Related papers: Nested Grover's Algorithm for Tree Search
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…
This is a note accompanying "CS 410/510: INTRO TO QUANTUM COMPUTING" I taught at Portland State University in Spring 2017. It is a review and summary of some early results related to Grover's quantum search algorithm in a consistent way. I…
We present an information geometric characterization of Grover's quantum search algorithm. First, we quantify the notion of quantum distinguishability between parametric density operators by means of the Wigner-Yanase quantum information…
Although entanglement is widely considered to be necessary for quantum algorithms to improve on classical ones, Lloyd has observed recently that Grover's quantum search algorithm can be implemented without entanglement, by replacing…
Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms…
This paper presents a novel approach to Grover adaptive search (GAS) for a combinatorial optimization problem whose objective function involves spin variables. While the GAS algorithm with a conventional design of a quantum dictionary…
We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph…
Motion planning is challenging when it comes to the case of imperfect state information. Decision should be made based on belief state which evolves according to the noise from the system dynamics and sensor measurement. In this paper, we…
We propose a couple of oracle construction methods for quantum pattern matching. We in turn show that one of the construct can be used with the Grover's search algorithm for exact and partial pattern matching, deterministically. The other…
This paper introduces a quantum-classical hybrid algorithm for generalized pattern search (GPS) algorithms. We introduce a quantum search step algorithm using amplitude amplification, which reduces the number of oracle calls needed during…
Searching and sorting used as a subroutine in many important algorithms. Quantum algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block)…
Searching a database is a central task in computer science and is paradigmatic of transport and optimization problems in physics. For an unstructured search, Grover's algorithm predicts a quadratic speedup, with the search time…
We invoke an efficient search algorithms as a key challenge in multi-qubit quantum systems. An original algorithm called dynamical quantum search algorithm from which Grover algorithm is obtained at a specified time is presented. This…
Solving optimisation problems is a promising near-term application of quantum computers. Quantum variational algorithms leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an…
This work tests the performance of Grover's search circuits on some IBM superconducting quantum devices in case of the size of search space $N=2^4$ and $N=2^5$. Ideally, we expect to get an outcome probability distribution that is clearly…
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…
Grover search is one of the most important quantum algorithms. In this paper, we consider a kind of search that the conditions of satisfaction $T$ can be rewritten as $T=T_1\bigcap T_2$. Then we present a new Grover search with smaller…
We present several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms. For these graphs, we construct quantum circuits that explicitly implement the full quantum walk…
Grover's algorithm for quantum searching of a database is generalized to deal with arbitrary initial amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the r marked and N-r…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…