Abstracts
Poster Abstracts | Talk Abstracts
Spectral Analysis of Product Formulas in Quantum Simulation
Presenting Author: Changhao Yi, University of New Mexico CQuIC
Contributing Author(s): Elizabeth Crosson
We consider Hamiltonian simulation using the first order Lie-Trotter product formula under the assumption that the initial state has a high overlap with an energy eigenstate, or a collection of eigenstates in a narrow energy band. This assumption is motivated by quantum phase estimation (QPE) and digital adiabatic simulation (DAS). Treating the effective Hamiltonian that generates the Trotterized time evolution using rigorous perturbative methods, we show that the Trotter step size needed to estimate an energy eigenvalue within precision $\epsilon$ using QPE can be improved in scaling from $\epsilon$ to $\epsilon^{1/2}$ for a large class of systems. For DAS we improve the asymptotic scaling of the Trotter error with the total number of gates $M$ from $\mathcal{O}(M^{-1})$ to $\mathcal{O}(M^{-2})$, and for any fixed circuit depth we calculate an approximately optimal step size that balances the error contributions from Trotterization and the adiabatic approximation. These results partially generalize to diabatic processes, which remain in a narrow energy band separated from the rest of the spectrum by a gap, thereby contributing to the explanation of the observed similarities between the quantum approximate optimization algorithm and diabatic quantum annealing at small system sizes.
Read this article online: https://arxiv.org/abs/2102.12655, https://arxiv.org/abs/2107.06404
- Home
- Program
- Guide for Gather.Town
- Instructions for Presenters
- Submit Your Abstract
- Code of Conduct
- Subscribe to the SQuInT Mailing List
- Past SQuInT Meetings
SQuInT Chief Organizer
Akimasa Miyake, Associate Professor
amiyake@unm.edu
SQuInT Co-Organizer
Brian Smith, Associate Professor
bjsmith@uoregon.edu
SQuInT Local Organizers
Philip Blocher, Postdoc
Pablo Poggi, Research Assistant Professor
Tzula Propp, Postdoc
Jun Takahashi, Postdoc
Cunlu Zhou, Postdoc
SQuInT Founder
Ivan Deutsch, Regents' Professor, CQuIC Director
ideutsch@unm.edu