Related papers: Predicting quantum advantage by quantum walk with …
The quantum walk is a powerful tool to develop quantum algorithms, which usually are based on searching for a vertex in a graph with multiple marked vertices, Ambainis's quantum algorithm for solving the element distinctness problem being…
Testing graph completeness is a critical problem in computer science and network theory. Leveraging quantum computation, we present an efficient algorithm using the Szegedy quantum walk and quantum phase estimation (QPE). Our algorithm,…
A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly, it has been shown that algorithmic properties of quantum walks with…
Sampling from the stationary distribution is one of the fundamental tasks of Markov chain-based algorithms and has important applications in machine learning, combinatorial optimization and network science. For the quantum case, qsampling…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
The quantum random walk is a possible approach to construct new quantum algorithms. Several groups have investigated the quantum random walk and experimental schemes were proposed. In this paper we present the experimental implementation of…
In this paper, we numerically study quantum walks on two kinds of two-dimensional graphs: cylindrical strip and Mobius strip. The two kinds of graphs are typical two-dimensional topological graph. We study the crossing property of quantum…
Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…
An enduring challenge in computer science is reducing the runtime required to solve computational problems. Quantum computing has attracted significant attention due to its potential to deliver asymptotically faster solutions to certain…
Quantum walks, in virtue of the coherent superposition and quantum interference, possess exponential superiority over its classical counterpart in applications of quantum searching and quantum simulation. The quantum enhanced power is…
A recent paper on quantum walks by Childs et al. [STOC'03] provides an example of a black-box problem for which there is a quantum algorithm with exponential speedup over the best classical randomized algorithm for the problem, but where…
Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…
Continuous time quantum walks on exponentially large, sparse graphs form a powerful paradigm for quantum computing: On the one hand, they can be efficiently simulated on a quantum computer. On the other hand, they are themselves…
In this letter we introduce the concept of a driven quantum walk. This work is motivated by recent theoretical and experimental progress that combines quantum walks and parametric down- conversion, leading to fundamentally different…
Some of the quantum searching models have been given by perturbed quantum walks. Driving some perturbed quantum walks, we may quickly find one of the targets with high probability. In this paper, we construct a quantum searching model…
Quantum kernels hold great promise for offering computational advantages over classical learners, with the effectiveness of these kernels closely tied to the design of the quantum feature map. However, the challenge of designing effective…
Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks.…
We present an introduction to coined quantum walks on regular graphs, which have been developed in the past few years as an alternative to quantum Fourier transforms for underpinning algorithms for quantum computation. We then describe our…
Quantum counting is a key quantum algorithm that aims to determine the number of marked elements in a database. This algorithm is based on the quantum phase estimation algorithm and uses the evolution operator of Grover's algorithm because…
Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…