相关论文: Tradeoffs in the Quantum Search Algorithm
Database search has wide applications and is used as a subroutine in many important algorithms. We shall consider a database with one target item. Quantum algorithm finds the target item in a database faster than any classical algorithm. It…
The discovery of derivatives and integrals was a tremendous leap in scientific knowledge and completely revolutionized many fields, including mathematics, physics, and engineering. The existence of higher-order derivatives means better…
The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search…
Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
We study the power of nonadaptive quantum query algorithms, which are algorithms whose queries to the input do not depend on the result of previous queries. First, we show that any bounded-error nonadaptive quantum query algorithm that…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
We show that quantum search can be used to compute the hardness to round an elementary function, that is, to determine the minimum working precision required to compute the values of an elementary function correctly rounded to a target…
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…
We propose an algebraic formulation for two distinct quantum algorithms: a quantum classification algorithm and a quantum search algorithm with a non-uniform initial distribution, both based on Clifford algebras and spinorial…
We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our algorithm allows generating quantum circuits that use asymptotically fewer additional quantum gates than the famous Grover's…
Many important computer science problems can be reduced to clause satisfaction problem. We are given $n$ Boolean variables $x_{k}$ and $m$ clauses $c_{j}$ where each clause is a function of values of some of the variables. We want to find…
PARITY is the problem of determining the parity of a string $f$ of $n$ bits given access to an oracle that responds to a query $x\in\{0,1,...,n-1\}$ with the $x^{\rm th}$ bit of the string, $f(x)$. Classically, $n$ queries are required to…
We consider the problem of inserting a new item into an ordered list of N-1 items. The length of an algorithm is measured by the number of comparisons it makes between the new item and items already on the list. Classically, determining the…
The search of an unstructured database amounts to finding one element having a certain property out of $N$ elements. The classical search with an oracle checking one element at a time requires on average $N/2$ steps. The Grover algorithm…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
Quantum search algorithm (also known as Grover's algorithm) lays the foundation for many other quantum algorithms. Although it is very simple, its implementation is limited on noisy intermediate-scale quantum (NISQ) processors. Grover's…
A general consideration on the phase rotations in quantum searching algorithm is taken in this work. As four phase rotations on the initial state, the marked states, and the states orthogonal to them are taken account, we deduce a phase…
We present a modification of the standard single-item quantum search procedure that acquires robustness from spontaneous decay of the qubits. This damps the usual oscillation of populations, driving the system to a steady state with a…
An essential component of many sophisticated metaheuristics for solving combinatorial optimization problems is some variation of a local search routine that iteratively searches for a better solution within a chosen set of immediate…