Related papers: Faster quantum walk algorithm for the two dimensio…
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…
Quantum walks (QWs) are of interest as examples of uniquely quantum behavior and are applicable in a variety of quantum search and simulation models. Implementing QWs on quantum devices is useful from both points of view. We describe a…
With the growing interest in quantum machine learning, the perceptron -- a fundamental building block in traditional machine learning -- has emerged as a valuable model for exploring quantum advantages. Two quantum perceptron algorithms…
This paper shows how a basic property of unitary transformations can be used for meaningful computations. This approach immediately leads to search-type applications, where it improves the number of steps by a square-root - a simple minded…
A randomly walking quantum particle evolving by Schr\"odinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time $\Theta(N^{3/4})$. In this paper, we give a weighted version of this graph that…
Based on the Dirac representation of Maxwell equations we present an explicit, discrete space-time, quantum walk-inspired algorithm suitable for simulating the electromagnetic wave propagation and scattering from inhomogeneities within…
In the typical model, a discrete-time coined quantum walk search has the same running time of $O(\sqrt{N} \log{N})$ for 2D rectangular, triangular and honeycomb grids. It is known that for 2D rectangular grid the running time can be…
A quantum search algorithm based on the partial adiabatic evolution\cite{Tulsi2009} is provided. We calculate its time complexity by studying the Hamiltonian in a two-dimensional Hilbert space. It is found that the algorithm improves the…
Can Grover's algorithm speed up search of a physical region - for example a 2-D grid of size sqrt(n) by sqrt(n)? The problem is that sqrt(n) time seems to be needed for each query, just to move amplitude across the grid. Here we show that…
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…
Quantum walk algorithms can speed up search of physical regions of space in both the discrete-time [arXiv:quant-ph/0402107] and continuous-time setting [arXiv:quant-ph/0306054], where the physical region of space being searched is modeled…
Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…
We investigate the application of quantum computing algorithms to enhance the efficiency of enumerating self-avoiding walks (SAWs), utilizing quantum properties such as superposition and interference. A Quantum Amplitude Estimation…
Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in $O(n \log n)$ time and space. Our goal in this paper is to reduce the space consumption while…
For a graph $G$ on $n$ vertices, naively sampling the position of a random walk of at time $t$ requires work $\Omega(t)$. We desire local access algorithms supporting $\text{position}(G,s,t)$ queries, which return the position of a random…
Quantum searching for one of $N$ marked items in an unsorted database of $n$ items is solved in $\mathcal{O}(\sqrt{n/N})$ steps using Grover's algorithm. Using nonlinear quantum dynamics with a Gross-Pitaevskii type quadratic nonlinearity,…
Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…
The spatial search problem aims to find a marked vertex of a finite graph using a dynamic with two constraints: (1) The walker has no compass and (2) the walker can check whether a vertex is marked only after reaching it. This problem is a…
A general quantum algorithm for solving a problem is discussed. The number of steps required to solve a problem using this method is independent of the number of cases that has to be considered classically. Hence, it is more efficient than…
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…