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

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Synthesised 2026-04-19

Narrative

The period from 2023 to April 2026 was defined by a competitive race among Google, IBM, and Microsoft—the three dominant frontier lab players—to achieve credible fault-tolerant quantum computing milestones. Google Quantum AI's 105-qubit Willow chip (December 2024, Nature) crossed the 'below-threshold' error correction barrier for the first time in history, meaning logical error rates fell as more physical qubits were added, and it further demonstrated what the lab called 'verifiable quantum advantage' in October 2025 with the Quantum Echoes algorithm running 13,000× faster than the Frontier supercomputer—though critics noted this remains a specialized benchmark rather than a practically useful computation. Google DeepMind's parallel contribution, AlphaQubit (November 2024, Nature), used a transformer-based neural network decoder that reduced errors by 6–30% over prior methods on the Sycamore and Willow processors, though it was still too slow for real-time superconducting decoding as of its publication. IBM's strategy in the same period pivoted decisively from surface codes to qLDPC (bivariate bicycle) codes, captured in a landmark March 2024 Nature paper by Bravyi, Cross, Gambetta et al., which showed the 'gross' code encodes 12 logical qubits in 288 physical qubits—10× more efficient than surface codes. IBM then published a full modular fault-tolerant architecture roadmap in June 2025, unveiled the Quantum Loon and Nighthawk processors at QDC November 2025, and set a 2029 target for the Quantum Starling system with 200 logical qubits executing 100 million operations. Microsoft's February 2025 Majorana 1 announcement—eight topological qubits on a chip designed for one million—generated the period's most contested moment: Nature's editorial team clarified the accompanying paper did not prove topological protection, and physicists at Cornell, NYU, and Caltech publicly questioned the data at the APS March Meeting 2025, citing the company's 2018 retraction as grounds for caution. Across all hardware modalities, neutral atoms emerged as an unexpectedly strong dark-horse platform, with Nature papers in 2025 reporting 3,000-qubit continuous operation, 6,100-qubit tweezer arrays, and a full fault-tolerant universal architecture demonstrated at Harvard/MIT, while photonic computing advanced through PsiQuantum's silicon-photonics Nature paper and the Aurora modular prototype. McKinsey's 2025 Quantum Technology Monitor synthesised the commercial picture, projecting $72 billion in quantum computing revenue by 2035 and noting start-up investment 50% higher in 2024 than 2023.

Sources

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.