发表机构
Google Quantum AI（谷歌量子人工智能）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出多变量量子信号处理框架，利用多端口IIR滤波器解析结构设计量子查询算法，改进多预言机问题的查询复杂度，并应用于哈密顿模拟、线性系统、基态制备等任务。
AI 中文摘要
我们发展了多变量量子信号处理，用于设计多个非交换非正规块编码矩阵的矩阵值变换。我们的框架为量子换能器配备了多端口无限脉冲响应（IIR）滤波器的解析结构，并建立了设计量子查询算法的传递函数方法论。可高效计算的解析界在预言机承诺中一致成立，产生具有对数误差依赖和接近单位成功概率的高效量子电路，与单变量QSP/QSVT的逼近理论保证相平行。我们提供了可实现传递函数的完整刻画以及解析IIR组件的原理库。我们的模块化设计大幅改进或解决了开放多预言机问题的每个预言机查询复杂度：（1）在$H=\sum_j H_j$下，以加权拟范数成本$\approx t\langle\vec\lambda,\vec C\rangle_{1/2}+\mathcal{O}(\\|\vec C\\|_1\log(1/\epsilon))$进行哈密顿模拟，其中$\vec\lambda$为块编码归一化，$\vec C$为成本；（2）以最优时间-范数$\Theta(\sqrt{d}\\|H\\|_{\rm 1\to2}t)$和加性误差依赖进行稀疏模拟；（3）在最小矩阵假设下求解线性系统和（4）微分方程，具有最优加权态制备和多术语成本；（5）基态制备和能量估计；（6）广义特征值问题。我们将这些应用于精确模拟下折叠哈密顿量，主导成本$t\langle\vec\lambda_{\rm eff},\vec C_{\rm eff}\rangle_{1/2}$进一步被粗粒化哈密顿量的分数动态相关能量贡献降低，并展示了通过Kron约简进行多尺度图分类的类似经典数据输入减少结果。我们还展示了流式量子数据的各向异性卡尔曼滤波的在线推广。
英文摘要
We develop Multivariate Quantum Signal Processing for designing matrix-valued transformations of multiple noncommuting nonnormal block-encoded matrices. Our framework equips quantum transducers with the analytic structure of multiport Infinite-Impulse-Response (IIR) filters and establishes a transfer-function methodology for designing quantum query algorithms. Efficiently computable analytic bounds that hold uniformly across the oracle promise yield efficient quantum circuits with logarithmic error dependence and near-unity success probability, paralleling the approximation-theoretic guarantees of univariate QSP/QSVT. We provide a complete characterization of achievable transfer functions and a principled library of analytic IIR components. Our modular designs greatly improve or resolve the per-oracle query complexity of open multi-oracle problems: (1) Hamiltonian simulation under $H=\sum_j H_j$ with weighted quasinorm cost $\approx t\langle\vecλ,\vec C\rangle_{1/2}+\mathcal{O}(\|\vec C\|_1\log(1/ε))$ for block-encoding normalizations $\vecλ$ and costs $\vec C$; (2) sparse simulation with optimal time--norm $Θ(\sqrt{d}\|H\|_{\rm 1\to2}t)$ and additive error dependence; (3) solving linear systems and (4) differential equations under minimal matrix assumptions with optimal weighted state-preparation and multi-term cost; (5) ground-state preparation and energy estimation; (6) generalized eigenvalue problems. We apply these to exactly simulate downfolded Hamiltonians with leading cost $t\langle\vecλ_{\rm eff},\vec C_{\rm eff}\rangle_{1/2}$ further reduced by fractional dynamic correlation energy contributions from coarse-grained Hamiltonians, and show similar classical-data-input-reduction results for multiscale graph classification via Kron reduction. We also show the online generalization with anisotropic Kalman filtering of streaming quantum data.
Comments305 pages, 34 figues, 14 tables
