标题： 非相对论性散射中的杂质和四元数来自量子存储器 显示英文标题

标题： Impurity and quaternions in nonrelativistic scattering from a quantum memory

摘要： 量子计算的模型依赖于量子存储器状态的变换。 我们研究了吴提出的一种模型的数学方面，其中通过入射粒子的散射来改变存储器状态。 此操作会导致存储器内容偏离纯态，即引入不纯性。 对于从两态存储器散射的非相对论粒子以及1+1维中足够一般的相互作用势，我们将不纯性表示为四元数对易子。 在此背景下，纯存储器状态对应于零双曲四元数。 在点相互作用的情况下，散射过程相当于频率域中四元数的适当旋转。 我们的工作补充了Margetis和Myers(2006 J. Phys. A 39 11567--11581)之前的分析。 显示英文摘要

摘要： Models of quantum computing rely on transformations of the states of a quantum memory. We study mathematical aspects of a model proposed by Wu in which the memory state is changed via the scattering of incoming particles. This operation causes the memory content to deviate from a pure state, i.e. induces impurity. For nonrelativistic particles scattered from a two-state memory and sufficiently general interaction potentials in 1+1 dimensions, we express impurity in terms of quaternionic commutators. In this context, pure memory states correspond to null hyperbolic quaternions. In the case with point interactions, the scattering process amounts to appropriate rotations of quaternions in the frequency domain. Our work complements a previous analysis by Margetis and Myers (2006 J. Phys. A 39 11567--11581).