Grover Search Inspired Alternating Operator Ansatz of Quantum
Approximate Optimization Algorithm for Search Problems
- URL: http://arxiv.org/abs/2204.10324v2
- Date: Fri, 28 Apr 2023 13:47:39 GMT
- Title: Grover Search Inspired Alternating Operator Ansatz of Quantum
Approximate Optimization Algorithm for Search Problems
- Authors: Chen-Fu Chiang and Paul M. Alsing
- Abstract summary: We use the mapping between two computation frameworks, Adiabatic Grover Search (AGS) and Adiabatic Quantum Computing (AQC)
We then apply Trotterization on the schedule-dependent Hamiltonian of AGS to obtain the values of variational parameters in the Quantum Approximate Optimization Algorithm (QAOA) framework.
- Score: 0.913755431537592
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: We use the mapping between two computation frameworks , Adiabatic Grover
Search (AGS) and Adiabatic Quantum Computing (AQC), to translate the Grover
search algorithm into the AQC regime. We then apply Trotterization on the
schedule-dependent Hamiltonian of AGS to obtain the values of variational
parameters in the Quantum Approximate Optimization Algorithm (QAOA) framework.
The goal is to carry the optimal behavior of Grover search algorithm into the
QAOA framework without the iterative machine learning processes.
Related papers
- 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) - Stochastic Ratios Tracking Algorithm for Large Scale Machine Learning
Problems [0.7614628596146599]
We propose a novel algorithm for adaptive step length selection in the classical SGD framework.
Under reasonable conditions, the algorithm produces step lengths in line with well-established theoretical requirements.
We show that the algorithm can generate step lengths comparable to the best step length obtained from manual tuning.
arXiv Detail & Related papers (2023-05-17T06:22:11Z) - Complement Grover's Search Algorithm: An Amplitude Suppression
Implementation [0.5352699766206808]
Grover's search algorithm was a groundbreaking advancement in quantum algorithms.
An extension of Grover's search algorithm is derived where the focus of the query is on the undesirable items.
Results are compared against QAOA.
arXiv Detail & Related papers (2022-09-21T16:38:36Z) - Quantitative approach to Grover's quantum walk on graphs [62.997667081978825]
We study Grover's search algorithm focusing on continuous-time quantum walk on graphs.
Instead of finding specific graph topologies convenient for the related quantum walk, we fix the graph topology and vary the underlying graph endowed Laplacians.
arXiv Detail & Related papers (2022-07-04T19:33:06Z) - Regret Bounds for Expected Improvement Algorithms in Gaussian Process
Bandit Optimization [63.8557841188626]
The expected improvement (EI) algorithm is one of the most popular strategies for optimization under uncertainty.
We propose a variant of EI with a standard incumbent defined via the GP predictive mean.
We show that our algorithm converges, and achieves a cumulative regret bound of $mathcal O(gamma_TsqrtT)$.
arXiv Detail & Related papers (2022-03-15T13:17:53Z) - Reflection-Based Adiabatic State Preparation [0.0]
Our algorithm deploys a sequence of reflections determined from eigenspaces of instantaneous Hamiltonians defined along an adiabatic schedule.
We provide numerical evidence suggesting that, for search problems, our algorithm can find a solution faster, on average, than Grover's search.
arXiv Detail & Related papers (2021-11-10T00:03:00Z) - Adaptive Approach For Sparse Representations Using The Locally
Competitive Algorithm For Audio [5.6394515393964575]
This paper presents an adaptive approach to optimize the gammachirp's parameters.
The proposed method consists of taking advantage of the LCA's neural architecture to automatically adapt the gammachirp's filterbank.
Results demonstrate an improvement in the LCA's performance with our approach in terms of sparsity, reconstruction quality, and convergence time.
arXiv Detail & Related papers (2021-09-29T20:26:16Z) - Provably Faster Algorithms for Bilevel Optimization [54.83583213812667]
Bilevel optimization has been widely applied in many important machine learning applications.
We propose two new algorithms for bilevel optimization.
We show that both algorithms achieve the complexity of $mathcalO(epsilon-1.5)$, which outperforms all existing algorithms by the order of magnitude.
arXiv Detail & Related papers (2021-06-08T21:05:30Z) - Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices.
We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT)
Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
arXiv Detail & Related papers (2020-10-01T18:14:11Z) - Convergence of adaptive algorithms for weakly convex constrained
optimization [59.36386973876765]
We prove the $mathcaltilde O(t-1/4)$ rate of convergence for the norm of the gradient of Moreau envelope.
Our analysis works with mini-batch size of $1$, constant first and second order moment parameters, and possibly smooth optimization domains.
arXiv Detail & Related papers (2020-06-11T17:43:19Z)
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.