Compiling the 2D Fermi-Hubbard ground-state energy estimation algorithm for active volume quantum architectures

Authors:Harriet Apel, Athena Caesura, Carys Harvey, Sam Heavey, Angus Kan, Jessica Lemieux, Ryan Levy, Sam Pallister, Joseph Peetz, William Pol, Sukin Sim, William A. Simon, Mark Steudtner, Gideon Uchehara

Abstract:As quantum computing enters the early fault-tolerant era, circuit compilation choices will increasingly depend on details of the underlying architecture rather than solely optimizing for generic proxies such as non-Clifford count. We present an active-volume-aware compilation of the ground-state energy estimation algorithm for the two-dimensional Fermi-Hubbard model using quantum phase estimation and Trotterized time evolution. The proposed compilation reduces the active volume across $L\times L$ square lattices with $L=4$ to $20$, achieving up to a $3.9\times$ reduction over prior work optimized for non-Clifford cost. As a by-product of these compilation improvements, the resulting circuits also achieve state-of-the-art Toffoli counts, with a ~$2\times$ reduction for the $L=20$ case. Lastly, the active volume architecture and recent execution scheduling advances provide a means of translating these reduction trends into runtime. This demonstrates the increasing importance of architecture-aware compilation for practical early fault-tolerant quantum computing.

arXiv:2609.05316 [quant-ph]

(or arXiv:2609.05316v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.05316 arXiv-issued DOI via DataCite (pending registration)