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A comparison of various classical optimizers for a variational quantum linear solver

Aidan Pellow-Jarman, Ilya Sinayskiy, Anban Pillay, Francesco Petruccione
2021 Quantum Information Processing  
We focus specifically on the Variational Quantum Linear Solver (VQLS), and examine the effect of several gradient-free and gradient-based classical optimizers on performance.  ...  Variational Hybrid Quantum Classical Algorithms (VHQCAs) are a class of quantum algorithms intended to run on noisy intermediate-scale quantum (NISQ) devices.  ...  The results of this work are based upon the performance of the various classical optimizers in a variational quantum linear solver; it is left to a future work to investigate whether similar results are  ... 
doi:10.1007/s11128-021-03140-x fatcat:mxkkfvnhlfes7l42lzaavnvmrm

Near Term Algorithms for Linear Systems of Equations [article]

Aidan Pellow-Jarman, Ilya Sinayskiy, Anban Pillay, Francesco Petruccione
2021 arXiv   pre-print
This paper focuses on the Variational Quantum Linear Solvers (VQLS), and other closely related methods.  ...  Finding solutions to systems of linear equations is a common prob\-lem in many areas of science and engineering, with much potential for a speedup on quantum devices.  ...  Variational Quantum Linear Solver The standard VHQCA approach for the quantum linear systems problem is the Variational Quantum Linear Solver, itself being a basic application of the VQE.  ... 
arXiv:2108.11362v2 fatcat:kg35j7vp7jaudiwwdff72kkt7u

Practical application-specific advantage through hybrid quantum computing [article]

Michael Perelshtein, Asel Sagingalieva, Karan Pinto, Vishal Shete, Alexey Pakhomchik, Artem Melnikov, Florian Neukart, Georg Gesek, Alexey Melnikov, Valerii Vinokur
2022 arXiv   pre-print
The feasible route in achieving practical quantum advantage goals is to implement a hybrid operational mode that realizes the cohesion of quantum and classical computers.  ...  Quantum computing promises to tackle technological and industrial problems insurmountable for classical computers.  ...  For instance, variational algorithms for quantum chemistry, optimization, and machine learning that are particularly adapted for NISQ devices [20] also involve a classical heuristic optimization routine  ... 
arXiv:2205.04858v1 fatcat:434i4xg2obaybgwvcghugvembi

Quantum Computation for Predicting Solids-state Material Properties [article]

Kamal Choudhary
2021 arXiv   pre-print
Quantum algorithms such as variational quantum eigen solver (VQE) and variational quantum deflation (VQD) algorithms have been mainly applied for molecular systems and there is a need to implement such  ...  The WTBH model solvers can be used for testing other quantum algorithms also.  ...  The author thanks National Institute of Standards and Technology for computational and funding support.  ... 
arXiv:2102.11452v1 fatcat:nq64lnx2xren3dktqd4tixp44i

Variational Quantum Linear Solver with Dynamic Ansatz [article]

Hrushikesh Patil, Yulun Wang, Predrag Krstic
2021 arXiv   pre-print
In our study we introduce the dynamic ansatz in the Variational Quantum Linear Solver for a system of linear algebraic equations.  ...  Variational quantum algorithms have found success in the NISQ era owing to their hybrid quantum-classical approach which mitigate the problems of noise in quantum computers.  ...  [6] proposed a VHQCA for solving a system of linear equations called Variational Quantum Linear Solver (VQLS).  ... 
arXiv:2107.08606v3 fatcat:qhgygwgznbgrzdnat3bogsgi2u

Network Community Detection On Small Quantum Computers [article]

Ruslan Shaydulin, Hayato Ushijima-Mwesigwa, Ilya Safro, Susan Mniszewski, Yuri Alexeev
2019 arXiv   pre-print
We present a hybrid quantum local search (QLS) approach that combines a classical machine and a small quantum device to solve problems of practical size.  ...  comparable to state-of-the-art solvers in terms of quality of the solution including reaching the optimal solutions.  ...  Additionally, we implement a subset optimization routine that uses the classical Gurobi solver [55] for quality comparison.  ... 
arXiv:1810.12484v4 fatcat:chbg552itrd7fplesxkesxf7g4

Quantum computing for energy systems optimization: Challenges and opportunities

Akshay Ajagekar, Fengqi You
2019 Energy  
new realm of programming quantum computers for solving systems optimization problems.  ...  The basic concepts underlying quantum computation and their distinctive characteristics in comparison to their classical counterparts are also discussed.  ...  Atkinson Center for a Sustainable Future. List of References [1]  ... 
doi:10.1016/ fatcat:zgf5p27lofhg5pyyoounp4hacy

Optimizing the Production of Test Vehicles using Hybrid Constrained Quantum Annealing [article]

Adam Glos, Akash Kundu, Özlem Salehi
2022 arXiv   pre-print
We conclude that the performance of the CQM solver is comparable to classical solvers in optimizing the number of test vehicles.  ...  We formulate a constrained quadratic model for the problem and use a greedy algorithm to configure the cars.  ...  We would like to thank the organizers of BMW Group Quantum Computing Challenge for providing us with the exemplary dataset used in this manuscript  ... 
arXiv:2203.15421v1 fatcat:lznme6nlsza6fhrtvsfl5geiyu

Qibo: a framework for quantum simulation with hardware acceleration [article]

Stavros Efthymiou, Sergi Ramos-Calderer, Carlos Bravo-Prieto, Adrián Pérez-Salinas, Diego García-Martín, Artur Garcia-Saez, José Ignacio Latorre, Stefano Carrazza
2020 arXiv   pre-print
We present Qibo, a new open-source software for fast evaluation of quantum circuits and adiabatic evolution which takes full advantage of hardware accelerators.  ...  In this work we introduce a new quantum simulation framework that enables developers to delegate all complicated aspects of hardware or platform implementation to the library so they can focus on the problem  ...  Acknowledgements The Qibo framework is supported by the Quantum Research Centre at the Technology Innovation Institute in the United Arab Emirates [55] and the Qilimanjaro Quantum Tech in Spain [56]  ... 
arXiv:2009.01845v1 fatcat:wlhx7qtc7zdq3ibuefh6tocuqu

Multilevel Combinatorial Optimization Across Quantum Architectures [article]

Hayato Ushijima-Mwesigwa, Ruslan Shaydulin, Christian F. A. Negre, Susan M. Mniszewski, Yuri Alexeev, Ilya Safro
2020 arXiv   pre-print
In this paper, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms.  ...  Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems.  ...  In this work, we train our variational quantum optimizer (which can be considered a version of QAOA as described in Section 2.2) purely classically in simulation.  ... 
arXiv:1910.09985v5 fatcat:vfiv7l3gcjblpou37em6dzccja

Solving nonlinear differential equations with differentiable quantum circuits

Oleksandr Kyriienko, Annie E. Paine, Vincent E. Elfving
2021 Physical Review A  
We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits.  ...  We describe a hybrid quantum-classical workflow where DQCs are trained to satisfy differential equations and specified boundary conditions.  ...  ACKNOWLEDGMENT We thank Benno Broer for useful discussions on the subject and reading the manuscript.  ... 
doi:10.1103/physreva.103.052416 fatcat:cne4grlhs5cazbesh4rmmkmnpy

Prospects and challenges of quantum finance [article]

Adam Bouland, Wim van Dam, Hamed Joorati, Iordanis Kerenidis, Anupam Prakash
2020 arXiv   pre-print
For each application we describe the extent of quantum speedup possible and estimate the quantum resources required to achieve a practical speedup.  ...  as quantum annealing heuristics for portfolio optimization.  ...  Acknowledgments We thank Kay Giesecke, Rajiv Krishnakumar, Ashley Montanaro, Nikitas Stamatopoulos, and Will Zeng for helpful discussions and comments on this manuscript.  ... 
arXiv:2011.06492v1 fatcat:mqzj2a2pzzaz5pdcllxgkr73oq

Quantum Approximate Optimization for Hard Problems in Linear Algebra [article]

Ajinkya Borle, Vincent E. Elfving, Samuel J. Lomonaco
2021 arXiv   pre-print
The Quantum Approximate Optimization Algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks.  ...  Here, we explore using QAOA for Binary Linear Least Squares (BLLS); a problem that can serve as a building block of several other hard problems in linear algebra, such as the Non-negative Binary Matrix  ...  The D-wave quantum annealer was able to beat those classical solvers for the benchmark, but the authors also mention that a combination of the two classical techniques would probably perform better than  ... 
arXiv:2006.15438v3 fatcat:roy5nf56kfcnxhx2zacobqonfq

Quantum Algorithms for Solving Ordinary Differential Equations via Classical Integration Methods

Benjamin Zanger, Christian B. Mendl, Martin Schulz, Martin Schreiber
2021 Quantum  
Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations.  ...  We consider two approaches: (i) basis encoding and fixed-point arithmetic on a digital quantum computer, and (ii) representing and solving high-order Runge-Kutta methods as optimization problems on quantum  ...  Acknowledgments We would like to thank Udo Helmbrecht and Wolfgang Gehrke from the research institute CODE at the Universität der Bundeswehr München for facilitating a preliminary exploration of arithmetic  ... 
doi:10.22331/q-2021-07-13-502 fatcat:etngvjyanncd3bttxucduwiesa

Solving nonlinear differential equations with differentiable quantum circuits [article]

Oleksandr Kyriienko, Annie E. Paine, Vincent E. Elfving
2020 arXiv   pre-print
We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits.  ...  We describe a hybrid quantum-classical workflow where DQCs are trained to satisfy differential equations and specified boundary conditions.  ...  A patent application for the method described in this manuscript has been submitted by Qu&Co BV with OK, AP and VE as inventors.  ... 
arXiv:2011.10395v1 fatcat:yeteji53zrav7kal4chtpemtre
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