Decoherence of Quantum Computers with Many Qubits

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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.