论文标题
去签名的哈密顿人进行绝热优化
De-Signing Hamiltonians for Quantum Adiabatic Optimization
论文作者
论文摘要
由非争夺哈密顿人驱动的量子波动已被认为是通过绝热优化获得量子优势的重要且可能缺失的成分。我们介绍了一个转换，该转换通过在计算基础上适当调整每个矩阵输入的相位，将经典哈密顿量末尾的每个非拼写绝热路径映射到相应的静绝热路径。我们比较了这些绝热路径的光谱间隙，并从理论上和数字上都发现，基于非storquastic hamiltonians的路径在地面和第一个激发态之间具有通常较小的光谱差距，这表明它们比量子级的量子型量子量不如降级的量子量。这些结果适用于任何绝热算法，该算法将其插入到计算基础上的对角线的最终哈密顿量。
Quantum fluctuations driven by non-stoquastic Hamiltonians have been conjectured to be an important and perhaps essential missing ingredient for achieving a quantum advantage with adiabatic optimization. We introduce a transformation that maps every non-stoquastic adiabatic path ending in a classical Hamiltonian to a corresponding stoquastic adiabatic path by appropriately adjusting the phase of each matrix entry in the computational basis. We compare the spectral gaps of these adiabatic paths and find both theoretically and numerically that the paths based on non-stoquastic Hamiltonians have generically smaller spectral gaps between the ground and first excited states, suggesting they are less useful than stoquastic Hamiltonians for quantum adiabatic optimization. These results apply to any adiabatic algorithm which interpolates to a final Hamiltonian that is diagonal in the computational basis.
