ICM 2026 Invited Section Lecture - Urmila Mahadev

Value of the Information & Strength of the Argument

The talk delivers high-value information by clearly explaining a subtle and advanced topic in quantum computing. The argumentation is logically sound: it builds from basic quantum mechanics to the cryptographic framework, then to the specific LWE-based construction. Mahadev carefully motivates each step, highlighting the inherent difficulties and how they are overcome. She effectively uses analogies, such as the impossibility of efficiently describing quantum states classically, and provides a concrete example (randomness generation) to illustrate the challenges. The reasoning is rigorous and accessible to a mathematically mature audience, and the transitions between concepts are smooth. The central claim—that LWE’s structure enables classical control—is convincingly supported by the outlined protocol, though detailed proofs are omitted in line with the lecture format.

Scientific Rigor, Source Quality, Title Accuracy

The scientific content is rigorous and aligns with current research in quantum cryptography. Mahadev accurately references foundational works, including Shor’s factoring algorithm and Gentry’s homomorphic encryption, and correctly situates LWE as a leading post-quantum assumption. The exposition is consistent with peer-reviewed literature. The title accurately reflects the talk’s scope and content. No external sources are provided in the description, but the talk itself references key results and concepts. The reasoning is carefully constructed with appropriate caveats (e.g., the unproven belief that quantum computers exceed classical ones). No attempt is made to overstate results, and the contribution is presented as a proof-of-concept rather than a practical implementation.

The title perfectly matches the content, which focuses on using the learning with errors problem to classically control and verify a quantum system.

9/10

The talk is presented by Urmila Mahadev, a leading researcher in quantum computation and cryptography. The content is mathematically rigorous, well-structured, and accurately reflects established results in the field. Technical details are explained clearly without oversimplification, and the exposition adheres to current scientific consensus.

Markers derived by PSI from the transcript: the creator did not define chapters.

• 02:00Introduction to quantum information and qubits, explaining superpositions and measurement collapse.
• 07:00Definition of classical verification of quantum computations and the adversarial model.
• 12:00Idea of using post-quantum cryptography to give the classical verifier leverage over the prover.
• 18:00Statement of the learning with errors (LWE) problem and its properties.
• 24:00Construction of encrypted quantum states using LWE and the verification protocol.
• 32:00Explanation of how LWE distinguishes quantum and classical machines, concluding remarks.

• Shor's algorithm — Mentioned as a famous example of quantum advantage in factoring.
• Homomorphic encryption — Cited as a major achievement built from LWE's structure, solved by Craig Gentry in 2009.
• Learning with errors (LWE) — Central cryptographic assumption discussed throughout the talk.