Block encoding with low gate count for second-quantized Hamiltonians

• URL: http://arxiv.org/abs/2510.08644v1
• Date: Thu, 09 Oct 2025 03:37:15 GMT
• Title: Block encoding with low gate count for second-quantized Hamiltonians
• Authors: Diyi Liu, Shuchen Zhu, Guang Hao Low, Lin Lin, Chao Yang,
• Abstract summary: Efficient block encoding of many-body Hamiltonians is a central requirement for quantum algorithms in scientific computing.<n>We introduce new explicit constructions for block encoding second-quantized Hamiltonians that substantially reduce Clifford+T gate complexity and ancilla overhead.
• Score: 5.455703400065318
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $O_C$, and a direct sampling method for the amplitude oracle $O_A$ with SELECT-SWAP architecture, we achieve a T count that scales as $\mathcal{\tilde{O}}(\sqrt{L})$ 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 $\eta$-particle subspace, thereby reducing the subnormalization factor from $\mathcal{O}(L)$ to $\mathcal{O}(\sqrt{L})$, 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.

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