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Twenty authors tied quantum chemistry and topological data analysis to Helios, Sol in 2027, Apollo in 2029, and Lumos in the 2030s. They called the roadmap an assumption-driven envelope, not a deterministic forecast.
The circuit needs fewer logical qubits than any estimate its authors compared but, in its latest version, 24 to 27 times the Toffoli gates of two earlier low-qubit designs. The authors did not estimate physical qubits or running time.
McKinsey built the range from expert interviews and 2035 baselines for seven finance segments. It footnoted the use cases' impact levers as the impact of quantum computing and AI. McKinsey also called its value estimates approximate.
The authors called the properties predictability, typicality, robustness, verifiability, and usefulness. They wrote that Shor's algorithm satisfies their criteria and proved that some advantages cannot be predicted with classical resources alone.
André Schrottenloher released circuits and code for the step repeated 28 times in an attack on Bitcoin's signature curve. Craig Gidney, a Google Quantum AI co-author of the March study, wrote that such work should be published openly.
Researchers have fit Shor's algorithm into 9,739 neutral-atom physical qubits, with elliptic-curve runs that lengthen from 10 days to about 1,000 as the count falls. The authors assumed error rates and clock speeds no machine has shown together.
In PNAS, Oxford's Tim Palmer proposed that quantum computers lose their advantage above about 1,000 perfect qubits. He wrote that his theory and standard quantum mechanics agree on small systems. No experiment has yet tested where they differ.
AQTI said in a release that "research extrapolations suggest" the JVG method "will require less than 5,000 qubits" to break RSA. The preprint gives no such qubit count, and its authors called their runtime projections indicative scaling trends.
