Related papers: Asymptotic Quantum Search and a Quantum Algorithm …

In this paper, we consider the partial database search problem where given a database on N items, we are required to determine the first k bits of an address x such that f(x)=1. We derive an algorithm and a lower bound for this problem in…

Quantum illumination employs entangled states to detect a weakly reflective target in a thermal bath. The performance of a given entangled state is evaluated from the minimum error probability in the asymptotic limit, which is compared…

Quantum annealing is a new method for finding extrema of multidimensional functions. Based on an extension of classical, simulated annealing, this approach appears robust with respect to avoiding local minima. Further, unlike some of its…

Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian…

We generalize the monotone local search approach of Fomin, Gaspers, Lokshtanov and Saurabh [J. ACM 2019], by establishing a connection between parameterized approximation and exponential-time approximation algorithms for monotone subset…

A framework is presented for the design and analysis of quantum mechanical algorithms, the sqrt(N) step quantum search algorithm is an immediate consequence of this framework. It leads to several other search-type applications - several…

Given two sets A and B and two oracles O(A) and O(B) that can identify the elements of these sets respectively, the goal is to find an element common to both sets using minimum number of oracle queries. Each application of either O(A) or…

A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be…

The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hypercube {0,1}^n, we show a lower bound of Omega(2^{n/4}/n) on…

In [Phys. Rev. Lett. 113, 210501 (2014)], to achieve the optimal fixed-point quantum search in the case of unknown fraction (denoted by $\lambda$) of target items, the analytical multiphase matching (AMPM) condition has been proposed. In…

Since Grover's seminal work, quantum search has been studied in great detail. In the usual search problem, we have a collection of n items and we would like to find a marked item. We consider a new variant of this problem in which…

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…

When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum…

A two-party quantum communication process with classical inputs and outcomes can be simulated by replacing the quantum channel with a classical one. The minimal amount of classical communication required to reproduce the statistics of the…

Procedures are given below to construct symmetric and anti-symmetric quantum functions. If hidden in an oracle, such functions can be identified exactly, without iterative interrogation. This is another example of quantum search. The…

In this work we address two questions concerning Grover's algorithm. In the first we give an answer to the question how to employ Grover's algorithm for actual search over database. We introduce a quantum model of an unordered phone book…

Finding a maximum or minimum is a fundamental building block in many mathematical models. Compared with classical algorithms, Durr, Hoyer's quantum algorithm (DHA) achieves quadratic speed. However, its key step, the quantum exponential…

Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…

This paper introduces a novel quantum embedding search algorithm (QES, pronounced as "quest"), enabling search for optimal quantum embedding design for a specific dataset of interest. First, we establish the connection between the…

We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…