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Wikipedia details Von Neumann expanded Koopman’s 1931 Hilbert-Space workquantum-computing

Wikipedia details Von Neumann expanded Koopman’s 1931 Hilbert-Space work

In 1931, Bernard Koopman published a paper in Proceedings of the National Academy of Sciences laying out a novel method for identifying functions representing observables on a classical system’s phase space as vectors in a Hilbert space; however, the full story of this now-ubiquitous technique, and its connection to quantum theory, reveals a complex history of attribution. John von Neumann followed up in 1932 with further development published in German Annals of Mathematics, papers that were never translated into English. As Jacob Barandes details in a new analysis, the method of “classical” wave functions often linked to Koopman and von Neumann was, in fact, independently developed starting with Mario Schönberg, with later key contributions from Angelo Loinger, Giacomo Della Riccia, Norbert Wiener, and E. C. George Sudarshan. Indeed, as Jordan and Sudarshan noted in 1961, the resulting Hilbert space “corresponds not to the space of state vectors in quantum mechanics but to the Hilbert space of operators on the state vectors.” A mathematical framework initially developed to bridge classical and quantum mechanics has, for decades, been subject to significant misattribution. While often referred to as the “Koopman–von Neumann (KvN) formulation,” the widely accepted understanding of this approach obscures the contributions of several key researchers who built upon the original work. Barandes details in recent research that Koopman’s initial formulation did not involve classical wave functions linked to probability distributions via the Born rule; rather, his Hilbert spaces “consisted of functions representing classical observables.” This erroneous association, exemplified by a 2021 conference and a 2022 Journal of Physics A special issue both titled “Koopman Methods in Classical and Classical-Quantum Mechanics,” which referenced “Koopman–von Neumann wave functions,” persists even in contemporary literature, including a 2025 Wikipedia entry stating that the approach. C

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WarpSpeed Says its AI cuts quantum encryption cracking cost sharplyquantum-computing

WarpSpeed Says its AI cuts quantum encryption cracking cost sharply

WarpSpeed’s artificial intelligence has designed a quantum circuit that cracks a standard cryptographic challenge with significantly improved efficiency, the company says. The system achieved a 2.5 times more efficient circuit than Google’s in cracking the ECDSA challenge, a benchmark used to assess the security of digital signatures underpinning cryptocurrencies like Bitcoin and Ethereum, according to WarpSpeed. This improvement exceeds the median improvement on the benchmark over the last month by about two and a half orders of magnitude; according to WarpSpeed, its circuit consists of only 993,181 Toffoli gates and 1,205 qubits, certified by a zero-knowledge proof. Beyond circuit design, the company’s agents also found gaps combining cryptography, performance engineering, and software security within the benchmark’s verification processes, the firm reports. WarpSpeed AI Achieves 2.5x Efficiency in ECDSA Cracking WarpSpeed’s artificial intelligence delivered a quantum circuit that reduces the computational cost of cracking the Elliptic Curve Digital Signature Algorithm (ECDSA) by a substantial margin, achieving a 2.5 times more efficient circuit than Google Quantum AI’s previously published designs, WarpSpeed claims. This leap in performance was demonstrated on the publicly available ecdsa.fail benchmark, which Eigen Labs created from the Google paper. The system achieved these results through self-improvement, by the company’s account. The core of the challenge revolves around efficiently calculating point addition on elliptic curves, a fundamental operation within the ECDSA cryptographic scheme. Shor’s algorithm, the quantum method used to break this encryption, relies heavily on the cost of this single operation; therefore, optimizing point addition directly impacts the overall attack complexity. WarpSpeed’s circuit achieves a spacetime score of 1.20 × 10⁹, utilizing 993,181 Toffoli gates and 1,205 qubits, a figure certified by a zero-knowledge proof released a

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Superconducting device develops continuous-variable quantum computingquantum-computing

Superconducting device develops continuous-variable quantum computing

Researchers at Universidade Federal de São Carlos (UFSCar) in Brazil have developed a building block for quantum computing utilizing continuous-variable computation. Published August 13, 2026, in Quantum Science and Technology with DOI 10.1088/2058-9565/ae9187, the work details a superconducting device exploring an approach that differs from more common qubit-based systems. This continuous-variable method exploits the infinite-dimensional Hilbert space of bosonic modes, potentially offering a distinct path toward scalable and universal quantum computation. The authors report that the system achieves high fidelities within current parameter ranges. This two-layer system utilizes a DC-SQUID as the foundational bosonic mode, circumventing limitations found in existing superconducting platforms and offering a different approach to scalability. The work demonstrates high fidelities across all gates within achievable experimental parameters, a crucial step toward practical continuous-variable quantum computers. The architecture integrates a fluxonium qubit to mediate nonlinear interactions essential for quantum processing, alongside two ancillary qubits that facilitate both Gaussian and multi-mode operations. By precisely tuning applied fluxes and frequencies, the team achieved control over rotation, displacement, squeezing, Kerr interactions, and beam splitting, the five gates comprising a universal continuous-variable set. This level of control is significant because it allows for the implementation of any quantum algorithm within the continuous-variable framework, which differs from the more common qubit-based approach. The researchers report that the modular design of the system is intended to allow for scaling to more complex circuits. This development addresses a key challenge in superconducting quantum computing; while superconducting qubits have shown promise, realizing universal continuous-variable computation has remained elusive. The team’s simulation indicates

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