Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGeneralization of Grovers Algorithm to Multiobject Search in Quantum Computing, Part II: General Unitary Transformations
74
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
There are major advantages in a newer version of Grovers quantum algorithm utilizing a general unitary transformation in the search of a single object in a large unsorted database. In this paper, we generalize this algorithm to multiobject search. We show the techniques to achieve the reduction of the problem to one on an invariant subspace of dimension just equal to two.
rate research
Read More
L. K. Grovers search algorithm in quantum computing gives an optimal, quadratic speedup in the search for a single object in a large unsorted database. In this paper, we generalize Grovers algorithm in a Hilbert-space framework for both continuous and discrete time cases that isolates its geometrical essence to the case where more than one object satisfies the search criterion.
We question whether the measurement based quantum computing algorithm is in fact Grovers algorithm or simply a similar oracular search method. The two algorithms share several qualitative features especially in the case of the trivial 4 element search, which is the largest size photonic search algorithm that has been experimentally implemented to date. This has led some to refer to both substantiations as Grovers algorithm. We compare multiple features of the two algorithms including the behavior of the oracle tags and the entanglement dynamics, both qualitatively and quantitatively. We find significant and fundamental differences in the operation of the two algorithms, particularly in cases involving searches on more than four elements.
We find that the Measurement Based Quantum Computing (MBQC) search algorithm on an unsorted list is not the same as Grovers search algorithm (GSA).
Let $H_1, H_2$ be Hilbert spaces of the same finite dimension $ge2$, and $C$ an arbitrary quantum circuit with (principal) input state in $H_1$ and (principal) output state in $H_2$. $C$ may use ancillas and produce garbage which is traced out. $C$ may employ classical channels and measurement gates. If $C$ computes, for each computation path $mu$ through the circuit, a unitary transformation $U_mu: H_1 to H_2$ then, for each $mu$, the probability that a computation takes path $mu$ is independent of the input.
Grovers quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude in Grovers algorithm. We study the algorithms intrinsic robustness when no quantum correction codes are used, and evaluate how much noise the algorithm can bear with, in terms of the size of the phone book and a desired probability of finding the correct result. The algorithm loses efficiency when noise is added, but does not slow down. We also study the maximal noise under which the iterated quantum algorithm is just as slow as the classical algorithm. In all cases, the width of the allowed noise scales with the size of the phone book as N^-2/3.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
