Search Results for « Quantum search algorithm »

We report the implementation of Grover's quantum search algorithm in the scalable system of trapped atomic ion quantum bits. Any one of four possible states of a two-qubit memory is marked, and following a single query of the search space, the marked element is successfully recovered with an average probability of 60(2)%. This exceeds the performance of any possible classical search algorithm, which can only succeed with a maximum average probability of 50%.

Faster, ultra-reliable, low-power, and secure communications has always been high on the wireless evolutionary agenda. However, the appetite for faster, more reliable, greener, and more secure communications continues to grow. The state-of-the-art methods conceived for achieving the performance targets of the associated processes may be accompanied by an increase in computational complexity. Alternatively, a degraded performance may have to be accepted due to the lack of jointly optimized system components. In this survey we investigate the employment of quantum computing for solving problems in wireless communication systems. By exploiting the inherent parallelism of quantum computing, quantum algorithms may be invoked for approaching the optimal performance of classical wireless processes, despite their reduced number of cost-function evaluations. In this contribution we discuss the basics of quantum computing using linear algebra, before presenting the operation of the major quantum algorithms, which have been proposed in the literature for improving wireless communications systems. Furthermore, we investigate a number of optimization problems encountered both in the physical and network layer of wireless communications, while comparing their classical and quantum-assisted solutions. Finally, we state a number of open problems in wireless communications that may benefit from quantum computing.

We investigate a set of discrete-time quantum search algorithms on the n -dimensional hypercube following a proposal by Shenvi et al (2003 Phys. Rev. A 67 052307). We show that there exists a whole class of quantum search algorithms in the symmetry-reduced space which perform a search of a marked vertex in time of order where N = 2 n , the number of vertices. In analogy to Grover's algorithm, the spatial search is effectively facilitated through a rotation in a two-level subspace of the full Hilbert space. In the hypercube, these two-level systems are introduced through avoided crossings. We give estimates on the quantum states forming the two-level subspaces at the avoided crossings and derive improved estimates on the search times.

We report on an experiment on Grover's quantum search algorithm showing that classical waves can search a N-item database as efficiently as quantum mechanics can. The transverse beam profile of a short laser pulse is processed iteratively as the pulse bounces back and forth between two mirrors. We directly observe the sought item being found in approximately square root[N] iterations, in the form of a growing intensity peak on this profile. Although the lack of quantum entanglement limits the size of our database, our results show that entanglement is neither necessary for the algorithm itself, nor for its efficiency.

We present two continuous-time quantum search algorithms similar to the adiabatic search algorithm, but now without the requirement of adiabatic evolution. Both algorithms can find the marked state in a time proportional to $\sqrt{N}$. The behavior of the first algorithm is, essentially, similar to Grover's algorithm, but the second model possesses the important property that one does not need to single out a given time in order to find the searched state. After a well-defined transition time, this second algorithm will converge towards the marked state with a high probability, provided the parameters of the Hamiltonian are chosen appropriately. This convergence shows a resemblance to quantum search algorithms with a fixed point [L. K. Grover, Phys. Rev. Lett. 95, 150501 (2005)].

We present a quantum signature scheme based on a two-qubit quantum search algorithm. For secure transmission of signatures, we use a quantum search algorithm that has not been used in previous quantum signature schemes. A two-step protocol secures the quantum channel, and a trusted center guarantees non-repudiation that is similar to other quantum signature schemes. We discuss the security of our protocol.