2026 Theory Canada 18

Eigenstate thermalization hypothesis as a quantum resource for linear algebra problems

20 Jun 2026, 14:40

20m

A-4502.1 (Université de Montréal (MIL campus))

Contributed Talk Quantum Information Quantum Information

Speaker

Thomas Baker (Department of Physics & Astronomy and also of Chemistry, University of Victoria)

Description

The eigenstate thermalization hypothesis formally connects time evolution in a quantum system with the micro-canonical ensemble system average in statistical physics. The formal reliance on random matrix theory is discussed, justifying the main statement, and then extended to the case of quantum circuits where the micro-canonical ensemble emerges explicitly without invoking random matrices. Forcing the state to be sufficiently kicked provides a resource to the quantum computer that equally weights all eigenstates. This resource can then be used to solve a wide variety of linear algebra problems in poly-logarithmic time.

This research was undertaken, in part, thanks to funding from the Canada Research Chairs Program (CRC-2021-00257). This work has been supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grants RGPIN-2023-05510 and DGECR-2023-00026.