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Quantum Computing Foundations - A Briefing Note with Sources
Quantum computing fundamentals briefing - error correction, hardware architectures, computational advantage, and where the field stands - key papers, expert commentary, and lab progress from January 2023 to April 2026
- Claude Opus 4.8
- academic
- frontier
- blogs
Synthesised 2026-04-19
Overview
Quantum computing entered its most consequential experimental window between January 2023 and April 2026, and the defining shift was concrete: error correction moved from theory to demonstrated hardware. Google's 105-qubit Willow chip crossed the "below-threshold" barrier for the first time, meaning logical error rates fell as physical qubits were added rather than rising, with a measured error suppression factor of Λ=2.14 per unit increase in code distance. Sources: Nature (2024) (↗); Google Quantum AI Blog (2024) (↗)
This matters because error correction is the gate through which every useful application must pass. A physical qubit decoheres in microseconds to seconds; a fault-tolerant logical qubit, built from many physical qubits running a stabiliser code, can in principle persist indefinitely. The surface code remains the experimental workhorse, requiring roughly d² physical qubits at code distance d, which means thousands of physical qubits per logical qubit for cryptographically relevant work. IBM's March 2024 bivariate bicycle codes attacked exactly this overhead, encoding 12 logical qubits in 288 physical qubits, roughly a tenfold reduction. Sources: Nature (2024) (↗); Nature (via PMC) (2024) (↗)
The second defining shift was the unexpected rise of neutral atoms. Harvard/QuEra's December 2023 processor ran 48 logical qubits on reconfigurable atom arrays, and follow-on work demonstrated fault-tolerant computation with 24 logical qubits, then scaled toward universal architectures on thousands of atoms. Reconfigurable all-to-all connectivity turned out to suit error-correction codes that would demand costly SWAP gates on fixed superconducting topologies. Sources: Nature (2023) (↗); arXiv (2024) (↗); Nature (2025) (↗)
The third shift was a sharper, more honest reckoning. Google's own November 2025 perspective conceded that earlier advantage claims from IBM's 127-qubit Eagle and from D-Wave were later simulated classically, and that the field's hardest unsolved problem is finding concrete problem instances, not sampling tasks, where quantum genuinely beats the best classical methods. Hardware improved dramatically. Algorithmic discovery did not. Sources: arXiv (2025) (↗)
Timeline
- Neutral-atom logical processor demonstrated (48 logical qubits)
- Neutral atom hardware reviewed as end-user platform
- Low-overhead qLDPC codes published (bivariate bicycle)
- Aaronson's "Between Hope and Hype" recalibrates optimism
- Below-threshold surface code achieved on Willow
- Neural-network decoders arrive (AlphaQubit)
- Fault-tolerant computation with 24 logical qubits
- Microsoft Majorana 1 announced and contested
- IBM publishes modular fault-tolerant roadmap
- QEC moves from concept to tangible hardware
- Continuous 3,000-qubit and 6,100-qubit atom systems
- Google claims verifiable advantage with Quantum Echoes
- IBM unveils Loon and Nighthawk, sets 2029 Starling target
- Honest "algorithm gap" consensus published
- 448-atom fault-tolerant architecture extends neutral-atom lead
- Riverlane predicts broad qLDPC adoption
Key Findings
Below-threshold error correction is real and reproduced. Google's Willow result is the most-cited milestone of the period, confirmed in Nature and echoed across independent commentary as a genuine inflection rather than a press-release artefact. Riverlane's engineering blog called 2025 the year QEC moved from theoretical concept to tangible hardware, documenting a jump from 36 to 120 peer-reviewed QEC papers in a single year. Even Scott Aaronson, the field's most careful sceptic, treated below-threshold as a step-change. Sources: Nature (2024) (↗); Riverlane Blog (2026) (↗); Shtetl-Optimized (Scott Aaronson's personal blog) (2024) (↗)
IBM's pivot to qLDPC codes reframed the overhead problem. The bivariate bicycle "gross" code encodes 12 logical qubits in 288 physical qubits, roughly tenfold more efficient than surface codes, but demands long-range connectivity that superconducting chips do not naturally provide. IBM's response was an architectural roadmap: the Loon and Nighthawk processors, and a 2029 Starling target of 200 logical qubits executing 100 million operations. The theoretical scaffolding came from good-qLDPC-code proofs of 2022 to 2024, which IBM made buildable. Sources: Nature (2024) (↗); IBM Quantum Blog (2025) (↗); IBM Newsroom (2025) (↗)
Neutral atoms became the surprise logical-qubit leader. The architectural argument is that physically movable atoms implement arbitrary connectivity, sidestepping the SWAP-gate cost that fixed-topology codes incur. A January 2026 Nature paper presented a fault-tolerant neutral-atom architecture for universal computation, building on continuous 3,000-qubit operation and a 6,100-qubit tweezer array with coherence times measured in seconds. IEEE Spectrum reporting placed both Microsoft/Atom Computing and QuEra on Level-2 logical machine timelines for 2026 to 2027. Sources: Nature (2026) (↗); Nature (2025) (↗); Nature (2025) (↗)
Microsoft's Majorana 1 is the period's clearest case of press-release culture colliding with peer review. Microsoft announced eight topological qubits on a chip designed for one million in February 2025, claiming the world's first topological qubit. Nature's own coverage and the accompanying peer-review file stated the paper contained no evidence for Majorana zero modes, and physicists at Cornell, NYU and Caltech challenged the data at the APS March Meeting. The 2018 retraction was cited repeatedly as grounds for caution. Sources: Microsoft Azure Quantum Blog (2025) (↗); Nature (2025) (↗); APS Physics (2025) (↗)
The honest expert reading is that hardware advanced while algorithms stalled. Google's Grand Challenge perspective and a June 2025 "Future of Quantum Computing" piece both centre the algorithm gap: no proven asymptotic advantage for a practically important problem has emerged since Shor (1994) and Grover (1996). Quantum simulation of chemistry and materials remains the consensus best near-term candidate, but classical competition from tensor networks and neural quantum states keeps advancing. A survey of the advantage landscape underscores how narrow demonstrated advantage still is. Sources: arXiv (2025) (↗); arXiv (2025) (↗); arXiv (2025) (↗)
Sampling advantage and useful advantage are different things, and conflating them drives most hype. Google's October 2025 Quantum Echoes algorithm ran 13,000 times faster than the Frontier supercomputer and was framed as "verifiable quantum advantage," but it remains a specialised benchmark, not a commercially meaningful computation. HPCwire's coverage captured both the achievement and the caveat. The distinction between distribution-sampling speed and computing a useful result is the single most important conceptual line for non-specialists. Sources: Google Quantum AI Blog (2025) (↗); HPCwire (2025) (↗)
Machine-learning decoders entered the QEC stack. Google DeepMind's AlphaQubit used a transformer-based neural decoder that cut errors by 6 to 30 per cent over prior methods on Sycamore and Willow, though it was still too slow for real-time superconducting decoding at publication. This signals that decoding, not just qubit fabrication, is now a frontier in its own right, with latency as the binding constraint. Sources: Nature (2024) (↗); Google DeepMind Blog (2024) (↗)
The skeptic tradition is internal to physics and remains live. Gil Kalai maintains that correlated noise will prevent any scalable demonstration, and his blog documented an ongoing dialogue with Aaronson through March 2026. This is not external commentary; it is a falsifiable physical claim debated in peer-reviewed venues. Aaronson's December 2025 post called near-term Shor a "live possibility," which Kalai contested directly, leaving the field's foundational bet unresolved. Sources: Combinatorics and More (Gil Kalai's blog) (2025) (↗); Combinatorics and More (Gil Kalai's blog) (2026) (↗); Shtetl-Optimized (Scott Aaronson's personal blog) (2025) (↗)
Commercial projections continue to slip while investment grows. McKinsey's 2025 Quantum Technology Monitor projected $72 billion in quantum computing revenue by 2035 and noted start-up investment 50 per cent higher in 2024 than 2023, while its December 2025 piece framed fault tolerance as the central engineering goal. The pattern of successive consultancy projections pushing useful-advantage dates forward is itself a documented feature of the hype cycle. Sources: McKinsey & Company (Quantum Technology Monitor) (2025) (↗); McKinsey & Company (2025) (↗)
Evidence & Data
The hard numbers cluster around error correction. Willow delivered Λ=2.14 logical error suppression per code-distance step, the first below-threshold result on a superconducting device. Sources: Nature (2024) (↗); arXiv (2024) (↗)
IBM's [[144,12,12]] bivariate bicycle code packs 12 logical qubits into 288 physical qubits, against the surface code's roughly d² physical qubits per logical qubit. Willow's single below-threshold logical qubit used distance-7 surface codes drawing on roughly 100 physical qubits, illustrating how far both numbers sit below Shor-on-RSA-2048 requirements. Sources: Nature (2024) (↗); Nature (2024) (↗)
Neutral-atom scale figures are striking: continuous operation of a 3,000-qubit system, a 6,100-qubit tweezer array, and reported coherence on the order of 12.6 seconds, alongside QuEra's algorithmic fault tolerance claiming 10 to 100 times overhead reduction. A Nature Physics result on polylogarithmic time and constant space overheads gives the theoretical counterpart. Sources: Nature (2025) (↗); Nature (2025) (↗); Medium (nehalmr) (2026) (↗); Nature Physics (2025) (↗)
On benchmarks, AlphaQubit's 6 to 30 per cent error reduction and Quantum Echoes' 13,000-fold speedup over Frontier are the headline performance figures, both carrying explicit caveats about real-time decoding latency and benchmark specificity respectively. On expert sentiment, the Global Risk Institute's 2024 survey of 47 experts placed a 34 per cent probability on cryptographically relevant quantum computers by 2034, up from 17 per cent in 2022. Sources: Nature (2024) (↗); HPCwire (2025) (↗); arXiv (2025) (↗)
On commercial scale, McKinsey's $72 billion-by-2035 revenue projection and the 50 per cent year-on-year start-up investment growth are the most-quoted market figures. Quantinuum's trapped-ion quantum volume exceeding 2 million anchors the fidelity case for ions. Sources: McKinsey & Company (Quantum Technology Monitor) (2025) (↗); EPJ Quantum Technology (Springer Nature) (2023) (↗)
Signals & Tensions
Topological qubits: overhyped now, possibly underrated long-term. The community received Majorana 1 sceptically, with Aaronson's FAQ noting the press release "speaks differently" from the paper and an arXiv critique challenging the validation method directly. Yet the underlying motivation, hardware-level error suppression rather than software overhead, remains genuinely attractive if it can ever be demonstrated. The tension is between a contested present and a structurally appealing future. Sources: Shtetl-Optimized (Scott Aaronson's personal blog) (2025) (↗); The Quantum Insider (2025) (↗); arXiv (2025) (↗)
No architecture winner has emerged, and the lanes agree on this. Superconducting leads on gate speed and fabrication maturity but fights coherence and cryogenics. Trapped ions lead on fidelity but lag on gate speed and scaling. Neutral atoms lead on logical-qubit demonstrations but face loading and gate-speed limits. A paper on "the cost of connectivity" frames the central architectural trade-off explicitly. Sources: arXiv (2025) (↗); EPJ Quantum Technology (Springer Nature) (2023) (↗)
Decoder latency is underreported relative to its importance. AlphaQubit's accuracy gains are widely cited, but the fact that it was too slow for real-time superconducting decoding is the more consequential detail. Useful fault tolerance needs decoding that keeps pace with gate cycles, and that constraint rarely surfaces in headline coverage. Sources: Nature (2024) (↗)
Quantum machine learning advantage is contested in real time. A December 2025 Nature Communications paper reported quantum advantage for learning shallow neural networks with natural data distributions, while a near-simultaneous arXiv piece argued quantum deep learning "still needs a quantum leap." Both appearing within weeks signals an unsettled subfield rather than a consensus. Sources: Nature Communications (2025) (↗); arXiv (2025) (↗)
The bull and bear cases are both held by serious people. Aaronson's "live possibility" of Shor before the next US election and Riverlane's prediction of broad qLDPC adoption in 2026 represent the credible optimistic read. Kalai's correlated-noise objection and the "More Is Different" warning against Moore's-law extrapolation of qubit-quality metrics represent the credible caution. Neither side is making an unserious argument. Sources: Shtetl-Optimized (Scott Aaronson's personal blog) (2025) (↗); Riverlane Blog (2026) (↗); More Is Different (Substack) (2025) (↗)
Open Questions
Can any concrete, non-sampling problem instance be found where quantum beats the best classical method? Google's own perspective names this as the field's hardest unsolved challenge, and it remains open. Sources: arXiv (2025) (↗)
Is correlated noise a fundamental barrier to scalable quantum computing, or an engineering nuisance? The Aaronson-Kalai dialogue through March 2026 has not resolved it, and it is the foundational physical question. Sources: Combinatorics and More (Gil Kalai's blog) (2026) (↗); Combinatorics and More (Gil Kalai's blog) (2025) (↗)
Will qLDPC codes deliver their overhead advantage on real hardware, given that they demand long-range connectivity superconducting chips lack? IBM's Loon and Kookaburra chips are designed to test exactly this, with results pending. Sources: IBM Newsroom (2025) (↗); IBM Quantum Blog (2025) (↗)
Did Microsoft demonstrate anything topological at all? The peer-review file said no evidence for Majorana zero modes, and the independent critique stands unrebutted in the sources here. Sources: Nature (2025) (↗); Nature (2025) (↗)
Can real-time decoding keep pace with superconducting gate cycles? AlphaQubit's latency problem is acknowledged but unsolved as of publication. Sources: Nature (2024) (↗)
Is IBM's 2029 Starling target (200 logical qubits, 100 million operations) a fabrication-and-systems problem now, as some independents argue, or still a physics problem? The roadmap asserts the former; the timeline is untested. Sources: IBM Quantum Blog (2025) (↗); Riverlane Blog (2026) (↗)
Will the next decade produce a genuinely new advantage-bearing algorithm, or will the post-1996 drought continue? Every honest assessment in the sweep treats this as the question that ultimately decides whether the hardware effort pays off. Sources: arXiv (2025) (↗); arXiv (2025) (↗)
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Sources
Summary: ↑ Back to summary
Academic & arXiv
| ID | Title | Outlet | Date | Significance |
|---|---|---|---|---|
| a1 | Quantum error correction below the surface code threshold | Nature | 2024-12 | Google's landmark Willow-chip paper demonstrating the first below-threshold surface code memories on superconducting processors, with logical error rates exponentially suppressed as code distance grows - widely cited as the definitive proof-of-concept for scalable QEC. |
| a2 | Quantum error correction below the surface code threshold (arXiv preprint) | arXiv | 2024-08 | Full technical arXiv version of Google's Willow QEC paper, providing detailed methodology including the Sparse Blossom real-time decoder achieving 63 µs latency at distance-5 over one million correction cycles. |
| a3 | High-threshold and low-overhead fault-tolerant quantum memory | Nature | 2024-03 | IBM's Bravyi et al. introduce the 'gross code' (bivariate bicycle qLDPC family) achieving 0.7–0.8% error threshold at 10x lower physical qubit overhead than the surface code, reshaping the roadmap for fault-tolerant quantum computing. |
| a4 | High-threshold and low-overhead fault-tolerant quantum memory (arXiv) | arXiv | 2023-08 | Preprint of IBM's qLDPC gross-code paper by Bravyi, Cross, Gambetta et al., which established that quantum LDPC codes can match surface-code error thresholds with far fewer physical qubits, triggering a wave of experimental follow-up. |
| a5 | Logical quantum processor based on reconfigurable atom arrays | Nature | 2023-12 | Bluvstein et al. (Harvard/MIT/QuEra) demonstrate the first programmable logical quantum processor with up to 48 logical qubits on 280 physical qubits in a neutral-atom array, heralding the era of early error-corrected computation. |
| a6 | Logical quantum processor based on reconfigurable atom arrays (arXiv) | arXiv | 2023-12 | Full arXiv version of the Harvard/QuEra logical processor paper demonstrating 228 logical two-qubit gates on 48 logical qubits, showing logical encoding substantially improves algorithmic performance over physical qubit fidelities. |
| a7 | Fault-tolerant quantum computation with a neutral atom processor | arXiv | 2024-11 | Reichardt et al. (Microsoft/Caltech) demonstrate fault-tolerant computation on a 256-qubit neutral Ytterbium atom processor, showing 24 logical qubits with erasure conversion and better-than-physical error rates on the Bernstein-Vazirani algorithm. |
| a8 | A fault-tolerant neutral-atom architecture for universal quantum computation | Nature | 2026-01 | Uses reconfigurable arrays of up to 448 neutral atoms to implement and combine key elements of a universal, fault-tolerant quantum processing architecture, including 2.14x below-threshold surface code performance with machine learning decoding. |
| a9 | Learning high-accuracy error decoding for quantum processors (AlphaQubit) | Nature | 2024-11 | Google DeepMind's AlphaQubit paper presenting a transformer-based neural network decoder that outperforms state-of-the-art decoders on real Sycamore hardware data for distance-3 and distance-5 surface codes, opening neural-network decoding for real hardware. |
| a10 | Demonstrating quantum error mitigation on logical qubits | Nature Communications | 2026-02 | Proposes and experimentally demonstrates zero-noise extrapolation applied to error correction circuits on superconducting processors, advancing early fault-tolerant quantum computing by combining error mitigation with error correction. |
| a11 | Experimental demonstration of logical magic state distillation | arXiv | 2024-12 | QuEra/Harvard team demonstrates logical magic state distillation on a neutral-atom processor - a critical missing ingredient for universal fault-tolerant computation beyond Clifford operations. |
| a12 | Microsoft unveils Majorana 1 - the world's first quantum processor powered by topological qubits | Microsoft Azure Quantum Blog | 2025-02 | Official announcement of the Majorana 1 chip, claiming the first hardware-protected topological qubit using an InAs-Al topoconductor, accompanied by a Nature paper on parity measurement and an arXiv device roadmap. |
| a13 | Roadmap to fault tolerant quantum computation using topological qubit arrays | arXiv | 2025-02 | Microsoft's four-generation device roadmap (Aasen et al.) for building fault-tolerant quantum computers using Majorana-based tetron qubits, spanning from single-qubit benchmarking through lattice surgery on two logical qubits. |
| a14 | Microsoft quantum-computing claim still lacks evidence: physicists are dubious | Nature | 2025-03 | Nature news article capturing the scientific community's skeptical reception of Microsoft's Majorana 1 claim, noting that attendees left a key presentation with questions unanswered about whether topological protection was truly demonstrated. |
| a15 | Microsoft quantum computing 'breakthrough' faces fresh challenge | Nature | 2025-03 | Reports a physicist's (H.F. Legg, arXiv:2502.19560) challenge to the measurement protocol underpinning Microsoft's topological qubit claim, representing the most substantive independent critical analysis of the Majorana 1 announcement. |
| a16 | Microsoft claims quantum-computing breakthrough - but some physicists are sceptical | Nature | 2025-02 | First Nature news response to the Majorana 1 announcement, explaining Microsoft's topological approach and documenting the initial wave of external skepticism about whether the demonstration constitutes a genuine qubit. |
| a17 | The Grand Challenge of Quantum Applications | arXiv | 2025-11 | Google Quantum AI perspective paper proposing a five-stage framework from quantum advantage discovery to deployment, candidly noting that advantage claims from IBM and D-Wave were later classically simulated and that identifying concrete advantage instances remains under-resourced. |
| a18 | Future of Quantum Computing | arXiv | 2025-06 | Panel summary authored by Barry Sanders with Scott Aaronson, Andrew Childs, Eddie Farhi, and Aram Harrow, providing a frank expert debate on hardware progress, algorithmic stagnation, and the field's honest disagreements about timelines and what counts as useful advantage. |
| a19 | The vast world of quantum advantage | arXiv | 2025-08 | Comprehensive arXiv survey mapping the landscape of proven and contested quantum advantages across computation, learning/sensing, and cryptography, noting the relentless competition from improving classical tensor network and ML-based simulation methods. |
| a20 | Quantum advantage for learning shallow neural networks with natural data distributions | Nature Communications | 2025-12 | Lewis et al. prove an exponential quantum advantage for learning periodic neurons over non-uniform distributions in the quantum statistical query model, one of the most rigorous recent demonstrations of quantum ML advantage beyond synthetic uniform cases. |
| a21 | Quantum Deep Learning Still Needs a Quantum Leap | arXiv | 2025-11 | Critical quantitative assessment arguing that quantum deep learning faces three structural barriers - qubit overhead, missing QRAM infrastructure, and narrow applicability of existing speedups - supported by hardware trend forecasts through the 2020s. |
| a22 | Quantum computing with atomic qubit arrays: confronting the cost of connectivity | arXiv | 2025-11 | Lecture-based review from a 2024 Varenna school (updated through summer 2025) providing a rigorous architectural analysis of neutral-atom quantum computing, focusing on connectivity costs, error correction protocols, and comparison with competing modalities. |
| a23 | Quantum computing: foundations, algorithms, and emerging applications | Frontiers in Quantum Science and Technology | 2025-12 | Comprehensive 2025 review synthesizing foundational theory, hardware architectures, and application readiness, critically noting that end-to-end resource analyses are frequently incomplete and benchmarking remains at an early, inconsistent stage. |
| a24 | FAQ on Microsoft's topological qubit thing (Scott Aaronson's Shtetl-Optimized blog) | Shtetl-Optimized (Scott Aaronson) | 2025-02 | Widely-read independent expert commentary by complexity theorist Scott Aaronson on the Majorana 1 announcement, providing a technically literate critical perspective that circulated widely in the research community as a reality-check on Microsoft's claims. |
| a25 | IBM lays out clear path to fault-tolerant quantum computing (IBM Quantum roadmap 2025) | IBM Quantum | 2025 | IBM's updated fault-tolerant roadmap detailing the Loon (2025), Kookaburra (2026), Cockatoo (2027), and Starling (2028) processor sequence for implementing qLDPC logical processing units, providing a concrete engineering timeline for independent assessment. |
Frontier Lab & Model News
| ID | Title | Outlet | Date | Significance |
|---|---|---|---|---|
| t1 | Meet Willow, our state-of-the-art quantum chip | Google Quantum AI Blog | 2024-12 | Official announcement of Willow's below-threshold quantum error correction and benchmark claim of completing a computation in under five minutes that would take a supercomputer 10 septillion years, a milestone celebrated and critiqued across the field. |
| t2 | Quantum error correction below the surface code threshold (Willow paper, Nature) | Nature | 2024-12 | Peer-reviewed Nature publication confirming Willow's first 'below-threshold' quantum error correction, with the error rate at the logical qubit level decreasing as more physical qubits are added - a three-decade milestone. |
| t3 | AlphaQubit: Google's research on quantum error correction | Google DeepMind Blog | 2024-11 | Announces AlphaQubit, a transformer-based AI decoder jointly developed by Google DeepMind and Google Quantum AI that makes 6% fewer errors than tensor-network methods and 30% fewer than correlated matching, published in Nature. |
| t4 | Our Quantum Echoes algorithm is a big step toward real-world applications for quantum computing | Google Quantum AI Blog | 2025-10 | Claims the first-ever verifiable quantum advantage on hardware: the Quantum Echoes (OTOC) algorithm ran 13,000× faster on Willow than the fastest classical supercomputer, with results published in Nature and independently verified against NMR data. |
| t5 | Google Claims Quantum Advantage with Willow Chip | HPCwire | 2025-10 | Detailed independent technical coverage of Google's Quantum Echoes Nature paper, including context on the distinction between verifiable quantum advantage and earlier supremacy claims, with caution about classical counterattacks. |
| t6 | Microsoft's Majorana 1 chip carves new path for quantum computing | Microsoft Source | 2025-02 | Official Microsoft announcement of Majorana 1, described as the world's first quantum chip with a Topological Core, placing eight topological qubits on a chip designed to scale to one million, with an accompanying Nature paper. |
| t7 | Microsoft unveils Majorana 1, the world's first quantum processor powered by topological qubits | Microsoft Azure Quantum Blog | 2025-02 | Technical blog post explaining the Majorana 1 roadmap, from single-qubit devices to quantum error correction arrays, detailing the role of Majorana Zero Modes, interferometric parity measurements, and hardware-protected topological qubits. |
| t8 | Microsoft's Claim of a Topological Qubit Faces Tough Questions | APS Physics | 2025-03 | Peer-reviewed expert commentary reporting that condensed-matter physicists at Cornell and NYU questioned Microsoft's topological qubit data at APS March Meeting, with Nature's editorial team noting the paper does not yet represent evidence for topological modes. |
| t9 | Microsoft's Topological Qubit Claim Faces Quantum Community Scrutiny | The Quantum Insider | 2025-02 | Captures the scientific community debate around Majorana 1, including Scott Aaronson's cautious endorsement and Microsoft's 2018 retraction history, providing balanced context on the contested nature of the announcement. |
| t10 | Topological quantum processor marks breakthrough in computing | UC Santa Barbara (The Current) | 2025-02 | Academic institution perspective from Microsoft Station Q's home institution, explaining the physics of Majorana zero modes in topological qubits and contextualizing the eight-qubit Majorana 1 as a proof-of-concept rather than a commercial device. |
| t11 | IBM lays out clear path to fault-tolerant quantum computing | IBM Quantum Blog | 2025-06 | IBM details its end-to-end modular framework for fault-tolerant quantum computing based on bivariate bicycle (qLDPC) codes, with the gross code encoding 12 logical qubits in 288 physical qubits - 10× more efficient than surface codes. |
| t12 | High-threshold and low-overhead fault-tolerant quantum memory (IBM bivariate bicycle Nature paper) | Nature (via PMC) | 2024-03 | The landmark IBM Nature paper (Bravyi, Cross, Gambetta et al.) introducing the bivariate bicycle qLDPC code, which became the foundation of IBM's entire fault-tolerant roadmap and sparked industry-wide adoption of high-rate LDPC codes. |
| t13 | IBM Delivers New Quantum Processors, Software, and Algorithm Breakthroughs on Path to Advantage and Fault Tolerance | IBM Newsroom | 2025-11 | IBM QDC 2025 announcement revealing Quantum Loon (all key processor components for fault-tolerant computing demonstrated) and Nighthawk (120-qubit, 5,000-gate processor), with real-time qLDPC decoding under 480 nanoseconds achieved one year ahead of schedule. |
| t14 | IBM Offers Roadmap Toward Large-Scale, Fault-Tolerant Quantum Computer at New IBM Quantum Data Center | The Quantum Insider | 2025-06 | Comprehensive coverage of IBM's Starling roadmap targeting a 200-logical-qubit, 100-million-operation fault-tolerant system by 2029, with intermediate steps Loon (2025), Kookaburra (2026), and Cockatoo (2027) clearly defined. |
| t15 | Engineering Fault Tolerance: IBM's Modular, Scalable Full-Stack Quantum Roadmap | The Quantum Insider | 2025-06 | Technical analysis of IBM's pivot from surface codes to qLDPC codes, explaining how bivariate bicycle codes reduce physical qubit overhead by up to 90% and enable the non-local connectivity critical to scalable fault-tolerant architectures. |
| t16 | Scaling for quantum advantage and beyond (IBM QDC 2025 blog) | IBM Quantum Blog | 2025-11 | IBM's official QDC 2025 state-of-the-union detailing Nighthawk's 120-qubit, 5,000-gate milestone, Heron's lowest-ever median two-qubit gate errors, and the company's dual-track strategy of near-term advantage and long-term fault tolerance. |
| t17 | A fault-tolerant neutral-atom architecture for universal quantum computation | Nature | 2025-11 | Harvard/MIT team demonstrates key elements of a universal fault-tolerant architecture using up to 448 reconfigurable neutral atoms, a peer-reviewed advance establishing neutral atoms as a credible path to fault-tolerant quantum computation. |
| t18 | Continuous operation of a coherent 3,000-qubit system | Nature | 2025-09 | Nature paper demonstrating continuous operation of more than 3,000 physical qubits in a neutral-atom array with coherent storage, enabling deep-circuit quantum evolution and real-time syndrome extraction without atom losses halting computation. |
| t19 | A tweezer array with 6,100 highly coherent atomic qubits | Nature | 2025-09 | Demonstrates an optical tweezer array of 6,100 neutral-atom qubits across 12,000 sites, indicating that quantum computing with 6,000+ qubits is a near-term prospect and providing a path toward QEC with hundreds of logical qubits. |
| t20 | A manufacturable platform for photonic quantum computing | Nature | 2025-02 | PsiQuantum-led Nature paper introducing silicon-photonics-based modules with photonic qubit state-preparation fidelity of 99.98%, providing the first demonstrated manufacturable platform architecture for photonic quantum computing. |
| t21 | Scaling and networking a modular photonic quantum computer | Nature | 2025-01 | Proof-of-principle study using 35 photonic chips (the 'Aurora' machine) demonstrating a complete photonic quantum computer architecture capable of universal and fault-tolerant operation once component performance thresholds are reached. |
| t22 | Fault-tolerant quantum computation with polylogarithmic time and constant space overheads | Nature Physics | 2025-11 | Theoretical proof that QLDPC codes combined with concatenated Steane codes achieve constant space overhead and polylogarithmic time overhead, resolving a longstanding gap in fault-tolerant quantum computation theory. |
| t23 | Making fault-tolerant quantum computers a reality | McKinsey & Company | 2025-12 | McKinsey's structured industry assessment of quantum error correction challenges across qubit modalities, with data showing quantum start-up investment was 50% higher in 2024 than 2023 and projecting the quantum market near $100 billion by 2035. |
| t24 | The Year of Quantum: From concept to reality in 2025 | McKinsey & Company (Quantum Technology Monitor) | 2025-06 | McKinsey's annual Quantum Technology Monitor estimating quantum technology revenue growing to $72 billion in computing alone by 2035, documenting $1.8 billion in government funding in 2024 and cataloguing error-correction progress across labs and start-ups. |
| t25 | Neutral atom quantum computing hardware: performance and end-user perspective | EPJ Quantum Technology (Springer Nature) | 2023-08 | Peer-reviewed industrial end-user review of neutral-atom quantum hardware covering physical qubit architecture, gate fidelities, connectivity, and fault-tolerant prospects, providing honest trade-off analysis against other modalities. |
Blogs & Independent Thinkers
| ID | Title | Outlet | Date | Significance |
|---|---|---|---|---|
| b1 | Quantum Computing: Between Hope and Hype | Shtetl-Optimized (Scott Aaronson's personal blog) | 2024-09 | Aaronson's most comprehensive 2024 state-of-the-field address, covering error correction progress, Google Willow, Microsoft's Quantinuum collaboration, and the honest gap between theoretical speedup and practical utility. |
| b2 | More on whether useful quantum computing is 'imminent' | Shtetl-Optimized (Scott Aaronson's personal blog) | 2025-12 | Aaronson's December 2025 reassessment, calling it a 'live possibility' that a fault-tolerant computer running Shor's algorithm could appear before the next US presidential election - a major update from his prior skeptical posture. |
| b3 | FAQ on Microsoft's topological qubit thing | Shtetl-Optimized (Scott Aaronson's personal blog) | 2025-02 | Aaronson's point-by-point FAQ on Microsoft's Majorana 1 claim, noting Nature's own reviewers found no direct evidence for Majorana zero modes and calling the commercial utility 'not yet' in unequivocal terms. |
| b4 | And yet quantum computing continues to progress | Shtetl-Optimized (Scott Aaronson's personal blog) | 2024-04 | Detailed tracking of Quantinuum and ion-trap progress in early 2024, with Aaronson comparing his 2024 skepticism of fault-tolerant QC to mid-1960s skepticism of moon landings - acknowledging unexpected obstacles remain possible. |
| b5 | Book Review: 'Quantum Supremacy' by Michio Kaku (tl;dr DO NOT BUY) | Shtetl-Optimized (Scott Aaronson's personal blog) | 2023-05 | Canonical debunking of popular quantum hype, illustrating the gap between media-friendly narratives and the rigorous consensus on what current NISQ devices can and cannot do. |
| b6 | Scott Aaronson's View of my View About Quantum Computing | Combinatorics and More (Gil Kalai's blog) | 2026-03 | Captures the definitive Aaronson-vs-Kalai debate in March 2026: Aaronson says Kalai's skeptic path 'has been getting narrower and narrower' as experimental milestones accumulate, offering the most current snapshot of the field's honest internal debate. |
| b7 | Quantum Computing Skepticism, Part 2: My View and Responses to Skeptical Claims | Combinatorics and More (Gil Kalai's blog) | 2025-02 | Kalai's 2025 restatement of his correlated-noise argument against scalable QC, updated with commentary on Microsoft's Majorana 1 claims and featuring counterpoints from Preskill, Aaronson, Harrow and Barak. |
| b8 | Quantum Computers: A Brief Assessment of Progress in the Past Decade | Combinatorics and More (Gil Kalai's blog) | 2025-12 | An ongoing reference post updated through December 2025, tracking where Kalai's skeptical predictions stand against accumulating evidence including Aaronson's revised timeline for Shor's algorithm on fault-tolerant hardware. |
| b9 | Five Perspectives on Quantum Supremacy | Combinatorics and More (Gil Kalai's blog) | 2024-08 | Kalai curates five expert views (Aaronson, Frolov, Emerson, Sondhi and himself) on whether and how quantum supremacy has or can be achieved, providing a multi-voice audit of the field's most contested claim. |
| b10 | Quantum computing: hype vs reality | More Is Different (Substack) | 2025-01 | Independent first-principles analysis from a physics-literate blogger, arguing that quantum volume scaling trends (doubling every ~4 months) are unlikely to sustain Moore's-law-style extrapolation, and that quantum optimization advantage claims remain 'far from settled'. |
| b11 | The YEAR in Quantum Computing – Wrapping up 2024! | Quantum Pirates (Substack) | 2024-12 | Practitioner-level year-in-review covering QEC milestones, Microsoft-Atom Computing 24-logical-qubit announcement, and the industry consensus that MegaQuOp machines - not NISQ - will define the next era. |
| b12 | Quantum 2025 Wrapped – The YEAR in Quantum Computing, December 29th, 2025 | Quantum Pirates (Substack) | 2025-12 | Comprehensive narrative review of 2025's quantum year, identifying the hybrid GPU-QPU stack (NVQLink, IBM-Fugaku) and Microsoft's contested Majorana 1 as the year's two defining story arcs, with early commercial wins from HSBC and D-Wave cited. |
| b13 | Quantum Predictions for 2025 | Quantum Zeitgeist (Substack) | 2024-12 | Independent prediction post calling the death of NISQ and the rise of logical qubits, with candid assessment that Microsoft's topological hardware 'hasn't yielded any working machines' and grades Microsoft a 'B–' relative to Google. |
| b14 | The Quantum Matrix | Quantum Zeitgeist (Substack) | 2026-04 | April 2026 landscape map arguing that the gap between lab demonstrations and commercial deployments is 'closing faster than almost anyone predicted', positioning capital flows and hardware shipping as the key acceleration signal. |
| b15 | Microsoft Quantum Majorana 1 Topological Qubit Approach | Substack (independent author) | 2025-02 | Sharply critical independent Substack analysis calling Microsoft's PR on Majorana 1 'a kind of illegal lobbying' and arguing topological qubits are a 'moonshot at best', citing Jensen Huang's 15–30-year timeline as more credible than Satya Nadella's framing. |
| b16 | 2025 Year-End News Digest: Quantum Error Correction (QEC) | Dr. Bob Sutor – Quantum and AI (Substack) | 2025-12 | Month-by-month 2025 QEC milestone log by IBM's former quantum chief, covering every major lab result across Google, IBM, QuEra, Quantinuum, Nord Quantique, and others - the most thorough single digest of the year's QEC activity. |
| b17 | Quantum – Dr. Bob Sutor Weekly Commentary (March 3 2025) | Dr. Bob Sutor – Quantum and AI (Substack) | 2025-03 | Practitioner commentary covering IonQ leadership change, AWS/Caltech cat-qubit QPU announcement, and the theme of cutting through hype - representative of Sutor's role as an authoritative weekly monitor of industry events. |
| b18 | Quantum Computing 2025: From Verifiable Advantage to Fault-Tolerant Architectures | Medium (nehalmr) | 2026-01 | Technical Medium post documenting 2025's seven key milestones including QuEra's Algorithmic Fault Tolerance (10–100× overhead reduction) and neutral-atom coherence times of 12.6 seconds at 6,100-atom scale - one of the most technically dense independent summaries found. |
| b19 | [Quantum Sundays | 47⟩ - From Qubit Counts to Logical Reality: Mapping the Modern Quantum Computing Landscape](https://medium.com/@adnanmasood/quantum-sundays-47-from-qubit-counts-to-logical-reality-mapping-the-modern-quantum-computing-9edff59a7383) | Medium (Adnan Masood, PhD) | 2026-01 |
| b20 | The Quantum Leap: How 2024–2025 Became the Turning Point for Quantum Computing | Medium (Arun Bansal) | 2025-10 | Accessible synthesis of the 2024–2025 inflection point, covering IBM's modular Starling roadmap, Jensen Huang's CES 2025 market-moving comments, and the investment pattern shift toward hardware over software - useful for the 'current state' research angle. |
| b21 | The Shocking Breakthroughs in Quantum Error Correction of 2025 | Medium (Shailendra Kumar) | 2025-09 | Accessible explainer on 2025's QEC advances including Google's AlphaQubit AI decoder and Microsoft's 4D geometric coding, bridging lab results to a non-specialist technical audience. |
| b22 | Quantum Error Correction: Our 2025 Trends and 2026 Predictions | Riverlane Blog | 2026-01 | Industry practitioner analysis from a leading QEC-specialist firm, documenting that 120 peer-reviewed QEC papers appeared January–October 2025 (up from 36 in 2024), identifying the QuOps metric as the new standard for progress measurement, and predicting mass adoption of qLDPC codes in 2026. |
| b23 | 2024's Quantum Error Correction Highlights (aka the 12 Days of QEChristmas) | Riverlane Blog | 2024-12 | Narrative recap of 2024's twelve most significant QEC events, including Quantinuum's 800× logical vs physical error rate reduction and IBM's bivariate bicycle codes - written by practitioners who build QEC decoders and therefore credibly distinguish hype from substance. |
| b24 | Quantum Error Correction Update 2024 | O'Reilly Radar | 2024 | Authoritative technical-practitioner survey of the 2024 QEC landscape, noting NISQ's commercial failure, the 'death' of hybrid NISQ-classical approaches, and the emergence of hardware-assisted logical qubits from Alice & Bob and Nord Quantique as the field's next phase. |
| b25 | Microsoft's Topological Qubit Claim Faces Quantum Community Scrutiny | The Quantum Insider | 2025-02 | Structured community-reaction piece aggregating expert responses to Microsoft's Majorana 1 announcement, including Aaronson's FAQ, Hensinger's critique of the press release vs. the Nature paper, and the key fact that the Nature editorial team itself found 'no evidence for Majorana zero modes'. |