A typology of quantum algorithms
- URL: http://arxiv.org/abs/2407.05178v1
- Date: Sat, 6 Jul 2024 20:41:05 GMT
- Title: A typology of quantum algorithms
- Authors: Pablo Arnault, Pablo Arrighi, Steven Herbert, Evi Kasnetsi, Tianyi Li,
- Abstract summary: We draw the current landscape of quantum algorithms, by classifying about 130 quantum algorithms.
The primary objectives include revealing trends of algorithms, identifying promising fields for implementations in the NISQ era, and identifying the key algorithmic primitives that power quantum advantage.
- Score: 1.967426628955258
- License: http://creativecommons.org/licenses/by-sa/4.0/
- Abstract: We draw the current landscape of quantum algorithms, by classifying about 130 quantum algorithms, according to the fundamental mathematical problems they solve, their real-world applications, the main subroutines they employ, and several other relevant criteria. The primary objectives include revealing trends of algorithms, identifying promising fields for implementations in the NISQ era, and identifying the key algorithmic primitives that power quantum advantage.
Related papers
- Performance Benchmarking of Quantum Algorithms for Hard Combinatorial Optimization Problems: A Comparative Study of non-FTQC Approaches [0.0]
This study systematically benchmarks several non-fault-tolerant quantum computing algorithms across four distinct optimization problems.
Our benchmark includes noisy intermediate-scale quantum (NISQ) algorithms, such as the variational quantum eigensolver.
Our findings reveal that no single non-FTQC algorithm performs optimally across all problem types, underscoring the need for tailored algorithmic strategies.
arXiv Detail & Related papers (2024-10-30T08:41:29Z) - On Quantum Algorithms for Efficient Solutions of General Classes of Structured Markov Processes [8.26313272946503]
We devise the first quantum algorithms for computing the stationary distribution of structured Markov processes.
Although motivated by structured Markov processes, our quantum algorithms have the potential for being exploited to address a much larger class of numerical computation problems.
arXiv Detail & Related papers (2024-04-27T17:06:16Z) - Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
Quantum computing sets the foundation for new ways of designing algorithms.
New challenges arise concerning which field quantum speedup can be achieved.
Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
arXiv Detail & Related papers (2024-02-26T09:32:07Z) - Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
The anticipated applications of quantum computers span across science and industry.
We present a survey of several potential application areas of quantum algorithms.
We outline the challenges and opportunities in each area in an "end-to-end" fashion.
arXiv Detail & Related papers (2023-10-04T17:53:55Z) - A Review on Quantum Approximate Optimization Algorithm and its Variants [47.89542334125886]
The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve intractable optimization problems.
This comprehensive review offers an overview of the current state of QAOA, encompassing its performance analysis in diverse scenarios.
We conduct a comparative study of selected QAOA extensions and variants, while exploring future prospects and directions for the algorithm.
arXiv Detail & Related papers (2023-06-15T15:28:12Z) - Quantum Annealing for Single Image Super-Resolution [86.69338893753886]
We propose a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem.
The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.
arXiv Detail & Related papers (2023-04-18T11:57:15Z) - An introduction to variational quantum algorithms for combinatorial optimization problems [0.0]
This tutorial provides a mathematical description of the class of Variational Quantum Algorithms.
We introduce precisely the key aspects of these hybrid algorithms on the quantum side and the classical side.
We devote a particular attention to QAOA, detailing the quantum circuits involved in that algorithm, as well as the properties satisfied by its possible guiding functions.
arXiv Detail & Related papers (2022-12-22T14:27:52Z) - A brief introduction to quantum algorithms [3.454865774480229]
We start from elucidating quantum parallelism, the basic framework of quantum algorithms and the difficulty of quantum algorithm design.
We then focus on a historical overview of progress in quantum algorithm research over the past three to four decades.
Finally, we clarify two common questions about the study of quantum algorithms, hoping to stimulate readers for further exploration.
arXiv Detail & Related papers (2022-12-21T03:00:25Z) - Quantum Phase Recognition via Quantum Kernel Methods [6.3286116342955845]
We explore the power of quantum learning algorithms in solving an important class of Quantum Phase Recognition problems.
We numerically benchmark our algorithm for a variety of problems, including recognizing symmetry-protected topological phases and symmetry-broken phases.
Our results highlight the capability of quantum machine learning in predicting such quantum phase transitions in many-particle systems.
arXiv Detail & Related papers (2021-11-15T06:17:52Z) - Synthesis of Quantum Circuits with an Island Genetic Algorithm [44.99833362998488]
Given a unitary matrix that performs certain operation, obtaining the equivalent quantum circuit is a non-trivial task.
Three problems are explored: the coin for the quantum walker, the Toffoli gate and the Fredkin gate.
The algorithm proposed proved to be efficient in decomposition of quantum circuits, and as a generic approach, it is limited only by the available computational power.
arXiv Detail & Related papers (2021-06-06T13:15:25Z) - Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra [53.46106569419296]
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression.
We argue that the previous quantum-inspired algorithms for these problems are doing leverage or ridge-leverage score sampling in disguise.
arXiv Detail & Related papers (2020-11-09T01:13:07Z)
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.