Shot-noise reduction for lattice Hamiltonians accepted to QCTiP 2025
By: Timo Eckstein, Refik Mansuroglu, Stefan Wolf, Ludwig Nützel, Stephan Tasler, Martin Kliesch, and Michael J. Hartmann.
Read the preprint here: https://arxiv.org/abs/2410.21251
Reducing the sampling cost is a major challenge both in the near-term as well as fault-tolerant era of quantum computing. We shift away from worst case (=Pauli weights) and average case (2-norm type) sampling strategies and study state-tailored close-to-best-case ones, where Var(H) still can be close to 0.
Typical applications of such a measurement strategy are energy estimation and state preparation algorithms, where one aims to precisely estimate with few measurements low-energy properties. We develop a measurement scheme for quantum lattice systems to obtain particularly efficient readout circuits by splitting the Hamiltonian into geometrically local patches instead of Pauli groups. Noticeably, we analytically show a guaranteed sampling complexity improvement compared to standard Pauli partitioning. We numerically check multiple two-dimensional lattice models incl. the transverse field XY- and Ising model as well as the Fermi Hubbard model, and find typical reductions in the required number of measurements by several orders of magnitude for the same sampling error.
Check out the other accepted talks here: https://qctip2025.com/program/
We acknowledge support from FAU Erlangen-Nürnberg, Max Planck Institute for the Science of Light, Universität Wien | University of Vienna, Hamburg University of Technology, Erlangen National High Performance Computing Center (NHR@FAU), Deutsche Forschungsgemeinschaft (DFG) – German Research Foundation (QuCoLiMa), Bundesministerium für Bildung und Forschung (EQUAHUMO), IMPRS Physics of Light, Fujitsu Germany GmbH
and Bavarian State Ministry of Science and the Arts via Munich Quantum Valley, Elite Network of Bavaria, Hightech Agenda Bavaria