Implementation of Continuous-Time Quantum Walks on Quantum Computers
- URL: http://arxiv.org/abs/2212.08889v1
- Date: Sat, 17 Dec 2022 14:59:21 GMT
- Title: Implementation of Continuous-Time Quantum Walks on Quantum Computers
- Authors: Renato Portugal and Jalil Khatibi Moqadam
- Abstract summary: Quantum walks are interesting candidates to be implemented on quantum computers.
We describe efficient circuits that implement the evolution operator of continuous-time quantum-walk-based search algorithms on three graph classes.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum walk is a useful model to simulate complex quantum systems and to
build quantum algorithms; in particular, to develop spatial search algorithms
on graphs, which aim to find a marked vertex as quickly as possible. Quantum
walks are interesting candidates to be implemented on quantum computers. In
this work, we describe efficient circuits that implement the evolution operator
of continuous-time quantum-walk-based search algorithms on three graph classes:
complete graphs, complete bipartite graphs, and hypercubes. For the class of
complete and complete bipartite graphs, the circuits implement the evolution
operator exactly. For the class of hypercubes, the circuit implements an
approximate evolution operator, which tends to the exact evolution operator
when the number of vertices is large. Our Qiskit simulations show that the
implementation is successful at finding the marked vertex even for
low-dimensional hypercubes.
Related papers
- Quantum Walk Search on Complete Multipartite Graph with Multiple Marked Vertices [7.922488341886121]
This paper examines the quantum walk search algorithm on complete multipartite graphs.
We employ the coined quantum walk model and achieve quadratic speedup.
We also provide the numerical simulation and circuit implementation of our quantum algorithm.
arXiv Detail & Related papers (2024-10-07T11:13:41Z) - Deterministic Search on Complete Bipartite Graphs by Continuous Time Quantum Walk [0.8057006406834466]
This paper presents a deterministic search algorithm on complete bipartite graphs.
We address the most general case of multiple marked states, so there is a problem of estimating the number of marked states.
We construct a quantum counting algorithm based on the spectrum structure of the search operator.
arXiv Detail & Related papers (2024-04-02T05:09:33Z) - QArchSearch: A Scalable Quantum Architecture Search Package [1.725192300740999]
We present textttQArchSearch, an AI based quantum architecture search package with the textttQTensor library as a backend.
We show that the search package is able to efficiently scale the search to large quantum circuits and enables the exploration of more complex models for different quantum applications.
arXiv Detail & Related papers (2023-10-11T20:00:33Z) - Unitary Coined Discrete-Time Quantum Walks on Directed Multigraphs [1.2183405753834557]
Unitary Coined Discrete-Time Quantum Walks (UC-DTQW) constitute a universal model of quantum computation.
Current quantum computers work based on the quantum circuit model of computation.
arXiv Detail & Related papers (2023-04-04T07:19:55Z) - The Basis of Design Tools for Quantum Computing: Arrays, Decision
Diagrams, Tensor Networks, and ZX-Calculus [55.58528469973086]
Quantum computers promise to efficiently solve important problems classical computers never will.
A fully automated quantum software stack needs to be developed.
This work provides a look "under the hood" of today's tools and showcases how these means are utilized in them, e.g., for simulation, compilation, and verification of quantum circuits.
arXiv Detail & Related papers (2023-01-10T19:00:00Z) - Quantum Clustering with k-Means: a Hybrid Approach [117.4705494502186]
We design, implement, and evaluate three hybrid quantum k-Means algorithms.
We exploit quantum phenomena to speed up the computation of distances.
We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version.
arXiv Detail & Related papers (2022-12-13T16:04:16Z) - QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional
Networks [124.7972093110732]
We propose quantum graph convolutional networks (QuanGCN), which learns the local message passing among nodes with the sequence of crossing-gate quantum operations.
To mitigate the inherent noises from modern quantum devices, we apply sparse constraint to sparsify the nodes' connections.
Our QuanGCN is functionally comparable or even superior than the classical algorithms on several benchmark graph datasets.
arXiv Detail & Related papers (2022-11-09T21:43:16Z) - From Quantum Graph Computing to Quantum Graph Learning: A Survey [86.8206129053725]
We first elaborate the correlations between quantum mechanics and graph theory to show that quantum computers are able to generate useful solutions.
For its practicability and wide-applicability, we give a brief review of typical graph learning techniques.
We give a snapshot of quantum graph learning where expectations serve as a catalyst for subsequent research.
arXiv Detail & Related papers (2022-02-19T02:56:47Z) - On Applying the Lackadaisical Quantum Walk Algorithm to Search for
Multiple Solutions on Grids [63.75363908696257]
The lackadaisical quantum walk is an algorithm developed to search graph structures whose vertices have a self-loop of weight $l$.
This paper addresses several issues related to applying the lackadaisical quantum walk to search for multiple solutions on grids successfully.
arXiv Detail & Related papers (2021-06-11T09:43:09Z) - Quantum walk processes in quantum devices [55.41644538483948]
We study how to represent quantum walk on a graph as a quantum circuit.
Our approach paves way for the efficient implementation of quantum walks algorithms on quantum computers.
arXiv Detail & Related papers (2020-12-28T18:04:16Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.