Black Hole and Quantum Information

我们给出了一个一般的框架，用来寻找量子力学中给定初始终态的最优量子演化，类似于经典力学中的臂叉配子体。该公式基于变分原理，其中哈密顿量既被看作是量子态，也被看作是动力学变量。现有的哈密顿量受到自然规律或实验装置等的约束，并作为约束加以处理。文中给出了几个简单的例子，并将该方法推广到任意初始态的情况，使之与量子计算有关。我们在典型的两个量子比特门中演示了它。为了放大到更多的量子比特，我们开发了一种强大的数值方法。通过测量，将该方法推广到混合状态情况。在某些情况下，通过混合态的量子轨道是更有效的，希望我们的方法对量子计算算法、量子控制和制造高效的量子器件有一定的帮助。

We have given a general frame work to find an optimal quantum evolution for given initial final states in quantum mechanics in analogy to brachistochrone in classical mechanics. The formulation is based on variational principle, in which the Hamiltonian is regarded as a dynamical variable as well as the quantum state. The available Hamiltonian is constrained by natural law or experimental set-up etc and taken care of as the constraints. A few simple examples are demonstrated.This method is extended to the case of arbitrary initial state so as to be relevant to quantum computation. We demonstrated it in typical two qubit gates. To scale-up to many qubits, we have developed a powerful numerical methods. The method is extended to mixed state cases by using measurement. In some cases, the quantum trajectory which passes mixed state is more efficient.We hope our method is useful for quantum computation algorithm, quantum control and Making efficient quantum devices.