论文标题
带有随机控制误差的孤立量子动力学中的阈值定理
Threshold theorem in isolated quantum dynamics with stochastic control errors
论文作者
论文摘要
我们研究了随机控制误差在时间依赖性的哈密顿量对孤立量子动力学的影响。控制误差被表述为施罗宾格方程中时间依赖性随机噪声。对于一类随机控制误差，我们建立了一个阈值定理，该定理提供了足够的条件来获得目标状态，应在无噪声的孤立量子动力学中确定，作为测量数量和噪声强度之间的关系。该定理保证，如果噪声强度的总和小于计算时间的倒数，则可以通过恒定阶数测量值获得目标状态。如果相反，则保证获得目标状态的测量数量将随着计算时间呈指数增长。我们的阈值定理可以应用于任何孤立的量子动力学，例如量子退火和绝热量子计算。
We investigate the effect of stochastic control errors in the time-dependent Hamiltonian on isolated quantum dynamics. The control errors are formulated as time-dependent stochastic noise in the Schrodinger equation. For a class of stochastic control errors, we establish a threshold theorem that provides a sufficient condition to obtain the target state, which should be determined in noiseless isolated quantum dynamics, as a relation between the number of measurements and noise strength. The theorem guarantees that if the sum of the noise strengths is less than the inverse of computational time, the target state can be obtained through a constant-order number of measurements. If the opposite is true, the number of measurements to guarantee obtaining the target state increases exponentially with computational time. Our threshold theorem can be applied to any isolated quantum dynamics such as quantum annealing and adiabatic quantum computation.
