发表机构
California Institute of Technology; Institute for Quantum Information and Matter; Marcus Center for Theoretical Chemistry（加州理工学院; 量子信息与物质研究所; 马库斯理论化学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出利用BSE框架的准粒子量子模拟方法，通过块编码和优化，显著降低Toffoli门和量子比特资源，实现高效的多激子态模拟。
AI 中文摘要
即使在完全容错量子计算机的未来时代，对现实尺寸的材料模型的完整电子哈密顿量进行第一性原理量子模拟似乎也令人望而生畏。相比之下，材料的激发态的经典模拟依赖于启发式准粒子框架，例如GW近似和Bethe-Salpeter方程，其中仅显式考虑少数准粒子。在此，我们详细描述了在BSE框架内对多激子态进行准粒子量子模拟的方法。我们开发了一种显式的第一量子化、基于轨道的块编码，用于多激子BSE哈密顿量的量子化，并通过积分分解和晶体对称性降低了其成本。对于尺寸为$N$的材料模型和固定数量的准粒子，所得算法需要$\widetilde{O}(N)$个Toffoli门和$O(\log N)$个逻辑量子比特，或者，利用时空权衡，需要$\widetilde{O}(\sqrt{N})$个Toffoli门和$\widetilde{O}(\sqrt{N})$个逻辑量子比特，与材料模拟中已探索的标准全哈密顿量模拟技术相比，Toffoli门数量最多可减少六次方，或量子比特数量最多可指数级减少。针对一系列具有现实物理尺寸（$O(10^3)$个原子）的半导体模型的三激子本征值估计这一经典难题的资源估算表明，我们的Toffoli优化实现相对于全哈密顿量模拟估算将Toffoli门数量减少了$10^6-10^7$倍，而量子比特优化实现仅需几百个逻辑量子比特。更广泛地说，这些结果表明，经典启发式框架在未来的容错量子算法设计中将是必不可少的。
英文摘要
The first-principles quantum simulation of the full electronic Hamiltonian of a material model of realistic size appears daunting even in a future era of fully fault-tolerant quantum computers. In contrast, classical simulations of material excited states rely on heuristic quasiparticle frameworks, such as the GW approximation and Bethe-Salpeter equation, where only a few quasiparticles are explicitly considered. Here we give a detailed description of quasiparticle quantum simulation for multi-excitonic states within the BSE. We develop an explicit first-quantized, orbital-based block encoding of the multi-exciton BSE Hamiltonian for qubitization, and reduce its cost using integral factorization and crystal symmetries. For a materials model of size $N$, and a fixed number of quasiparticles, the resulting algorithms require $\widetilde{O}(N)$ Toffoli gates and $O(\log N)$ logical qubits, or, using space-time tradeoffs, $\widetilde{O}(\sqrt{N})$ Toffoli gates and $\widetilde{O}(\sqrt{N})$ logical qubits, achieving up to a sixth power reduction in Toffoli count, or up to exponential reduction in qubit count, versus standard full Hamiltonian simulation techniques that have been explored in materials simulation. Resource estimates for the classically challenging problem of triexcitonic eigenvalue estimation across a range of semiconductor models of a realistic physical size of $O(10^3)$ atoms, show that our Toffoli-optimized implementation reduces the Toffoli count by $10^6-10^7$ relative to full Hamiltonian simulation estimates, while a qubit-optimized implementation requires only a few hundred logical qubits. More broadly, these results show that classical heuristic frameworks will be essential in the design of future fault-tolerant quantum algorithms for materials.
Comments31 pages, 9 figures
