Related papers: Amplitude Amplification and Estimation using a Flo…
We review our recent works on the dynamical localization in the quantum kicked rotator (QKR) and the related properties of the classical kicked rotator (the standard map, SM). We introduce the Izrailev $N$-dimensional model of the QKR and…
Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification…
Grover's quantum search and its generalization, quantum amplitude amplification, provide quadratic advantage over classical algorithms for a diverse set of tasks, but are tricky to use without knowing beforehand what fraction $\lambda$ of…
Amplitude amplification is a central tool used in Grover's quantum search algorithm and has been used in various forms in numerous quantum algorithms since then. It has been shown to completely eliminate one-sided error of quantum search…
Quantum search/amplitude amplification algorithms are designed to be able to amplify the amplitude in the target state linearly with the number of operations. Since the probability is the square of the amplitude, this results in the success…
Amplitude estimation algorithms are based on Grover's algorithm: alternating reflections about the input state and the desired outcome. But what if we are given the ability to perform arbitrary rotations, instead of just reflections? In…
We present an analytic theory of quantum interference and Anderson localization in the quantum kicked rotor (QKR). The behavior of the system is known to depend sensitively on the value of its effective Planck's constant $\he$. We here show…
In this work, we show the characterization of quantum iterations that would generally construct quantum amplitude amplification algorithms with a quadratic speedup, namely, quantum amplitude amplification operators (QAAOs). Exact quantum…
The quantum kicked rotor (QKR) driven by $d$ incommensurate frequencies realizes the universality class of $d$-dimensional disordered metals. For $d>3$, the system exhibits an Anderson metal-insulator transition which has been observed…
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…
Quantum search is among the most important algorithms in quantum computing. At its core is quantum amplitude amplification, a technique that achieves a quadratic speedup over classical search by combining two global reflections: the oracle,…
The phenomenon of quantum antiresonance (QAR), i.e., exactly periodic recurrences in quantum dynamics, is studied in a large class of nonintegrable systems, the modulated kicked rotors (MKRs). It is shown that asymptotic exponential…
We review some of quantum algorithms for search problems: Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the recent quantum algorithms based on…
Amplitude amplification is one of primary tools in building algorithms for quantum computers. This technique generalizes key ideas of the Grover search algorithm. Potentially useful modifications are connected with changing phases in the…
This paper concerns the Grover algorithm that permits to make amplification of quantum states previously tagged by an Oracle. Grover's algorithm allows searches in an unstructure database of n entries finding a marked element with a…
The atomic Quantum Kicked Rotor is an outstanding "quantum simulator" for the exploration of transport in disordered quantum systems. Here we study experimentally the phase-shifted quantum kicked rotor, which we show to display properties…
Grover's search algorithm was a groundbreaking advancement in quantum algorithms, displaying a quadratic speed-up of querying for items. Since the creation of this algorithm it has been utilized in various ways, including in preparing…
The landmark Grover algorithm for amplitude amplification serves as an essential subroutine in various type of quantum algorithms, with guaranteed quantum speedup in query complexity. However, there have been no proposal to realize the…
We present a full implementation and simulation of a novel quantum reinforcement learning method. Our work is a detailed and formal proof of concept for how quantum algorithms can be used to solve reinforcement learning problems and shows…
Grover's 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…