Southwest Quantum Information and Technology

Squeezed state ansatz for quantum Sherrington-Kirkpatrick model and its applications to quantum annealing

Presenting Author: Sergey Knysh, NASA Ames

A question of fundamental importance in the physics of quantum annealing is its scalability. Recent work predicts a crossover from polynomial to exponential complexity for quantum annealing of spin glasses and relates the problem size at which this occurs to the "density" of spin glass bottlenecks [1]. An exact solution has been obtained for a toy problem, but rigorous analysis has remained elusive for realistic spin glass models where naive mean field fails. The present work takes a step in that direction by investigating thermodynamics of quantum Sherrington-Kirkpatrick model without resorting to replicas. The approach uses hard-core boson representation of a spin-1/2 model, with "modes" corresponding to delocalized eigenvectors of the interaction matrix. Hard-core nature of bosons is taken into account by appropriate renormalization factors. In this formulation, the ground state of paramagnetic phase is approximated by applying mode-dependent amount of squeezing/anti-squeezing to a vacuum, and the low-energy excitations correspond to Bogolyubov quasiparticles. Spin-glass phase is characterized by macroscopic occupation of a finite fraction of modes. Theoretical predictions are compared with known numerical results. [1] S. Knysh, "Zero-temperature quantum annealing bottlenecks in the spin-glass phase", Nature Communications 7, 12370 (2016).

(Session 9c : Friday from 5:15pm - 5:45pm)