相关论文: Synthesizing NMR analogues of Einstein-Podolsky-Ro…

Grover's algorithm for quantum searching is generalized to deal with arbitrary initial complex amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the marked and unmarked…

State preparation is a fundamental routine in quantum computation, for which many algorithms have been proposed. Among them, perhaps the simplest one is the Grover-Rudolph algorithm. In this paper, we analyse the performance of this…

The Groverian entanglement measure, G(psi), is applied to characterize a variety of pure quantum states |psi> of multiple qubits. The Groverian measure is calculated analytically for certain states of high symmetry, while for arbitrary…

We investigate the necessary and sufficient conditions in order that a unitary operator can amplify a pre-assigned component relative to a particular basis of a generic vector at the expense of the other components. This leads to a general…

A construction is given for simulating any deterministic finite state machine (FSM) on a quantum computer in a space-efficient manner. By constructing a superposition of input strings of lengths K or less, questions can be asked about the…

We show that iteration of a few ( $\sim N^{1/4}$) unitary steps of Grover's algorithm suffices to perfectly prepare a Dicke state of $N$ atoms in a cavity. We also show that a few subsequent Grover steps can be employed to generate GHZ and…

We describe a simple quantum algorithm for preparing $K$ copies of an $N$-dimensional quantum state whose amplitudes are given by a quantum oracle. Our result extends a previous work of Grover, who showed how to prepare one copy in time…

In the multitarget Grover algorithm, we are given an unstructured N-element list of objects S_i containing a T-element subset tau and function f, called an oracle, such that f(S_i)=1 if S_i is in tau, otherwise f(S_i) = 0. By using quantum…

We present a continuous time quantum search algorithm analogous to Grover's. In particular, the optimal search time for this algorithm is proportional to $\sqrt{N}$, where $N$ is the database size. This search algorithm can be implemented…

We generalize Grover algorithm with two arbitrary phases in a density matrix set up. We give exact analytic expressions for the success probability after arbitrary number of iteration of the generalized Grover operator as a function of…

Einstein-Podolsky-Rosen(EPR)steering is a kind of powerful nonlocal quantum resource in quantum information processing such as quantum cryptography and quantum communication. Many criteria have been proposed in the past few years to detect…

The Groverian entanglement measure introduced earlier for pure quantum states [O. Biham, M.A. Nielsen and T. Osborne, Phys. Rev. A 65, 062312 (2002)] is generalized to the case of mixed states, in a way that maintains its operational…

For quantum computation, we investigate the conjecture that the superposition of macroscopically distinct states is necessary for a large quantum speedup. Although this conjecture was supported for a circuit-based quantum computer…

We generalize Grover's unstructured quantum search algorithm to enable it to use an arbitrary starting superposition and an arbitrary unitary matrix simultaneously. We derive an exact formula for the probability of the generalized Grover's…

A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching…

The universal quantum homogeniser can transform a qubit from any state to any other state with arbitrary accuracy, using only unitary transformations to perform this task. Here we present an implementation of a finite quantum homogeniser…

We propose a quantum algorithm that emulates the action of an unknown unitary transformation on a given input state, using multiple copies of some unknown sample input states of the unitary and their corresponding output states. The…

Nuclear magnetic resonance techniques are used to realize a quantum algorithm experimentally. The algorithm allows a simple NMR quantum computer to determine global properties of an unknown function requiring fewer function ``calls'' than…

Since the final quantum state in the Grover search algorithm is the normalized marked quantum state from the Gram-Schmidt process, Abrams and Lloyd [1] has shown that we can generate this vector by using a non-unitary gate. Following their…

Grover's search algorithm is designed to be executed on a quantum mechanical computer. In this paper, the probabilistic wp-calculus is used to model and reason about Grover's algorithm. It is demonstrated that the calculus provides a…