AI 中文总结
本研究提出量子信号处理（QSP）算法实现精确手征对称性的交叠费米子哈密顿量量子模拟，相较畴壁费米子可降低量子比特成本，其缩放特性反映交叠费米子的深层物理。
AI 中文摘要
我们提出一种用于交叠费米子哈密顿量的量子信号处理（QSP）算法，该算法可将Ginsparg-Wilson关系保持到可控误差ε_e。具有精确手征对称性的狄拉克费米子量子模拟近乎无额外开销：应用交叠哈密顿量的成本仅比Wilson-Dirac哈密顿量多一个与ε_e成对数关系的因子。与畴壁费米子相比，其电路复杂度有适度开销，但量子比特成本降低。我们展示了QSP如何在模拟交叠算子时有效构造额外维度，表明量子算法的缩放特性反映了畴壁费米子边界处产生的交叠费米子的深层物理。
英文摘要
We give a quantum signal processing (QSP) algorithm for the overlap fermion Hamiltonian which preserves the Ginsparg-Wilson relation up to a controllable error $ε_e$. Quantum simulations of Dirac fermions with exact chiral symmetry are thus nearly free: applying the overlap Hamiltonian costs only a factor logarithmic in $ε_e$ more than the Wilson-Dirac Hamiltonian. Comparing to domain-wall fermions, a mild overhead is found in circuit complexity while reducing qubit costs. We show how QSP effectively constructs an extra dimension when simulating the overlap operator, illustrating that the scaling of quantum algorithms reflects the deeper physics of overlap fermions arising at the boundary of domain-wall fermions.
Comments10 pages
