Alexander Zlokapa - Average-case quantum complexity from glassiness - IPAM at UCLA
Recorded 13 January 2026. Alexander Zlokapa of the Massachusetts Institute of Technology presents "Average-case quantum complexity from glassiness" at IPAM's New Frontiers in Quantum Algorithms for Open Quantum Systems Workshop.Abstract: In the classical setting, glassiness characterizes many natural problems (e.g., random k-SAT) and underlies average-case hardness by obstructing a family of "stable" classical algorithms (e.g., constant-time Langevin dynamics). In this talk, we discuss analogous quantum results. Our techniques, based on quantum optimal transport, differ significantly from classical probabilistic approaches due to the sign problem in the absence of a known eigenbasis. We show that quantum glassiness obstructs stable quantum algorithms, including constant-time Lindbladian dynamics (even when starting from the maximally mixed state). Using the replica trick, we also find that random 3-local Pauli Hamiltonians are quantumly hard and give evidence that random k-local Hamiltonians are quantumly easy for sufficiently large constant k. This differs from the analogous classical (Ising, glassy phase for all k) and fermionic (SYK, never glassy for any k) k-local ensembles. Based on arXiv:2510.08497.
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/new-frontiers-in-quantum-algorithms-for-open-quantum-systems/ Receive SMS online on sms24.me
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