We study imperfection effects on time evolution of Grover's algorithm on quantum computer. We introduce an effective two-level model with dissipation and stochasty, which is based upon the idea that ideal Grover's algorithm operates in 2 dimensional Hilbert space. The simulation results of both are compared and it is found that they are in good agreement for appropriately tuned parameters. It turns out that the main features of Grover's algorithm with imperfections can be understood in terms of two basic mechanisms, i.e., a diffusion of probability density into full Hilbert space and a stochastic rotation within the original 2 dimensional Hilbert space.
Abstract Imperfections and noise in realistic quantum computers may seriously affect the accuracy of quantum algorithms. In this article we explore the impact of static imperfections on quantum entanglement as well as non-entangled quantum correlations in Grover’s search algorithm. Using the metrics of concurrence and geometric quantum discord, we show that both the evolution of entanglement and quantum discord in Grover algorithm can be restrained with the increasing strength of static imperfections. For very weak imperfections, the quantum entanglement and discord exhibit periodic behavior, while the periodicity will most certainly be destroyed with stronger imperfections. Moreover, entanglement sudden death may occur when the strength of static imperfections is greater than a certain threshold.
As the development of Quantum computers becomes reality, the implementation of quantum algorithms is accelerating in a great pace. Grover's algorithm in a binary quantum system is one such quantum algorithm which solves search problems with numeric speed-ups than the conventional classical computers. Further, Grover's algorithm is extended to a
d-ary quantum system for utilizing the advantage of larger state space. In qudit or
d-ary quantum system n-qudit Toffoli gate plays a significant role in the accurate implementation of Grover's algorithm. In this paper, a generalized
n-qudit Toffoli gate has been realized using qudits to attain a logarithmic depth decomposition without ancilla qudit. Further, the circuit for Grover's algorithm has been designed for any d-ary quantum system, where d >= 2, with the proposed
n-qudit Toffoli gate so as to get optimized depth as compared to state-of-the-art approaches. This technique for decomposing an n-qudit Toffoli gate requires access to higher energy levels, making the design susceptible to leakage error. Therefore, the performance of this decomposition for the unitary and erasure models of leakage noise has been studied as well.