Pseudorandomness against AM circuits and new oracle separations

Pseudorandomness against AM circuits and new oracle separations

Title history
  • Pseudorandomness against AM circuits and new oracle separations — observed on 20261101-0409 UTC (YouTube)
🎙 Andrew Huang 👥 78K 📅 October 30, 2026 ⏱ 42 min 👁 826 📄 original study 🧭 2026-11-01
Available in: English (current) Français

Keywords

BQPIPAM circuitspseudorandomnessforrelation

Summary

The talk addresses the question of whether a quantum prover (in BQP) can efficiently convince a classical verifier of the correctness of a quantum computation. After reviewing known results, including Mahadev’s protocol (with cryptographic assumptions) and multi-prover approaches (Reichardt-Unger-Vazirani with entanglement), the speaker presents new oracle separations. The main result constructs an oracle relative to which BQP is not contained in IP, and consequently IP and MIP separate. The proof leverages a pseudorandomness result against average-max (AM) circuits, which are the circuit analog of interactive proof systems. The pseudorandom distribution is the forrelation distribution introduced by Aaronson, which is easy for quantum algorithms but hard for AM circuits. The technical core involves showing that AM circuits with polylog depth and queries cannot distinguish forrelation from uniform. The proof uses structural properties: such circuits are convex, and via a smoothing argument with Gaussian noise, the pseudorandomness bound is obtained. The talk also discusses implications and open questions, such as the role of convexity and comparisons with AC0 circuits and tropical circuits.

170 words

Critical Evaluation

Value of the Information & Strength of the Argument

The value of the information is substantial for the theoretical computer science community, as it provides new oracle separations that advance the understanding of quantum versus classical interactive proof systems. The argumentation is solid: the speaker carefully derives the equivalence between IP protocols and average-max circuits, then proves a pseudorandomness theorem for those circuits. The proof outline is rigorous, with key technical steps (smoothing, covariance bounds) clearly explained. The speaker also addresses clarifying questions, which reinforces the depth of the argument. The novel contribution is significant, as it had not been known before that such a separation holds, and the pseudorandomness result against AM circuits is a standalone contribution.

Scientific Rigor, Source Quality, Title Accuracy

The talk demonstrates high scientific rigor, referencing prior work (Mahadev, McKague, Reichardt et al., Aaronson, etc.) and building on the IP=PSPACE theorem. The quality of sources is high, as all cited works are well-known in the field. The title accurately reflects the content: the talk indeed focuses on pseudorandomness against AM circuits and proves new oracle separations. The description link to the Simons Institute provides access to the talk page, which is a reliable institutional source. No discrepancies were found between the title and the content.

210 words

Quality & Reliability

8/10

The talk presents new research results in computational complexity theory, delivered at the Simons Institute by a researcher from UC Berkeley. The content is rigorous, built on established theorems (IP=PSPACE, etc.) and recent works. The speaker engages with audience questions and provides proof sketches, indicating high technical accuracy.

Key Moments

Cited Sources

Contribution & Novelties

The main novelty is the first oracle separation between BQP and IP, and a pseudorandomness result against average-max circuits. This breaks the relativizing barrier for efficient interactive proofs for BQP. The proof introduces a technique of approximating AM circuits with smooth functions and leveraging convexity, which is a new idea in this context.

Pour aller plus loin :

103 words

Radar Profile

The radar profile shows very high technical level and quality of information, with a slightly lower but still strong score in quantity and reliability. This reflects a highly specialized, deep presentation that is reliable but dense, requiring expert background.

Reliability 8/10