Related papers: Performance of Equal Phase-Shift Search for One It…
This work considers a generalization of Grover's search problem, viz., to find any one element in a set of acceptable choices which constitute a fraction f of the total number of choices in an unsorted data base. An infinite family of…
Boolean satisfiability (SAT) problem is of fundamental importance in computer science and many application domains. For Grover's algorithm, solving the SAT problem requires $\mathcal{O}(\sqrt{2^n})$ queries--where n denotes the number of…
Spatial search on graphs is one of the most important algorithmic applications of quantum walks. To show that a quantum-walk-based search is more efficient than a random-walk-based search is a difficult problem, which has been addressed in…
We provide a tight analysis of Grover's recent algorithm for quantum database searching. We give a simple closed-form formula for the probability of success after any given number of iterations of the algorithm. This allows us to determine…
We consider a phase retrieval problem, where the goal is to reconstruct a $n$-dimensional complex vector from its phaseless scalar products with $m$ sensing vectors, independently sampled from complex normal distributions. We show that,…
We propose a continuous time quantum search algorithm using a generalization of the Jaynes-Cummings model. In this model the states of the atom are the elements among which the algorithm realizes the search, exciting resonances between the…
I show that the power iteration method applied to the phase retrieval problem converges under special conditions. One is given the relative phases between small non-overlapping groups of pixels of a recorded intensity pattern, but no…
A sequential application of the Grover algorithm to solve the iterated search problem has been improved by Ozhigov by parallelizing the application of the oracle. In this work a representation of the parallel Grover as dynamic system of…
Given a parameterized quantum circuit such that a certain setting of these real-valued parameters corresponds to Grover's celebrated search algorithm, can a variational algorithm recover these settings and hence learn Grover's algorithm? We…
The goal of this paper is to derive the detailed description of the Enumeration Based Search Algorithm from the high level description provided in [16], analyze the experimental results from our implementation of the Enumeration Based…
We formulate and optimize a computational search strategy for detecting gravitational waves from isolated, previously-unknown neutron stars (that is, neutron stars with unknown sky positions, spin frequencies, and spin-down parameters). It…
Traditional phase-shifting interferometry technique cannot be used to measure time-varying phase distributions. But single shot techniques could resolve the problem. Many efforts have been made on the phase retrieval methods from a single…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
It is well known that matched filtering techniques cannot be applied for searching extensive parameter space volumes for continuous gravitational wave signals. This is the reason why alternative strategies are being pursued. Hierarchical…
Inspired by the classical fractional cascading technique, we introduce new techniques to speed up the following type of iterated search in 3D: The input is a graph $\mathbf{G}$ with bounded degree together with a set $H_v$ of 3D hyperplanes…
Evolution of entanglement with the proceeding of quantum algorithms affects the outcome of the algorithm. Particularly, the performance of Grover's search algorithm gets worsened if the initial state of the algorithm is an entangled one.…
Grover's search algorithm is one of the first quantum algorithms to exhibit a provable quantum advantage. It forms the backbone of numerous quantum applications and is widely used in benchmarking efforts. Here, we report…
In this paper we will present a quantum algorithm which works very efficiently in case of multiple matches within the search space and in the case of few matches, the algorithm performs classically. This allows us to propose a hybrid…
For the unsorted database quantum search with the unknown fraction $\lambda$ of target items, there are mainly two kinds of methods, i.e., fixed-point or trail-and-error. (i) In terms of the fixed-point method, Yoder et al. [Phys. Rev.…
We describe an improved version of the Hough transform search for continuous gravitational waves from isolated neutron stars assuming the input to be short segments of Fourier transformed data. The method presented here takes into account…