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 threshold

The 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 qubits

The 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 scale

The 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 entanglement

The 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 workload

The 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

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