论文标题
数字绝热状态准备中的猪跑误差的自我修复
Self-healing of Trotter error in digital adiabatic state preparation
论文作者
论文摘要
绝热时间的演化可用于从一个更容易合成的复杂量子多体状态来制备复杂的量子多体状态，并且可以使用Trotterization来数字化实现此类演变。非绝热性和数字化之间的复杂相互作用会影响此过程的不忠。 We prove that the first-order Trotterization of a complete adiabatic evolution has a cumulative infidelity that scales as $\mathcal O(T^{-2} δt^2)$ instead of $\mathcal O(T^2 δt^2)$ expected from general Trotter error bounds, where $δt$ is the time step and $T$ is the total time.该结果表明了一种自我修复机制，并解释了为什么尽管增加了$ t $，但对固定的固定性不良数字的不忠化仍然减少了各种各样的哈密顿人。它还建立了量子近似优化算法（QAOA）和数字化量子退火之间的对应关系。
Adiabatic time evolution can be used to prepare a complicated quantum many-body state from one that is easier to synthesize and Trotterization can be used to implement such an evolution digitally. The complex interplay between non-adiabaticity and digitization influences the infidelity of this process. We prove that the first-order Trotterization of a complete adiabatic evolution has a cumulative infidelity that scales as $\mathcal O(T^{-2} δt^2)$ instead of $\mathcal O(T^2 δt^2)$ expected from general Trotter error bounds, where $δt$ is the time step and $T$ is the total time. This result suggests a self-healing mechanism and explains why, despite increasing $T$, infidelities for fixed-$δt$ digitized evolutions still decrease for a wide variety of Hamiltonians. It also establishes a correspondence between the Quantum Approximate Optimization Algorithm (QAOA) and digitized quantum annealing.
