Introduction to Variational Quantum Algorithms
- URL: http://arxiv.org/abs/2402.15879v1
- Date: Sat, 24 Feb 2024 18:14:13 GMT
- Title: Introduction to Variational Quantum Algorithms
- Abstract summary: It provides an explanation of the basic variational algorithms, such as Variational Quantum Eigensolver (VQE) and Quantum Approximate Algorithm Optimization (QAOA)
It also describes some more advanced techniques that can be used to make these algorithms more efficient, as well as the challenges associated with using them.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: This document is a pdf version of the series of blogposts about variational
quantum algorithms (VQA) I originally posted on my blog Musty Thoughts. It
provides an explanation of the basic variational algorithms, such as
Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization
Algorithm (QAOA), as well as a more general framework for VQAs. It also
describes some more advanced techniques that can be used to make these
algorithms more efficient, as well as the challenges associated with using
them.
Related papers
- An Introduction to the Quantum Approximate Optimization Algorithm [51.56484100374058]
The tutorial begins by outlining variational quantum circuits and QUBO problems.<n>Next, it explores the QAOA in detail, covering its Hamiltonian formulation, gate decomposition, and example applications.<n>The tutorial extends these concepts to higher-order Hamiltonians and discussing the associated symmetries and circuit construction.
arXiv Detail & Related papers (2025-11-23T09:54:20Z) - From Theory to Practice: Analyzing VQPM for Quantum Optimization of QUBO Problems [0.0]
The variational quantum power method (VQPM) adapts the classical power algorithm for quantum settings.<n>We present detailed strategies for applying VQPM to QUBO problems by leveraging these locking mechanisms.<n>Our results indicate that VQPM can be employed as an effective quantum optimization algorithm on quantum computers for QUBO problems.
arXiv Detail & Related papers (2025-05-19T11:27:49Z) - Quantum Algorithms for tensor-SVD [10.96131926459428]
We introduce two new quantum t-SVD (tensor-SVD) algorithms.
First algorithm is largely based on previous work that proposed a quantum t-SVD algorithm for context-aware recommendation systems.
Second algorithm uses a hybrid variational approach largely based on a known variational quantum SVD algorithm.
arXiv Detail & Related papers (2024-05-29T20:01:11Z) - 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) - Generalized quantum Arimoto-Blahut algorithm and its application to
quantum information bottleneck [55.22418739014892]
We generalize the quantum Arimoto-Blahut algorithm by Ramakrishnan et al.
We apply our algorithm to the quantum information bottleneck with three quantum systems.
Our numerical analysis shows that our algorithm is better than their algorithm.
arXiv Detail & Related papers (2023-11-19T00:06:11Z) - Benchmarking Adaptative Variational Quantum Algorithms on QUBO Instances [0.0]
Adaptative VQAs dynamically modify the circuit structure by adding and removing, and optimize their parameters during the training.
We analyze three Adaptative VQAs: Variational Quantum Eigensolver (EVQE), Variable Ansatz (VAns), and Random Adapt-VQE (RA-VQE), a random approach we introduce as a baseline.
Our analysis sets benchmarks for Adaptative VQAs designed for near-term quantum devices.
arXiv Detail & Related papers (2023-08-03T14:39:02Z) - 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) - QNEAT: Natural Evolution of Variational Quantum Circuit Architecture [95.29334926638462]
We focus on variational quantum circuits (VQC), which emerged as the most promising candidates for the quantum counterpart of neural networks.
Although showing promising results, VQCs can be hard to train because of different issues, e.g., barren plateau, periodicity of the weights, or choice of architecture.
We propose a gradient-free algorithm inspired by natural evolution to optimize both the weights and the architecture of the VQC.
arXiv Detail & Related papers (2023-04-14T08:03:20Z) - 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 Comparative Study On Solving Optimization Problems With Exponentially
Fewer Qubits [0.0]
We evaluate and improve an algorithm based on Variational Quantum Eigensolver (VQE)
We highlight the numerical instabilities generated by encoding the problem into the variational ansatz.
We propose a classical optimization procedure to find the ground-state of the ansatz in less iterations with a better objective.
arXiv Detail & Related papers (2022-10-21T08:54:12Z) - Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle.
We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm.
We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
arXiv Detail & Related papers (2022-05-26T20:32:36Z) - Quantum Error Mitigation Relying on Permutation Filtering [84.66087478797475]
We propose a general framework termed as permutation filters, which includes the existing permutation-based methods as special cases.
We show that the proposed filter design algorithm always converges to the global optimum, and that the optimal filters can provide substantial improvements over the existing permutation-based methods.
arXiv Detail & Related papers (2021-07-03T16:07:30Z)
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.