Decoherence of Quantum Computers with Many Qubits

首先，我们建立了一个关于多体量子系统稳定性的一般理论。我们证明了加性算子的最大涨落是多体量子系统宏观纠缠的一个合理指标。其次，我们证明了由该指标定义的宏观纠缠在量子计算机中的应用。也就是说，(a)当量子计算机比经典计算机更快地解决问题时，总是使用宏观纠缠态；这意味着宏观纠缠态的使用在量子计算中是必不可少的，(b)宏观纠缠态有时甚至在量子计算机解决经典计算机可以轻松解决的问题时也被使用；这意味着现有的量子算法并没有优化，因为它们浪费了宏观纠缠态。在此基础上，运用现代量子测量理论对量子芝诺效应进行了分析，发现了许多否定前人研究结果的事实。我们在《物理报告》上发表了一篇特邀评论论文。此外，我们将宏观纠缠的概念和定义推广到包括混合态在内的一般态。我们还提出了一种检测宏观纠缠的一般方法。

Firstly, we have constructed a general theory of stability of many-body qauntum systems. We have shown there that the maximum fluctuation of additive operators is a reasonable index of macroscopic entanglement of many-body qauntum systems. Secondly, we have shown that the macroscopic entanglement as defined by this index is used in quantum computers. That is, (a) a macroscopically entangled state(s) is always used when a quantum computer solves problems much faster than classical computers ; this means that the use of macroscopically entangled states is essential in quantum computation, (b) a macroscopically entangled state(s) is sometimes used even when a quantum computer solves problems which can be solved easily with classical computers ; this implies that existing quantum algorithms are not optimized in the sense that they waste macroscopically entangled states. Furthermore, we have analyzed the quantum Zeno effect using the modern theory of quantum measurement, and found many facts that denied results of the previous works. We have published an invited review paper on this subject in Physics Report. Moreover, we have generalized the concept and definition of the macroscopic entanglement to general states including mixed states. We have also proposed a general method of detecting the macroscopic entanglement.