterative adjustment [2].The implications extend beyond theory. Nested learning reframes debates about model scaling, architectural novelty, and transfer learning. It suggests that progress may come less from ever deeper networks and more from better understanding and controlling learning dynamics. This has practical consequences for reproducibility, safety, and deployment, since nested optimization can introduce path dependence and sensitivity to training regimes that are difficult to observe or audit.In the broader context of the AI marketplace, this work reinforces a recurring theme. Fluency and performance do not necessarily imply understanding. As with recent neuroscience critiques of language models, nested learning highlights how impressive outputs can emerge from mechanisms that lack stable, interpretable internal structure [3]. That gap matters when systems are deployed in high stakes environments where reliability, robustness, and reasoning are essential.We will see how this plays out in 2026 and what new research will ultimately shift the landscape.Footnotes:[1] Behrouz, A., Razaviyayn, M., Zhong, P., & Mirrokni, V. “Nested learning: The illusion of deep learning architectures.” Advances in Neural Information Processing Systems 39 (2025). https://abehrouz.github.io/files/NL.pdf[2] Raghu, M., Poole, B., Kleinberg, J., Ganguli, S., & Dickstein, J. “On the expressive power of deep neural networks.” Proceedings of the 34th International Conference on Machine Learning (2017). https://arxiv.org/abs/1606.05336[3] Riley, B. “Large language mistake: Cutting edge research shows language is not the same as intelligence.” The Verge (2025). https://www.theverge.com/ai-artificial-intelligence/827820/large-language-models-ai-intelligence-neuroscience-problemsWhat’s next for the Lindahl Letter? New editions arrive every Friday. If you are still listening at this point and enjoyed this content, then please take a moment and share it with a friend. If you are new to the Lindahl Letter, then please consider subscribing. Make sure to stay curious, stay informed, and enjoy the week ahead! This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit www.nelsx.com

Thank you for tuning in to week 216 of the Lindahl Letter publication. A new edition arrives every Friday. This week the topic under consideration for the Lindahl Letter is, “The biggest unsolved problems in quantum computing.”The field of quantum computing has accelerated rapidly during the last decade, yet its most important breakthroughs remain incomplete. The core research challenges that stand between today’s prototypes and large scale, industrially relevant systems are now visible with unusual clarity. I think we are on the path to seeing this technology realized. These challenges are increasingly framed not as incremental milestones but as structural bottlenecks that shape the entire trajectory of the field. This week’s analysis focuses on the five most critical problems that must be solved for quantum computing to reach fault tolerant, economically meaningful operation. These gaps define where research investment, national strategy, and competitive advantage will be determined in the coming decade.1. A fully fault tolerant logical qubit with logical error rates below thresholdThe first and most fundamental problem is the absence of a fully fault tolerant logical qubit. I know, I know, people are getting close, but this technology is not fully realized just yet. Theoretical thresholds for fault tolerance are well studied, and progress has been reported through surface codes, low density parity check codes, and recent advances in magic state distillation. Several groups have demonstrated logical qubits whose performance exceeds their underlying physical qubits, and some trapped-ion experiments now show better than break-even behavior under repeated rounds of error correction. However, no team has yet realized a logical qubit that maintains below-threshold logical error rates in a fully integrated setting that combines encoding, stabilizer measurement, real time decoding, and continuous correction across arbitrarily deep circuits. Experiments such as the University of Osaka’s zero level magic state distillation results and Quantinuum’s recent logical circuit demonstrations illustrate meaningful progress, yet a complete fault tolerant logical qubit build rolling off the assembly line has not been achieved [1]. This missing element prevents reliable execution of deep circuits and stands as the central research challenge of the field. I am also tracking a leaderboard of efforts aimed at increasing the number and stability of logical qubits as new systems emerge [2].2. A scalable and manufacturable quantum architecture that supports thousands of high fidelity qubitsThe second unsolved problem is the absence of a scalable, manufacturable quantum architecture capable of supporting thousands of high fidelity qubits. Superconducting platforms continue to face wiring congestion, cross talk, and fabrication variability across large wafers, which limits reproducibility at scale. Trapped-ion systems achieve some of the highest gate fidelities reported, but their physical footprint, control volume, and relatively slow gate speeds constrain system growth. Neutral atom arrays offer large qubit counts, yet they have not demonstrated uniform, high fidelity two qubit gates across arrays large enough to support fault tolerant codes. Photonic and spin qubits continue to advance but remain earlier in their development for universal, gate based architectures. Across all platforms, the transition from laboratory systems to repeatable, wafer scale manufacturing has not occurred. Most resource estimates indicate that tens of thousands of physical qubits will be required for practically useful, error corrected applications, and no architecture is yet positioned to deliver this scale with consistent fidelity. I am tracking universal gate based physical qubit leaders closely, and I expect to see significant shifts in 2026 as fabrication strategies evolve [3].3. Integrated cryogenic classical control systems capable of real time decoding at scaleThe third unsolved problem concerns the integration of classical control systems capable of operating efficiently at cryogenic temperatures. Quantum processors rely on classical electronics to generate precise control pulses, read measurement outcomes, and perform real time decoding. As devices grow, these classical requirements become a dominant engineering bottleneck. Current systems depend on extensive room temperature hardware and thousands of coaxial lines, an approach that is not viable for scaling beyond a few hundred qubits. Research into cryogenic CMOS, multiplexed readout architectures, and fast low noise routing has shown meaningful progress, and prototype decoders have demonstrated sub microsecond performance. However, the field still lacks a fully integrated classical to quantum control stack that can operate near the device, support large scale decoding throughput, and eliminate the wiring overhead required for million channel systems. Solving this challenge is as essential as improving qubit fidelity, because fault tolerant computation will require tightly coupled classical and quantum subsystems functioning in real time at cryogenic depths.4. A modular, networked quantum architecture with reliable chip to chip entanglementThe fourth major unsolved problem involves modularity and quantum networking. Large scale quantum computers will not be monolithic systems. They will require distributed architectures in which multiple chips or modules exchange entanglement to support error corrected computation across larger systems. Research groups have demonstrated chip to chip photonic links, heralded entanglement generation, and short range coupling between trapped-ion and superconducting devices, but these demonstrations remain small scale and experimental. No team has yet produced a modular architecture capable of sustaining reliable inter module entanglement rates, routing operations, and error corrected logical circuits across networked components. A practical quantum interconnect, whether photonic or microwave based, would redefine system design by enabling large logical qubit counts without relying on a single monolithic wafer. Developing these networked architectures is now seen as one of the highest value targets for national research programs, because modularity is likely the only viable path to systems with millions of physical qubits.5. A verified quantum advantage tied to a real scientific or industrial workloadThe fifth unsolved problem is the absence of a widely accepted, independently verified quantum advantage tied to a real scientific or industrial workload. Quantum supremacy experiments have demonstrated that certain random circuit sampling tasks are exceptionally difficult for classical systems to simulate, but these tasks do not translate into chemistry, materials, optimization, or cryptography workloads. Several vendors have recently reported domain specific quantum advantages, including applications in quantum navigation and narrow optimization tasks, but these demonstrations have not yet achieved broad community validation or independent replication under strict verification and resource accounting. A robust demonstration of advantage requires a computation that is infeasible for classical systems within realistic time and energy constraints, produces an output that can be meaningfully verified, and operates using real hardware error rates rather than idealized gates. Achieving this milestone would mark a decisive shift in the strategic landscape of the field and would accelerate commercial investment into fault tolerant platforms.Together, these five problems outline the most important questions I’m tracking that are facing quantum computing today. This is based on my research interests. Please feel free to let me know if something else jumps out when you read this list. Each topic represents an opportunity for technical leadership, research investment, and industrial strategy. That does not mean my list is complete. It’s directionally accurate for late 2025, but things in the quantum computing space are changing rapidly. These elements called out also define the hurdles that stand between early laboratory demonstrations and the large-scale quantum platforms required for transformative scientific progress.What’s next for the Lindahl Letter? New editions arrive every Friday. If you are still listening at this point and enjoyed this content, then please take a moment and share it with a friend. If you are new to the Lindahl Letter, then please consider subscribing. Make sure to stay curious, stay informed, and enjoy the week ahead!Links I’m sharing this week!You may not have watched Linus Torvalds build a computer on your watch list for 2025, but I’m sharing that link anyway. I truly enjoyed watching this video.This video made me chuckle several times and was delightful.Footnotes:[1] Itogawa, T., Takada, Y., Hirano, Y., & Fujii, K. (2024). Even more efficient magic state distillation by zero-level distillation. arXiv preprint arXiv:2403.03991. http://arxiv.org/pdf/2403.03991[2] Top quantum computers by logical qubit[3] Updating my top 10 quantum computer leaderboard This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit www.nelsx.com

Thank you for tuning in to week 214 of the Lindahl Letter publication. A new edition arrives every Friday. This week the topic under consideration for the Lindahl Letter is, “The great manufacturing reset.”Boston Dynamics captured public imagination when they introduced Spot the dog-like robot back in 2016. Things have changed. Robots that walk around are beginning to enter the commercial landscape, and new entrants continue to appear. A humanoid robot product from Russia built by the company Idol surfaced last week [1]. Other companies such as Agility Robotics (USA), Figure AI (USA), Boston Dynamics (USA), UBTECH (China), and 1X Technologies (Norway/USA) are all working toward delivering humanoid robots. Optimus, the Tesla bot introduced conceptually in 2021 and now in its third-generation prototype which remains part of an internal program and has not yet reached commercial deployment is also being talked about.The stage is now set, and we are at a point where robotics, autonomous fabrication systems, and advanced materials are converging into a new industrial baseline. The last decade brought low-cost filament printers into hobbyist and commercial spaces at massive scale, and the next decade is poised to move far beyond that early wave. Industrial additive manufacturing has already expanded into metals, composites, and high-performance polymers, with global revenue expected to accelerate over the coming years. At the same time, the field is absorbing rapid advancements in AI-enabled calibration, defect detection, and real-time optimization, allowing machinery to tune production parameters autonomously. That capability shifts what it means to operate a modern fabrication workflow. Things are changing rapidly.Alongside these developments, humanoid and semi-autonomous industrial robots are transitioning from research demonstrations to contract manufacturing deployments. Several builders are scaling up pilot programs in which general-purpose robots support assembly, materials handling, and repetitive manufacturing tasks. These systems benefit from advances in reinforcement learning, enhanced sensors, and cloud-based model updates. Industrial robotics shipments are increasing rapidly, driven by global demand for flexible production lines and labor-augmentation strategies. The supply side of robotics is not only expanding but also becoming modular and more interoperable across fabrication environments.The most significant shift may come from the emergence of machines that build machines. That is a topic I’m focused on understanding. Historically, tooling design required long lead times, significant manual labor, and specialized expertise. Today, automated CAM pipelines, printable tooling, adaptive CNC systems, and robotically tended fabrication cells allow factories to generate and regenerate their own production processes. Some aerospace and automotive facilities already deploy these closed-loop systems to create fixtures, jigs, and replacement components internally. This form of self-manufacturing reduces dependency on external suppliers and removes friction from engineering iteration cycles. We are moving toward a world where design, testing, and tooling are all integrated within an AI-guided, robotics-driven feedback loop. That integration is the foundation of the great manufacturing reset.For the United States, these technologies open a realistic path to reshoring custom and small-batch manufacturing in ways that were not economically viable during the offshoring wave of the late twentieth century. Rising labor costs in traditional manufacturing hubs, geopolitical risk, and supply chain disruptions have already encouraged firms to reconsider where they build things. Additive manufacturing and flexible robotics change the cost structure by reducing reliance on large minimum-order quantities, expensive hard tooling, and long logistics chains. A factory that can print tooling on demand, deploy modular robots, and run AI-optimized production scheduling can serve shorter runs and more specialized designs while remaining geographically close to end customers. In effect, the United States can replace scale-driven arbitrage with speed, customization, and resilience. That is why we are at the inflection point for the great manufacturing reset.Policy and infrastructure are beginning to support this transition. Federal programs such as Manufacturing USA and its associated network of advanced manufacturing institutes are working to diffuse next-generation production technologies across domestic firms and regions [2]. Investments in semiconductor fabrication, battery plants, and clean-energy hardware have already catalyzed billions of dollars in new onshore manufacturing commitments. The same capabilities that support large facilities can extend to mid-market and smaller manufacturers through shared tooling libraries, regional robotics integrators, and standardized digital design pipelines. Universities and community colleges can align curricula with this reset by emphasizing mechatronics, robotics programming, and design-for-additive principles that translate directly to a modern factory floor.If the United States leans into this transition, the great manufacturing reset will not simply re-create legacy industrial capacity. It will establish a distributed network of automated, digitally coordinated micro-factories specializing in custom work, rapid prototyping, and short-run production. The strategic advantage will be the ability to move from concept to physical part in days instead of months, while retaining critical capabilities within domestic borders. The risk is that other regions may scale faster and capture the integrator role that coordinates robots, additive systems, and AI platforms across global supply chains. The next few years will determine whether the United States treats these technologies as incremental enhancements or as foundational infrastructure for a new manufacturing baseline. Ideally, this reset will create conditions for a new wave of startups delivering smaller manufacturing runs, bespoke development cycles, and entirely new product categories.Things to consider:* The economics of reshoring depend as much on automation and design speed as on wage differentials.* Policy support for advanced manufacturing will matter most where it connects directly to tooling, robotics, and workforce upskilling.* Custom, short-run production could become a core competitive advantage for regions that adopt additive and robotics early.* The integrators that connect robots, printers, and AI software may end up more powerful than any single hardware vendor.* Manufacturing resilience will increasingly be measured by how quickly domestic systems can reconfigure to new designs and shocks.What’s next for the Lindahl Letter? New editions arrive every Friday. If you are still listening at this point and enjoyed this content, then please take a moment and share it with a friend. If you are new to the Lindahl Letter, then please consider subscribing. Make sure to stay curious, stay informed, and enjoy the week ahead!Links I’m sharing this week!Footnotes:[1] Mesa, J. (2025, November 11). Russia ‘human’ robot falls on stage during debut. Newsweek. https://www.newsweek.com/russia-human-robot-falls-stage-during-debut-11031104[2] Manufacturing USA. (n.d.). Home. https://www.manufacturingusa.com/ This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit www.nelsx.com

Thank you for tuning in to week 212 of the Lindahl Letter publication. A new edition arrives every Friday. This week the topic under consideration for the Lindahl Letter is, “The edge of realized technology.”Welcome to the start of season 5. Don’t panic, we are still covering advancing technology including quantum, robotics, and artificial intelligence within the Lindahl Letter. I’ll be writing about the intersection of technology and modernity until the singularity. For better or worse, modernity’s shadow will continue to be the edge of realized technology. We are on the path to seeing a bunch of different technologies end up being realized in the not so distant future. That is why I’m so focused on the path toward realizing robotics, quantum, and agentic. That is where season 5 of the Lindahl Letter is going to pick up and start to dig into those topics at the edge of realized technology. To that end, I started to make a graphic of the timeline of major financial bubbles and extended it out to emerging technologies expected to deliver before 2045 [1]. You can modify the Python visualization code for this one if you want, I shared an executable version of it on GitHub.Within that visualization I started to sketch out the next 10 most likely technologies we will see realized. Within each path toward realization is where private investment and ultimately retail investors will crowd into the market before it gets commoditized to the point where the initial leaders in the space have no first mover advantage and some type of bubble ensues. That does not mean these things won’t be game changing. I’m just expecting some type of financial crowding followed by pressure against expected profits that won’t be realized. Resulting from that would be some type of financial bubble which might very well be led by a huge windfall of some sort. People made money on tulips and pepper before those markets crashed out.* 2026, “AI Bubble”, “Tech”* 2028, “Metaverse and XR Bubble”, “Tech/Speculative”* 2029, “Robotics Bubble”, “Tech”* 2031, “Climate Tech Bubble”, “Climate Tech”* 2032, “Space Economy Bubble”, “Space Economy”* 2033, “Biotech and Longevity Bubble”, “Biotech/Longevity”* 2034, “Synthetic Biology and Food Tech Bubble”, “Synthetic Bio/Food Tech”* 2035, “Quantum Bubble”, “Tech”* 2035, “Neurotech and BCI Bubble”, “Neurotech/BCI”* 2040, “Fusion Energy Bubble”, “Energy”These edges of technology realization might not be in the right order or tied exactly to the right year, but I do think that directionally this list will prove to be an accurate prediction of when technology will be achieved and we will see meaningful changes to modernity. Futurist considerations abound for what might end up happening. This was my swing at predicting what’s next. Only time will tell if it was an accurate swing or it will be disrupted by some other emerging technology.Going forward you are going to see my weekly writing efforts get split into 4 distinct buckets. My general weekly think pieces will stay here within the relative safety of the standard Lindahl Letter publication, writing about civics, civility, and civil society will be over on the Civic Honors domain, blogging will be done within the Functional Journal, and my hope is to resume daily posting back over on the nels.ai domain. Ideally, enough content will be generated in the major domains that only a small amount of blogging will occur. Going forward it is far better to produce meaningful work than to complete passages of extended navel gazing. Sure being a reflective practitioner and blogging has its place, but sometimes all that writing about the process ends up being more circular than forward looking.What’s next for the Lindahl Letter? New editions arrive every Friday. If you are still listening at this point and enjoyed this content, then please take a moment and share it with a friend. If you are new to the Lindahl Letter, then please consider subscribing. Make sure to stay curious, stay informed, and enjoy the week ahead!Links I’m sharing this week!Footnotes:[1] https://github.com/nelslindahlx/Data-Analysis/blob/master/TimelineofMajorFinancialBubbles.ipynb This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit www.nelsx.com

Thank you for tuning in to week 210 of the Lindahl Letter publication. A new edition arrives every Friday. This week the topic under consideration for the Lindahl Letter is, “AI Is Burning Through Graphics Cards.”Generational wealth is being invested into data centers for AI. It’s so prevalent that you hear about it on the nightly news and municipalities are dealing with the power demands. The clock is ticking on graphics cards being used for AI inference. The current generation of GPUs was never designed to run around the clock under inference loads. These chips were originally built for bursts of rendering, not continuous model execution at scale. What we are seeing now is an industry trying to stretch gaming hardware into a role it was never meant to fill. The result is heat, power consumption, and a ticking clock based on the inevitable wear.Each graphics card has a limited operational lifespan. These are not like bricks being used to build a house; they are just expensive computer hardware. The more intensive the workloads, the shorter that lifespan becomes. Fans fail, thermal paste dries out, and the silicon itself begins to degrade. Inference tasks, particularly when stacked across large fleets of GPUs, magnify this effect. The relentless pace of AI workloads accelerates the failure curve, turning once-premium cards into temporary consumables. I’m actually really curious what is going to happen to all of them at the end of this cycle. A secondary market does exist for these used devices and companies like Iron Mountain will help data centers with secure disposal.By most reasonable estimates, there are now between 3.5 and 4.5 million NVIDIA data-center GPUs actively deployed in production environments. Hyperscalers such as Meta, Microsoft, and Google each operate hundreds of thousands of units, while smaller data centers fill out the rest of the global total. Each GPU represents a remarkable amount of compute density, but also a constant thermal and economic liability. Even with optimized cooling, sustained inference loads drive high thermal stress and power draw that shorten component life. These systems were never meant to run 24 hours a day, 365 days a year.Under heavy duty cycles, many GPUs experience significant degradation within one to three years of continuous operation. The warranties often match that window, which reflects a design expectation rather than coincidence. Silicon aging and persistent thermal cycling all take their toll. Even when the hardware technically survives longer, it becomes economically obsolete as new architectures quickly double efficiency and throughput. The pace of improvement ensures that by 2027 or 2028, most of today’s fleet will either be retired, resold, or relegated to low-priority inference tasks. Right now TSMC would have to make the chips to replenish this fleet of GPUs which would be outrageously expensive. Both NVIDIA and TSMC manufacturing teams could be looking at a huge impending need for production or a shift to a new type of technology.That replacement cycle has massive implications. The cost of refreshing millions of GPUs every few years is enormous, and the environmental impact of manufacturing and disposing of that much silicon is even harder to ignore. As AI inference continues to scale, this churn becomes unsustainable. Companies are already exploring purpose-built accelerators, ASICs, and FPGAs that can deliver better efficiency and longer service life. These designs aim to handle continuous inference without the same thermal or aging limitations that plague graphics cards.Sustainability will define the next phase of AI infrastructure. The transition away from general-purpose GPUs is underway, but what comes after silicon remains uncertain. Research into photonic computing, quantum processors, and neuromorphic architectures offers glimpses of what a post-GPU world might look like. Each of these alternatives seeks to break free from the limits of traditional chips while extending useful lifespans. The next leap in AI hardware will not be measured by sheer speed, but by how well it can endure the relentless demands of inference at scale.What’s next for the Lindahl Letter? New editions arrive every Friday. If you are still listening at this point and enjoyed this content, then please take a moment and share it with a friend. If you are new to the Lindahl Letter, then please consider subscribing. Make sure to stay curious, stay informed, and enjoy the week ahead!Links I’m sharing this week! This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit www.nelsx.com

Day after release update: I guess it was the 208th post where we hit the proverbial wall with a dud of a post. This post in retrospect turned out to be one of my weaker efforts. I thought it was a strong take about dealing with the rate of change in model development, but it was just not focused and targeted based on delivering quality and insights.Thank you for tuning in to week 208 of the Lindahl Letter publication. A new edition arrives every Friday. This week the topic under consideration for the Lindahl Letter is, “Building with constant model churn.”Developers have spent a lot of time in the past patching software. That happens based on vulnerabilities, edge cases, and performance issues. All this vibe-coded content and things built on models are not getting any patches to make them better going forward. You may get a new release or a new model, but that patch to save you from vulnerabilities is not being developed and is not on the way. It is the nature of modern development. The ecosystem of dependencies is real. However, the pace of model development has created an unusual environment for anyone trying to build durable systems.You cannot really hot swap models within production systems. That just does not work. In the last five years, we have seen large language model releases from OpenAI, Anthropic, Google, Meta, Mistral, Cohere, and several open-source groups. Each iteration has been faster, larger, and sometimes more efficient than the one before. What has not been stable is the interface between models and the systems people build around them. Even seemingly small changes in context window size, output quality, or API availability ripple outward and cause redesigns, migrations, and sudden pivots. Sometimes these changes happen with no warning whatsoever.For builders, this creates a paradox. The potential upside of adopting a newer model is undeniable: better reasoning, lower costs, and expanded capabilities. At the same time, the risk of betting on an API or framework that may be deprecated in months is a constant concern. Some developers chase every release, weaving the newest model into their applications as quickly as possible. Others step back, building abstractions and wrappers that allow for switching models without disrupting core workflows. Neither path offers complete insulation from this wave of almost continuous churn.The history of technology offers parallels. Software engineers have long had to deal with shifting operating systems, frameworks, and libraries. What makes this moment different is the velocity of change and the sheer dependency of emerging applications on model behavior. The model is not just another dependency, it is the foundation of the system. When that foundation shifts, everything built on top of it must be reconsidered.There is also a deeper strategic question. Should builders lean into constant change and accept churn as a feature of the landscape? Or should they try to design in ways that minimize dependency, focusing more on proprietary data pipelines, unique integrations, and distinctive user experiences? Both strategies reflect an awareness that stability is not guaranteed in this ecosystem. The companies that endure will be the ones that treat churn not as an annoyance but as a design constraint.Things to consider:* The lack of patching for AI models makes long-term maintenance difficult.* Model churn introduces structural instability into modern systems.* Abstraction layers help, but they cannot prevent cascading change.* Treating churn as a core design constraint is a pragmatic approach.* Builders must balance innovation speed with long-term stability.What’s next for the Lindahl Letter? New editions arrive every Friday. If you are still listening at this point and enjoyed this content, then please take a moment and share it with a friend. If you are new to the Lindahl Letter, then please consider subscribing. Make sure to stay curious, stay informed, and enjoy the week ahead! This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit www.nelsx.com

Thank you for tuning in to week 206 of the Lindahl Letter publication. A new edition arrives every Friday. This week the topic under consideration is “The Great Tokenapocalypse.”As large language models reach deeper into consumer devices, the cost of running them becomes the real bottleneck. So many tokens get burned with no ROI or use case for the company burning them; it's really out of control. Almost as out of control as the sunk cost of data centers that will probably be regretted at some point in the next 5 years. It’s sort of the unspoken reality of an arms race where building data centers that just depreciate and spending compute resources without any plan for recovering the cost is happening. This week explores how token economics is silently shaping the deployment strategies of Google and Apple.You may have noticed something strange about the rollout of generative AI: despite Google’s global reach and technical infrastructure, Gemini is not yet present on every device. It isn’t quietly running in the background on your Nest Hub, it doesn’t summarize content on your Pixel Watch, and it hasn’t taken over the always-on interactions that dominate the smart home experience. On paper, Gemini could power all of this: but in practice, it doesn’t. The reasons are not technical, but economic.It’s the tokens. Each time a large language model like Gemini processes a prompt or generates a response, it consumes tokens which are effectively a unit of computation that translate directly into cost. This cost is not abstract. It is real-time, metered, and at scale becomes wildly continuous with enough uses. When you ask Gemini to summarize an email or rewrite a paragraph, you’re triggering a live cloud inference cycle that draws directly on Google’s TPU infrastructure. At a small scale, these requests are manageable. But when deployed across millions of devices, in billions of micro-interactions, the financial and infrastructure burden becomes extreme. What looks like product restraint is actually cost containment. Google is avoiding what could become a tokenapocalypse which would be a runaway escalation of inference demand that outpaces both compute supply and operating budget.Gemini was designed for centralized, high-performance environments. It was not optimized for low-power edge devices or offline operation. Its rollout has been concentrated in strategic, high-leverage use cases: Workspace productivity, Pixel exclusives, and experimental features inside Search Labs. These are high-value zones where the cost per token can be justified. Gemini has not been deployed ambiently in the wild on smart speakers, in Android Auto, or on lightweight wearables mostly because those endpoints offer little to no margin against token cost. The model cannot run constantly without triggering exponential cloud expenditure. Until inference becomes drastically cheaper or edge-native Gemini variants emerge, Google is likely to continue rationing its deployment to protect against economic overextension.Apple, by contrast, has chosen an entirely different path forward. They elected a path that avoids the token problem from the outset. Its 2024 rollout of “Apple Intelligence” emphasized a local-first architecture built around on-device models. Instead of sending every prompt to the cloud, Apple routes the vast majority of inference through its A-series and M-series silicon. This strategy means that users can rewrite notes, summarize messages, or interact with Siri entirely offline, with zero token cost to Apple. When tasks exceed the capability of local models, they are sent to Apple’s “Private Cloud Compute” system, but this fallback is used selectively, with strict privacy and latency guarantees.Apple’s approach isn’t just a branding play. It reflects a fundamental architectural decision to avoid the economics of inference altogether. Apple doesn’t operate a hyperscale public cloud business, so it has no incentive to absorb or monetize cloud-based generative AI usage. Its profits come from hardware margins and platform services. This gives Apple the freedom to constrain usage, limit interaction complexity, and push AI to the edge. A strategy they can get away with, ultimately without incurring the compounding costs that Google faces. It’s a token-avoidant strategy, and it may prove to be the more sustainable one.Where Google builds outward from a full-stack cloud foundation, Apple builds inward from a controlled edge. Google’s strategy scales across models and modalities, but each expansion amplifies cost. Apple’s strategy constrains functionality but keeps economics stable. Both are reacting to the same underlying pressure: token costs are rising faster than monetization models can support. The more embedded the model becomes, the more tokens flow. A stark reality comes into existence where it becomes more urgent to rethink deployment patterns. This isn’t just a question of technical feasibility. It’s a matter of financial survivability.The race to deploy generative AI at scale is quickly becoming a race to control token exposure. Inference cost and not model quality may be the key determinant of which platforms can sustainably integrate AI across the stack. If cloud economics don’t shift, and if token optimization doesn’t advance, then ambient LLMs may remain a luxury reserved for premium endpoints and enterprise tasks. The real future of ubiquitous AI may depend less on how powerful models become, and more on how efficiently they run in the wild.Things to consider:* Google’s restraint in deploying Gemini across its device ecosystem likely reflects real-time token cost constraints rather than technical limits.* Every cloud-based Gemini interaction consumes metered compute, making global deployment economically unstable without stronger monetization.* Apple avoids these problems by designing for on-device inference and constraining AI functionality to remain token-light.* Token economics are now shaping the strategic posture of every major platform, defining where and how AI appears in consumer workflows.* Sustained deployment of generative models may depend less on breakthrough architecture and more on advances in inference efficiency and local compute.As the tokenapocalypse looms, we’ll be watching how companies respond. That response could be through model compression, edge acceleration, hybrid routing, and new monetization strategies. In the coming weeks, we’ll explore how these constraints are shaping research priorities, ecosystem fragmentation, and what it means to run AI sustainably across global networks. If you see an AI endpoint that should exist but doesn’t, it may be because someone, somewhere, did the token math.What’s next for the Lindahl Letter? New editions arrive every Friday. If you are still listening at this point and enjoyed this content, then please take a moment and share it with a friend. If you are new to the Lindahl Letter, then please consider subscribing. Make sure to stay curious, stay informed, and enjoy the week ahead! This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit www.nelsx.com

Thank you for tuning in to week 204 of the Lindahl Letter publication. A new edition arrives every Friday. This week the topic under consideration for the Lindahl Letter is, “Context window garbage collection.”Here we are this week contemplating how to clean up the mess from all these celebrated LLM chat sessions. It’s a disjointed mess that lacks federation or dare we say portability. We are at the point where we need to think about how context window garbage collection explores the deeper process based idea of how large language models might manage overflowing histories, selectively pruning, discarding, or compressing tokens to maintain efficiency without losing coherence. Certainly my thoughts on this is that we would all benefit from portable knowledge sharding, but that is just one way to look at the potential set of solutions that need to be built. Another way to slice the apple up and put just the best parts back together again would be to build out some context window garbage collection.When you open a long conversation with a large language model, the context window eventually fills with tokens from your prompts and the model’s replies. These windows have strict limits, whether 128k tokens, 200k tokens, or more, and yet our usage tends to grow indefinitely. As prompts expand, sessions become inefficient and costly, sometimes degrading in coherence as irrelevant or outdated details pile up. We have all run into hallucinations and just weird output from models. At this point in the experience the next best question then becomes very clear. We have to evaluate how models should manage their overflowing context windows at the end or during a chat session.In programming, garbage collection has long been the answer to similar problems. Long garbage collection problems have literally kept me up at night. Computer systems with finite memory must constantly decide what to keep and what to discard. Techniques such as reference counting, mark-and-sweep, and generational garbage collection have been developed to handle this challenge. The analogy we can build out here is very straightforward: in a world where context is the working memory of LLMs, garbage collection could provide the rules and processes for pruning, summarizing, or discarding tokens without breaking continuity.Several strategies already hint at how this could work. Some systems automatically prune less relevant history, while others compress sections of text into summaries or embeddings that can be retrieved later. I would run a knowledge reduce function based on my previously shared research, but I always think that is the answer. User-directed pinning, where important content is marked as permanent, is another possible feature. In longer interactions, models could run background “cleanup passes,” automatically condensing earlier exchanges into portable knowledge shards. Each of these approaches mirrors classic computing strategies while being adapted to the new problem space of language models.The risks are obvious. Things could go sideways. We face a direct computing time cost associated with this effort. Poorly designed garbage collection could lead to subtle context loss, missing small but crucial details. Summarization may introduce semantic drift or hallucinations. I would argue that properly structured context will actually reduce drift or hallucinations. Users may also resist invisible pruning, questioning whether they can trust a model that silently discards information. The challenge lies in balancing efficiency, fidelity, and transparency, ensuring that garbage collection makes interactions smoother rather than introducing new points of failure.Looking forward, context window garbage collection could become a fundamental layer of model architecture. Standardized processes and even some APIs might emerge to expose garbage collection logs to users or allow customization of pruning strategies. Entire ecosystems of agents could share compressed or pruned context shards across models, creating interoperability where today there is only fragmentation. Just as garbage collection enabled more scalable and reliable programming environments, context window garbage collection may become the invisible backbone of scalable AI interaction.Things to consider:* Should context garbage collection be visible and user-controllable?* Can models balance efficiency with fidelity when pruning?* What lessons from programming garbage collection apply directly to LLMs?* Does context GC make interoperability between models easier or harder?What’s next for the Lindahl Letter? New editions arrive every Friday. If you are still listening at this point and enjoyed this content, then please take a moment and share it with a friend. If you are new to the Lindahl Letter, then please consider subscribing. Make sure to stay curious, stay informed, and enjoy the week ahead! This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit www.nelsx.com

Thank you for tuning into the podcast. This is week 202 of the Lindahl Letter publication. A new edition arrives every Friday. This week the topic under consideration for the Lindahl Letter is, “Personalized context bubbles.”Last week we took a deeper look into content window fragmentation. That is just the right amount of foundation to start to consider personalized content bubbles. Don’t panic; no foundation model pun intended. I even talked about it on YouTube during a recent Nelscast episode. It has been years since I actively livestreamed on YouTube. Live streaming is apparently a lot like riding a bicycle and you pick it back up pretty quickly.The context bubbles we are focusing on today are model-specific and ultimately memory-driven. Functionally they are hidden from the outside world and only interacted with by the user. The whole experience is highly gated and mostly hidden by design. Unlike the algorithmic filter bubbles of the social media era, highly personalized context bubbles in LLMs emerge from user-specific interaction histories and model memory. They are shaped by prompts, preferences, and usage over time. Some people have ridiculously deep context in memory and have radically changed how the model even interacts with them on an ongoing basis. Some people even call this a type of modal rot where things worked better initially and then over time degraded.This type of both hidden and blatantly obvious fragmentation is increasing across AI ecosystems. There is no interoperability between different models’ memory systems. A user’s context in GPT-4o does not translate to Claude, Gemini, or Mistral, leading to siloed experiences that fragment continuity and collaboration. It means the only point of continuity is individual to the user and fundamentally disjointed to any external view.Ultimately what we are talking about is that private AI interactions are creating isolated knowledge spaces. As more users rely on fine-tuned personal agents and persistent memory features, the result is a proliferation of parallel digital realities, each uniquely shaped by the individual’s bubble of past interactions. It takes everything that was creating conflict within our broader social fabric and exacerbates it both in terms of isolation and from an observability consideration it remains completely invisible.The risk of invisible epistemic bias is growing. Personalized bubbles can limit intellectual perspective and reinforce confirmation bias, particularly when LLMs refine outputs based solely on a user’s prior behavior and inputs. You can basically create a walled garden of very optimistic reinforcement that just celebrates whatever perspective, the bubble has fostered for the end user.I would argue that this is happening because no standards for portability of data exist. Truly at this point in the ecosystem there is a lack of standards for context portability. Without a framework to export or synchronize context across tools or agents, users remain locked into proprietary silos, impeding collaborative and transparent knowledge generation.What’s next for the Lindahl Letter? New editions arrive every Friday. If you are still listening at this point and enjoyed this content, then please take a moment and share it with a friend. If you are new to the Lindahl Letter, then please consider subscribing. Make sure to stay curious, stay informed, and enjoy the week ahead! This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit www.nelsx.com

Thank you for tuning in this week. Not only will this not be an audio only presentation this week and you will have to check YouTube at some point in the not so distant future for more details on that, but also I have tweaked the noise gate in GarageBand to improve the overall audio quality. This is week 200 of the Lindahl Letter publication. A new edition arrives every Friday. This week, the topic under consideration for the Lindahl Letter is, “My 200th Lindahl Letter Explained.”My very first Substack post was published on January 26, 2021, at 5:44 p.m. We can safely say that was about 236 weeks and 3 days ago at the point I started this draft. You probably have figured out that 36 weeks in that window did not receive any Lindahl Letter. That inaction does reflect a series of gaps in my publishing schedule. It happened. It happens. It might very well happen again at some point. Sometimes that is the way things go during an ongoing writing project. Today, however, you are getting the 200th cumulative week of my writing efforts for the Lindahl Letter publication. We have arrived at this major milestone in my writing efforts, and we should take a moment and celebrate. It is pretty exciting. I had compiled the previous years into manuscripts you can find online. At this point, it would probably make sense to assemble the year 4 edition of that writing project.For this 200th milestone post, it really does make sense to spotlight five topics that capture both the breadth of coverage and the depth of research that have defined the Lindahl Letter. Those weekly research notes don’t self-generate.The first topic would be from our recent shift to understanding quantum computing. It was a big shift from covering AI/ML to talking about quantum computing. That series included posts such as Magic state distillation explained and Quantum computing near Denver, which showcased detailed explorations of cutting-edge hardware breakthroughs and the regional tech ecosystem. I really do think that quantum computing is getting near a key breakthrough point where it will be more accessible. I’m not talking about it being widespread or used for everyday compute, but we are getting very close to the edge of possibility where quantum workloads are going to be a part of daily processes.The second topic relates to machines that build machines, a series examining advanced robotics, automation, and manufacturing systems that has been a defining theme of the current season. As we move forward, understanding prototyping and building the means of manufacturing is important to the next phase of building. We are going to see a movement from 3D printing to small-scale prototyping. Generally, I do not provide the same talk over and over again, but I think my elevator pitch on this topic needs some work.Third, we spent a lot of time discussing AI governance and ethics. That effort has been among the most engaged-with posts, offering insights into regulation, societal impact, and the responsible development of large language models. This topic just seems to be a known thing that we need, but it just does not end up being at the forefront of considerations.The fourth topic would have to be my all-time favorite topic to consider. That would be the intersection of technology and modernity, a recurring theme that connects technology trends to broader cultural and societal contexts. At some point, I plan on finishing my magnum opus on that topic. It should be a good read.Finally, the fifth topic would be worth rewinding back to my earliest foundational topics that were all just adapted talks, including my very first post in January 2021, which ultimately would provide you with a clear sense of how far the publication has evolved over 200 weeks. That key foundational topic was all about ROI and how to ensure you are aligning your priorities with actual dollars from the budget.As we move forward, the Lindahl Letter will continue along this new trajectory of research based on focusing on 3 topics: quantum computing, robotics, and enabled agents. I’m not sure if I will end up writing another 200 Lindahl Letters, but it is an interesting moment to consider having reached 200 of them and still be considering what’s next. I have considered moving to a monthly cadence where a paper is produced vs. a weekly research note. We will see where that ends up going during the next few weeks.What’s next for the Lindahl Letter? New editions arrive every Friday. If you are still listening at this point and enjoyed this content, then please take a moment and share it with a friend. If you are new to the Lindahl Letter, then please consider subscribing. Make sure to stay curious, stay informed, and enjoy the week ahead! This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit www.nelsx.com

Thank you for tuning in to this audio-only podcast presentation. This is week 197 of the Lindahl Letter publication. A new edition arrives every Friday. This week, the topic under consideration for the Lindahl Letter is, “Magic state distillation explained.”We have spent the last 3 weeks digging into quantum computing. That journey involved looking at the top 10 quantum computer leaderboard, annealing vs. gate-based systems, and the reality of enterprise plays. Trying to figure out where the edge of what is possible for quantum computing actually exists is a tricky proposition. A lot of roadmaps and promises exist in this space. People have plans, and they seem reasonable. It however, is hard to figure out what parts of them are actually real and delivering. We have seen some major movement in announcements for quantum error-reduction, which is a major step or part of a lot of roadmaps. News is going to keep breaking as we get closer to fault-tolerance. One of those breakthroughs is explained in a paper about magic state distillation that was submitted back in 2024, but just officially was published this month. The good people at the University of Osaka published a paper called, “Efficient Magic State Distillation by Zero-Level Distillation” [1]. The full citation for that 12-page paper happens to be:Tomohiro Itogawa, Yugo Takada, Yutaka Hirano, Keisuke Fujii. Efficient Magic State Distillation by Zero-Level Distillation. PRX Quantum, 2025; 6 (2) DOI: 10.1103/thxx-njr6Sure, improving how we use magic states is a key element of unlocking one of the top bottlenecks in quantum hardware design. The more base hardware elements that can be incorporated the lower the ceiling falls for practical implementation of quantum systems. You can read the PDF online, and the paper is readable if you are willing to look up a few terms that are commonly used in the quantum computing space [2]. You are probably well aware by now that I’m super duper interested in better understanding where gate-based quantum computing is heading in the next couple of years. This paper happens to dig into a subset of gate-based quantum computing called the Clifford operations. This is where a lot of things start as it is a well defined space. A Clifford operation is a quantum gate operation or circuit that maps Pauli operators to other Pauli operators under conjugation and can be composed of Hadamard, Phase, and CNOT gates. Think base actions or building blocks that need to be taken as part of a quantum system. A Pauli operator is one of the four fundamental 2×2 matrices (I, X, Y, Z) used to represent quantum bit-flip, phase-flip, and identity operations, forming the core building blocks of quantum error correction and circuit analysis.This paper introduces a new technique called zero-level distillation, which dramatically simplifies how quantum computers prepare the special “magic” states needed for universal computation. Traditionally, this process required error-corrected logical qubits, making it slow and resource-intensive. The team at the University of Osaka figured out how to do this more efficiently at the physical qubit level, verify the state using error-detecting circuits, and then teleport the result into a fully protected logical qubit. This method reduces both error rates and resource costs, bringing us one step closer to practical, large-scale quantum computers. It will be interesting to see how this advancement gets built into practical hardware implementations. I was digging into an advance shared by the Microsoft Quantum team related to a new four-dimensional geometric code method trying to figure out if this used a hardware-based method or something post-hardware [3]. That paper is 40 pages long and goes into a degree of depth that is interesting, but could have benefited from a brief summary beyond the provided abstract.Aasen, D., Hastings, M. B., Kliuchnikov, V., Bello-Rivas, J. M., Paetznick, A., Chao, R., ... & Svore, K. M. (2025). A Topologically Fault-Tolerant Quantum Computer with Four-Dimensional Geometric Codes. arXiv preprint arXiv:2506.15130.Still wanting to learn more? You can pretty easily do a Google Scholar search for “efficient magic state distillation” and you will get a bunch of different papers you can read [4]. It did not hold my interest enough for me to pull out key papers for you, but it was a thread that almost got pulled.This week I want to include a bonus topic from a video I watched on YouTube, “Quantum Complexity: Scott Aaronson on P vs NP and the Future.”Aaronson explains that while P ≠ NP is widely believed, quantum computing does not resolve this distinction or solve NP-complete problems efficiently. He introduces BQP or Bounded-Error Quantum Polynomial Time as the class of problems solvable by quantum computers, noting that quantum speedups like those from Grover’s and Shor’s algorithms can apply only to problems with specific structure. Aaronson concludes that quantum computing offers significant but limited advantages, and that future breakthroughs will depend on understanding the deep complexity boundaries that define its capabilities. You could dig into the very large paper Aaronson released about computational complexity [5]. It’s 59 pages and I downloaded it to give it a read later this week.What’s next for the Lindahl Letter? New editions arrive every Friday. If you are still listening at this point and enjoyed this content, then please take a moment and share it with a friend. If you are new to the Lindahl Letter, then please consider subscribing. Make sure to stay curious, stay informed, and enjoy the week ahead!Footnotes:[1] The University of Osaka. (2025, June 26). Quantum breakthrough: ‘Magic states’ now easier, faster, and way less noisy. ScienceDaily. Retrieved July 12, 2025 from www.sciencedaily.com/releases/2025/06/250621233816.htm[2] Tomohiro Itogawa, Yugo Takada, Yutaka Hirano, Keisuke Fujii. Efficient Magic State Distillation by Zero-Level Distillation. PRX Quantum, 2025; 6 (2) DOI: 10.1103/thxx-njr6 https://journals.aps.org/prxquantum/abstract/10.1103/thxx-njr6https://journals.aps.org/prxquantum/pdf/10.1103/thxx-njr6[3] https://azure.microsoft.com/en-us/blog/quantum/2025/06/19/microsoft-advances-quantum-error-correction-with-a-family-of-novel-four-dimensional-codes/ you can read the paper here https://arxiv.org/abs/2506.15130[4] https://scholar.google.com/scholar?hl=en&as_sdt=0%2C6&q=Efficient+Magic+State+Distillation&btnG=[5] Scott Aaronson, “Why Philosophers Should Care About Computational Complexity” https://www.scottaaronson.com/papers/philos.pdf This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit www.nelsx.com

Thank you for tuning in to this audio only podcast presentation. This is week 195 of the Lindahl Letter publication. A new edition arrives every Friday. This week the topic under consideration for the Lindahl Letter is, “Annealing vs. gate based quantum computing.”You may have picked up from the last edition of the Lindahl Letter that I’m more focused on gate based quantum computing than I am concerned about the current advances in annealing based systems. This week I went back over and dug out some gems on Google Scholar related to annealing quantum computing [1]. Some of these academic articles have a few hundred citations, but none of them seem to be breakout articles with thousands of citations. Within a small academic discipline you will see a paper pick up citations under 100 and that is probably a well read paper. Some of the mega papers in the AI space have 100,000 citations and those are foundational and very well read academic papers. Honestly, the only things that might be better read are books that break into the public mind and become bestsellers. I don’t think anything that I have found in the annealing based quantum computing space would qualify as breakout or bestseller.Here are 5 papers that are highly cited that I thought were interesting this week:Das, A., & Chakrabarti, B. K. (2008). Colloquium: Quantum annealing and analog quantum computation. Reviews of Modern Physics, 80(3), 1061-1081. https://arxiv.org/pdf/0801.2193Pudenz, K. L., Albash, T., & Lidar, D. A. (2014). Error-corrected quantum annealing with hundreds of qubits. Nature communications, 5(1), 3243. https://www.nature.com/articles/ncomms4243.pdfHauke, P., Katzgraber, H. G., Lechner, W., Nishimori, H., & Oliver, W. D. (2020). Perspectives of quantum annealing: Methods and implementations. Reports on Progress in Physics, 83(5), 054401. https://arxiv.org/pdf/1903.06559Morita, S., & Nishimori, H. (2008). Mathematical foundation of quantum annealing. Journal of Mathematical Physics, 49(12). https://arxiv.org/pdf/0806.1859Yarkoni, S., Raponi, E., Bäck, T., & Schmitt, S. (2022). Quantum annealing for industry applications: Introduction and review. Reports on Progress in Physics, 85(10), 104001. https://arxiv.org/pdf/2112.07491What exactly is annealing quantum computing?Let’s answer this question the hard way by first stating that universal gate based quantum computing is built out to a set of qubits where any type of computation could be worked using the available qubits. If you have quantum computing work, then you are good to go within the universal gate-based system. Now let’s say you were a company like D-Wave Systems and you wanted to take a different direction than universal gate-based quantum computing and lean into the annealing quantum computing world. You would start to build a system that works toward being optimized for special use cases and you might write a nice presentation about it which you could read [2]. Based on what D-Wave Systems is sharing, annealing quantum computing system uses a method that solves optimization problems by gradually evolving a quantum system toward its lowest energy state, or ground state. It leverages the quantum adiabatic theorem, which ensures that a system will remain in its ground state if changes to its energy landscape are made slowly enough. Instead of using logic gates, annealing encodes a problem into a Hamiltonian (which is a mathematical function that describes the total energy of a quantum system), and the solution emerges as the system relaxes. This model excels at solving complex combinatorial optimization problems. Unlike gate-based systems, annealers are not universal quantum computers but offer practical advantages for certain narrow tasks. It’s like special quantum computing vs. general quantum computing.What’s next for the Lindahl Letter? New editions arrive every Friday. If you are still listening at this point and enjoyed this content, then please take a moment and share it with a friend. If you are new to the Lindahl Letter, then please consider subscribing. Make sure to stay curious, stay informed, and enjoy the week ahead!Footnotes:[1] https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=annealing+quantum+computing&oq=Annealing+qu[2] https://s201.q4cdn.com/339170267/files/doc_presentations/2025/Mar/31/20250331_D-Wave-Technology-and-the-Competitive-Landscape.pdf This is a public episode. If you would like to discuss this with other subscribers or get access to bonus episodes, visit www.nelsx.com