Related papers: Quantum search on the two-dimensional lattice usin…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…
In this paper we present genetic algorithms based search technique for the linear optics schemes, performing two-qubit quantum gates. We successfully applied this technique for finding heralded two-qubit gates and obtained the new schemes…
We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a…
In this tutorial, which contains some original results, we bridge the fields of quantum computing algorithms, conservation laws, and many-body quantum systems by examining three algorithms for searching an unordered database of size $N$…
The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph. We analytically prove that lackadaisical quantum walks can find a unique marked vertex on any regular…
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…
Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable…
We propose an implementation of a two-dimensional $\mathbb{Z}_2$ lattice gauge theory model on a shallow quantum circuit, involving a number of single and two-qubits gates comparable to what can be achieved with present-day and near-future…
This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…
Nowadays, quantum simulation schemes come in two flavours. Either they are continuous-time discrete-space models (a.k.a Hamiltonian-based), pertaining to non-relativistic quantum mechanics. Or they are discrete-spacetime models (a.k.a…
A quantum particle evolving by Schr\"odinger's equation contains, from the kinetic energy of the particle, a term in its Hamiltonian proportional to Laplace's operator. In discrete space, this is replaced by the discrete or graph Laplacian,…
Hanoi network has a one-dimensional periodic lattice as its main structure with additional long-range edges, which allow having efficient quantum walk algorithm that can find a target state on the network faster than the exhaustive…
In this work, we present a new algorithm for generating quantum circuits that efficiently implement continuous time quantum walks on arbitrary simple sparse graphs. The algorithm, called matching decomposition, works by decomposing a…
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…
We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) $P$ on a graph with a set of unknown marked vertices, one can define a…
Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…
The extended Hubbard model on a two-dimensional lattice captures key physical phenomena, but is challenging to simulate due to the presence of long-range interactions. In this work, we present an efficient quantum algorithm for simulating…
In this survey paper we give an intuitive treatment of the discrete time quantization of classical Markov chains. Grover search and the quantum walk based search algorithms of Ambainis, Szegedy and Magniez et al. will be stated as quantum…
Closed quantum systems follow a unitary time evolution that can be simulated on quantum computers. By incorporating non-unitary effects via, e.g., measurements on ancilla qubits, these algorithms can be extended to open-system dynamics,…