Analysing adiabatic computation through the lens of closest approximate symmetries

Analysing adiabatic computation through the lens of closest approximate symmetries

Seminar author:Ana Palacios

Event date and time:03/12/2026 02:30:pm

Event location:GIQ Seminar Room

Event contact:

In Adiabatic Quantum Computation (AQC), we compute by (adiabatically) interpolating between an initial Hamiltonian A, in whose ground state we initialise, and a final Hamiltonian B, whose ground state we want to prepare. The hardness of this process is then, loosely speaking, determined by the structural differences between A and B. In the adiabatic theorem, these “structural differences” materialise through transition matrix elements between instantaneous eigenstates, carrying information about shared symmetries, and instantaneous energy gaps, which carry the aftermath of the complex interplay between the eigenvalues and eigenspaces of A and B. This work puts forth a new framework to unravel this interplay based on the idea of Closest Approximate Symmetries (CAS) by recursively projecting onto reduced representations of A and B, such that the error between this (largely simplified) representation of the computation and the original one is minimised. This method provides an analytical estimate of the energy landscape that can be used to make statements about the hardness of the process, both qualitative (e.g., the gap will remain large), as well as quantitative (e.g., estimates on minimum gap locations, bounds on the maximum size of the minimum gap along the computation). The CAS framework has also revealed a new heuristic for classical optimisation problems when applied to the standard quantum annealing setting, and we believe it could have further applications in the design of analog algorithms or the study of phase diagrams.