2025/10/09 by Diyi Liu, Shuchen Zhu, Liu, Diyi +7
Computer Science · Materials Science · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Machine Learning in Materials Science #Numerical Analysis (math.NA) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2510.08644
openalex publication_date 2025/10/09 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
Efficient block encoding of many-body Hamiltonians is a central requirement for quantum algorithms in scientific computing, particularly in the early fault-tolerant era. In this work, we introduce new explicit constructions for block encoding second-quantized Hamiltonians that substantially reduce Clifford+T gate complexity and ancilla overhead. By utilizing a data lookup strategy based on the SWAP architecture for the sparsity oracle OC, and a direct sampling method for the amplitude oracle OA with SELECT-SWAP architecture, we achieve a T count that scales as \mathcalO(√(L)) with respect to the number of interaction terms L in general second-quantized Hamiltonians. We also achieve an improved constant factor in the Clifford gate count of our oracle. Furthermore, we design a block encoding that directly targets the η-particle subspace, thereby reducing the subnormalization factor from O(L) to O(√(L)), and improving fault-tolerant efficiency when simulating systems with fixed particle numbers. Building on the block encoding framework developed for general many-body Hamiltonians, we extend our approach to electronic Hamiltonians whose coefficient tensors exhibit translation invariance or possess decaying structures. Our results provide a practical path toward early fault-tolerant quantum simulation of many-body systems, substantially lowering resource overheads compared to previous methods.