Related references
Note: Only part of the references are listed.
Article
Quantum Science & Technology
Stuart Hadfield et al.
Summary: We propose a framework for analyzing layered quantum algorithms and demonstrate its applications in various settings. The framework provides interpretable and insightful analysis of quantum alternating operator ansatze (QAOA) behavior and allows for the derivation of exact expressions for expectation values. Furthermore, we show that for certain parameter regimes, probability flows from lower to higher cost states in the QAOA(1) circuit. We also develop a classical random algorithm that emulates QAOA(1) with small error in the small-parameter regime. In addition, we extend the framework to deeper QAOA(p) circuits and demonstrate its superiority over random guessing in various scenarios.
QUANTUM SCIENCE AND TECHNOLOGY
(2023)
Review
Physics, Multidisciplinary
Kishor Bharti et al.
Summary: NISQ computers, composed of noisy qubits, are already being used in various fields. This review provides a comprehensive summary of NISQ computational paradigms and algorithms and introduces various benchmarking and software tools for programming and testing NISQ devices.
REVIEWS OF MODERN PHYSICS
(2022)
Article
Mathematics
Daniil Rabinovich et al.
Summary: The quantum approximate optimisation algorithm combines quantum processing and classical outer-loop optimisation to approximately minimise the problem's generator. The optimal algorithm parameters reduce to one free variable in certain conditions, and a linear relation between circuit parameters is found due to the vanishing gradients of the overlap function.
Article
Physics, Multidisciplinary
Martin Larocca et al.
Article
Physics, Multidisciplinary
Akel Hashim et al.
Summary: This work focuses on optimizing the execution of SWAP networks for QAOA by utilizing native hardware operations and equivalent circuit averaging techniques to reduce errors in quantum circuits.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Quantum Science & Technology
Daniel J. Egger et al.
Summary: This paper discusses the application of quantum algorithms in integer programming and combinatorial optimization problems, as well as combining quantum algorithms with classical algorithms' performance guarantees through warm start. Experimental results in different problem domains show that warm-starting quantum algorithms is particularly beneficial at low depths and leads to systematic improvements for specific problems.
Article
Physics, Multidisciplinary
Matthew P. Harrigan et al.
Summary: Research demonstrates the application of Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems. Performance depends on problem type and circuit depth, with subpar results for non-native problems, suggesting a need for more focus.
Article
Physics, Multidisciplinary
Lucas T. Brady et al.
Summary: Quantum annealing (QA) and quantum approximate optimization algorithm (QAOA) are two special cases for controlling quantum state energy minimization. Analytical application of optimal control theories showed that optimal procedures have a mix of pulsed (QAOA-like) structure at beginning and end, and smooth annealing structure in middle. Simulation results on Ising models support the theory, suggesting bang-anneal-bang protocols are more common than previously thought and provide guidelines for experimental implementations.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Andrew M. Childs et al.
Summary: The Lie-Trotter formula and its higher-order generalizations offer a direct approach to decomposing the exponential of a sum of operators, with a theory of Trotter error developed to provide tighter error bounds. This theory, which exploits the commutativity of operator summands, has applications in digital quantum simulation and quantum Monte Carlo methods, improving algorithms for various systems and simulations. The analysis shows that product formulas can preserve the locality of the simulated system, allowing for simulations of local observables with complexity independent of system size for power-law interacting systems.
Article
Optics
Pablo Diez-Valle et al.
Summary: Quantum variational optimization is proposed as an alternative approach for solving optimization problems faster and at larger scale than classical methods. The study focuses on the role of entanglement, the structure of quantum circuits, and the optimization problem's structure, showing advantages in adapting entangling gates distribution to problem topology and applying conditional value-at-risk cost functions. Results suggest the potential of outperforming existing NISQ architectures in certain regimes.
Review
Physics, Applied
M. Cerezo et al.
Summary: Variational quantum algorithms, utilizing classical optimizers to train parameterized quantum circuits, have emerged as a leading strategy to address the limitations of quantum computing. Despite challenges, they appear to be the best hope for achieving quantum advantage.
NATURE REVIEWS PHYSICS
(2021)
Article
Optics
V Akshay et al.
Summary: The quantum approximate optimization algorithm (QAOA) exhibits parameter concentrations, with optimal parameters focusing in an inverse polynomial fashion with problem size. This provides an optimistic outlook for circuit training efficiency.
Article
Computer Science, Artificial Intelligence
Max Wilson et al.
Summary: Variational quantum algorithms, a class of quantum heuristics, are promising candidates for useful quantum computation. Meta-learners show higher performance and resistance to noise compared to other optimizers like evolutionary strategies, L-BFGS-B, and Nelder-Mead methods, making them integral for the application of noisy near-term quantum computers.
QUANTUM MACHINE INTELLIGENCE
(2021)
Article
Optics
Michael Streif et al.
Summary: Quantum circuits with local particle-number conservation restrict computation to a subspace and can provide more resource-efficient error-mitigation techniques. This study analyzes the probability of staying in symmetry-preserved subspaces under noise, specifically local depolarizing noise, and applies these findings to evaluate the symmetry robustness of the XY quantum alternating operator Ansatz under depolarizing noise. Additionally, the influence of encoding choice on symmetry robustness and a simple adaption of the bit-flip code to correct for symmetry-breaking errors are discussed.
Article
Optics
Ernesto Campos et al.
Summary: The widely held belief in the trainability of quantum circuits in a layered manner has been proven wrong, as there are cases where abrupt transitions occur, showing that not all circuits can be trained piecewise.
Article
Quantum Science & Technology
Alicia B. Magann et al.
Summary: The development of quantum technologies has made significant progress over the past decade. While fault-tolerant devices are still years away, current noisy intermediate-scale quantum devices can be used for other purposes. Variational quantum algorithms (VQAs) are a leading candidate, but their implementations on quantum devices have yet to show improvements over classical capabilities. This Perspective discusses various ways in which the performance of VQAs could be enhanced by quantum optimal control theory, highlighting the importance of sufficient control resources in VQA implementations and addressing open questions for the future.
Article
Physics, Multidisciplinary
V Akshay et al.
PHYSICAL REVIEW LETTERS
(2020)
Article
Quantum Science & Technology
Panagiotis Kl. Barkoutsos et al.
Article
Physics, Multidisciplinary
Leo Zhou et al.
Article
Multidisciplinary Sciences
Article
Physics, Multidisciplinary
Sergey Bravyi et al.
PHYSICAL REVIEW LETTERS
(2020)
Article
Engineering, Electrical & Electronic
Deanna M. Abrams et al.
NATURE ELECTRONICS
(2020)
Article
Quantum Science & Technology
Roeland Wiersema et al.
Article
Optics
Zhihui Wang et al.
Article
Physics, Multidisciplinary
Li Li et al.
PHYSICAL REVIEW RESEARCH
(2020)
Article
Computer Science, Artificial Intelligence
Stuart Hadfield et al.
Proceedings Paper
Computer Science, Theory & Methods
Minsung Kim et al.
SIGCOMM '19 - PROCEEDINGS OF THE ACM SPECIAL INTEREST GROUP ON DATA COMMUNICATION
(2019)
Article
Physics, Multidisciplinary
Ian D. Kivlichan et al.
PHYSICAL REVIEW LETTERS
(2018)
Article
Multidisciplinary Sciences
Jarrod R. McClean et al.
NATURE COMMUNICATIONS
(2018)
Article
Quantum Science & Technology
Davide Venturelli et al.
QUANTUM SCIENCE AND TECHNOLOGY
(2018)
Article
Multidisciplinary Sciences
Abhinav Kandala et al.
Article
Physics, Multidisciplinary
Zhi-Cheng Yang et al.
Article
Optics
F Vatan et al.
