In parity-time-symmetric ( -symmetric) Hamiltonian theory, the optimal evolution time can be reduced drastically and can even be zero. In this article, we report our experimental simulation of the fast evolution of a -symmetric Hamiltonian in a nuclear magnetic resonance quantum system. The experimental results demonstrate that the -symmetric Hamiltonian system can indeed evolve much faster than the quantum system, and the evolution time can be arbitrarily close to zero.

It is well known that quantum computers are superior to classical computers in efficiently simulating quantum systems. Here we report the first experimental simulation of quantum tunneling through potential barriers, a widespread phenomenon of a unique quantum nature, via NMR techniques. Our experiment is based on a digital particle simulation algorithm and requires very few spin-1/2 nuclei without the need of ancillary qubits. The occurrence of quantum tunneling through a barrier, together with the oscillation of the state in potential wells, are clearly observed through the experimental results. This experiment has clearly demonstrated the possibility to observe and study profound physical phenomena within even the reach of small quantum computers.

Weak cross-Kerr media provides additional degrees of freedom of qubits in quantum information processing. In this paper, by exploiting weak cross-Kerr nonlinearity, we propose an optical implementation scheme of one-dimensional quantum random walks. The random walks are described by the interaction of single photons with cross-Kerr media. The proposed scheme can also be used to implement one-dimensional quantum random walks on an infinite line. quantum random walks, cross-Kerr mediaCitation: Wang C, Li Y S, Hao L. Optical implementation of quantum random walks using weak cross-Kerr media. Chinese Sci Bull, 2011Bull, , 56: 2088Bull, -2091 10.1007/s11434-011-4545-5Quantum computers, which are based on the principles of quantum mechanics, provide a speedup of classical computers. Quantum algorithms are the key ingredients of quantum computation for specific problems. In 1994, Shor proposed the quantum factoring algorithm, which challenges the security of classical encryption systems [1]. The proposed algorithm can factorize a large number with two prime numbers within a finite time. Later in 1997, Grover constructed the quantum search algorithm that searches for a marked item with very high probability from an unsorted database with N items using the Grover algorithm with only O( √ N) steps [2]. It has been shown that under phase matching [3][4][5], one can find a marked state with certainty [6]. Much progress was made in quantum algorithms and quantum computation in the following decade [7][8][9][10][11][12][13][14]. However, it is difficult to find new quantum algorithms for quantum information processing.Classical random walks are well known to solve NPcomplete problems. In the process of classical random walking, a particle moves along a two-way lattice. At each step, the particle moves to the left or to the right on the basis of the result of a coin flip. Quantum random walks are the quan-*Corresponding author (email: wangchuan82@gmail.com) tum version of classical random walks, in which the classical coin is replaced with a quantum coin, which is used to extend the set of quantum algorithms. There are two different types of quantum random walks: discrete and continuous quantum random walks. In 1993, Aharonov et al. first proposed the idea of quantum walks that require an additional quantum coin to allow discrete unitary evolution [15]. Later, Farhi and Gutmann proposed another quantum random walk algorithm based on continuous unitary evolution [16]. Shenvi et al. demonstrated that a search algorithm based on quantum walks can achieve speeds as high as that of Grover's algorithm [17]. In the following decades, quantum random walks attracted a variety of interest and have been a topic of research in the field of quantum information processing. Methods for possible implementations of one dimensional quantum random walks have been suggested by different groups in various physical systems. In 2002, Travaglione et al. proposed the method of quantum random walks using ion traps [18]. Zähringer et al. experimentall...

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We present a modified protocol for the realization of a quantum private query process on a classical database. Using one-qubit query and CNOT operation, the query process can be realized in a two-mode database. In the query process, the data privacy is preserved as the sender would not reveal any information about the database besides her query information, and the database provider cannot retain any information about the query. We implement the quantum private query protocol in a nuclear magnetic resonance system. The density matrix of the memory registers are constructed.