标题： 构建有效哈密顿量的量子增强密度矩阵下折叠要求 显示英文标题

标题： Requirements for building effective Hamiltonians using quantum-enhanced density matrix downfolding

摘要： 密度矩阵下折叠（DMD）是一种从量子多体哈密顿量回归低能有效哈密顿量的技术。 经典实现的DMD精度的一个限制因素是在近似的低能子空间上采样量子多体系统的可观测量时存在的难以量化系统误差。 我们提出了一种混合量子-经典协议来克服这一局限性，依赖于量子计算机高效准备和以系统可改进的精度从定义明确的低能子空间中采样的潜在能力。 我们提出了在这种情况下可行的三个要求，包括一种可压缩性概念，用于量化可能使量子DMD高效的哈密顿量及其低能子空间的特征。 假设这些要求得到满足，我们分析了协议的设计选择，并提供了在掺杂二维费米-哈伯德模型和铜氧化物超导体的从头算模型中实现量子增强DMD的资源估算。 显示英文摘要

摘要： Density matrix downfolding (DMD) is a technique for regressing low-energy effective Hamiltonians from quantum many-body Hamiltonians. One limiting factor in the accuracy of classical implementations of DMD is the presence of difficult-to-quantify systematic errors attendant to sampling the observables of quantum many-body systems on an approximate low-energy subspace. We propose a hybrid quantum-classical protocol for circumventing this limitation, relying on the prospective ability of quantum computers to efficiently prepare and sample from states in well-defined low-energy subspaces with systematically improvable accuracy. We introduce three requirements for when this is possible, including a notion of compressibility that quantifies features of Hamiltonians and low-energy subspaces thereof for which quantum DMD might be efficient. Assuming that these requirements are met, we analyze design choices for our protocol and provide resource estimates for implementing quantum-enhanced DMD on both the doped 2-D Fermi-Hubbard model and an ab initio model of a cuprate superconductor.