Theory Seminar: Arkopal Dutt, "Learning stabilizer structure of quantum states."
- Sponsor
- Research Area of Theory and Algorithms
- Speaker
- Arkopal Dutt
- Contact
- Makrand Sinha
- msinha@illinois.edu
- Originating Calendar
- Siebel School Speakers Calendar
Abstract: We consider the task of learning a structured stabilizer decomposition of an arbitrary n-qubit quantum state. Our goal is to approximate any state by a compact superposition of stabilizer states and a residual state having low stabilizer fidelity. We first show the existence of such decompositions using the recently established inverse theorem for the Gowers-3 norm of quantum states [AD,STOC'25]. We then give a quasipolynomial-time protocol for learning such structured stabilizer decompositions of quantum states, which can be improved to polynomial-time assuming the algorithmic polynomial Frieman-Rusza conjecture in the high doubling regime (whose combinatorial version was recently resolved in a breakthrough [GGMT,Annals of Math.'25]). This gives a quantum analogue of the well-known classical quadratic Goldreich-Levin theorem [TW14]. As our main application, we show the above protocols can be utilized for learning quantum states promised to have low stabilizer extent or rank. As far as we know, learning arbitrary states with even stabilizer-rank 2 was previously unknown.
Based on joint work (arxiv2510.05890, STOC'26) with Srinivasan A.
Bio: Arkopal is a researcher at IBM Research working on quantum learning theory and quantum algorithms. He obtained his PhD from MIT in 2024 where he was advised by Isaac Chuang.