具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
摘要：
我们研究了含时哈密顿量中的随机控制误差对孤立量子动力学的影响。在薛定谔方程中，控制误差被表示为时间相关的随机噪声。对于一类随机控制误差，我们建立了一个阈值定理，提供了一个充分条件，以获得目标状态，这应该是确定在无噪声的孤立量子动力学，作为测量的数量和噪声强度之间的关系。该定理保证，如果噪声强度之和小于计算时间的倒数，目标状态可以通过一个常数阶数的测量获得。如果相反，则保证获得目标状态的测量数量随计算时间呈指数增加。我们的阈值定理可以应用于任何孤立的量子动力学，如量子退火和绝热量子计算。
英文摘要：
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.
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