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Multistart Methods for Quantum Approximate Optimization [article]

Ruslan Shaydulin, Ilya Safro, Jeffrey Larson
2019 arXiv   pre-print
Hybrid quantum-classical algorithms such as the quantum approximate optimization algorithm (QAOA) are considered one of the most promising approaches for leveraging near-term quantum computers for practical  ...  We also demonstrate that reusing the optimal parameters from similar problems can improve the performance of classical optimization methods, expanding on similar results for MAXCUT.  ...  Clemson University is acknowledged for generous allotment of compute time on Palmetto cluster.  ... 
arXiv:1905.08768v3 fatcat:wcx6pxev4ne3vfzigmvprapjuu

Combining a Local Search and Grover's Algorithm in Black-Box Global Optimization

D. W. Bulger
2007 Journal of Optimization Theory and Applications  
Grover's quantum algorithm promises a quadratic acceleration for any problem formulable as a search. For unstructured search problems, its implementation and performance are well understood.  ...  This paper addresses the application of Grover's algorithm when a local search technique is available, thereby combining the quadratic acceleration with the acceleration seen in the multistart method.  ...  for pure random search and multistart, and upper bounds for the expected number of objective function oracle operations for Dürr and Høyer's method and the quantum basin hopper.  ... 
doi:10.1007/s10957-007-9168-2 fatcat:bsl6gjgyczfdfetwblaq3lb32a

Approaching the Quantum Speed Limit with Global-Local Optimization [article]

Jens Jakob Sørensen, Mikel Aranburu, Till Heinzel, Jacob Sherson
2018 arXiv   pre-print
We propose a Global-Local optimization algorithm for quantum control that combines standard local search methodologies with evolutionary algorithms.  ...  Jensen for useful discussions.  ...  The search for the most time-optimal control or Quantum Speed Limit (QSL) has attracted much attention in the literature [6] [7] [8] [9] .  ... 
arXiv:1802.07521v1 fatcat:s2i4zvunkzdvzgogw6gujcbacy

Accelerating Noisy VQE Optimization with Gaussian Processes [article]

Juliane Mueller, Wim Lavrijsen, Costin Iancu, Wibe de Jong
2022 arXiv   pre-print
We build this as a framework on top of local optimizations, for which we choose Implicit Filtering (ImFil) in this study.  ...  Hybrid variational quantum algorithms, which combine a classical optimizer with evaluations on a quantum chip, are the most promising candidates to show quantum advantage on current noisy, intermediate-scale  ...  In Section II, we provide a brief review of state-of-the-art optimizers used in quantum hybrid optimization, elaborating on the benefits and pitfalls of various optimization methods.  ... 
arXiv:2204.07331v3 fatcat:iatyhjq7prct5oubqj3kqdytpu

LEAP: Scaling Numerical Optimization Based Synthesis Using an Incremental Approach [article]

Ethan Smith, Marc G. Davis, Jeffrey Larson, Ed Younis, Costin Iancu, Wim Lavrijsen
2021 arXiv   pre-print
Despite its heuristics, LEAP has generated optimal circuits for many test cases with a priori known solutions.  ...  LEAP draws on the design of the optimal synthesis algorithm QSearch by extending it with an incremental approach to determine constant prefix solutions for a circuit.  ...  optimization-based methods.  ... 
arXiv:2106.11246v2 fatcat:6ed4ih26xjhrzmjrrcehc3fyjm

Syndrome decoding by quantum approximate optimization [article]

Ching-Yi Lai, Kao-Yueh Kuo, Bo-Jyun Liao
2022 arXiv   pre-print
We use the quantum approximate optimization algorithm (QAOA) to solve the syndrome decoding problem with elegantly-designed generator- and check-based cost Hamiltonians for classical and quantum codes.  ...  In addition, we show that a combinatorial optimization problem with additional redundant clauses may be more suitable for QAOA, while the number of qubits remains the same.  ...  Farhi, Goldstone, and Gutmann proposed a class of heurisitic algorithms, the quantum approximate optimization algorithm (QAOA), which can find approximate solutions to combinatorial optimization problems  ... 
arXiv:2207.05942v1 fatcat:pghxq5hoifd6tddj25cdtzygu4

Multistart Algorithm for Identifying All Optima of Nonconvex Stochastic Functions [article]

Prateek Jaiswal, Jeffrey Larson
2022 arXiv   pre-print
We demonstrate the performance of an implementation of our algorithm on nonconvex stochastic optimization problems, including identifying optimal variational parameters for the quantum approximate optimization  ...  We propose a multistart algorithm to identify all local minima of a constrained, nonconvex stochastic optimization problem.  ...  Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Accelerated Research for Quantum Computing program, under contract number DE-AC02-06CH11357.  ... 
arXiv:2108.13504v3 fatcat:gmypbychbvbejgqgvjicfwbaka

Exploring the quantum speed limit with computer games

Jens Jakob W. H. Sørensen, Mads Kock Pedersen, Michael Munch, Pinja Haikka, Jesper Halkjær Jensen, Tilo Planke, Morten Ginnerup Andreasen, Miroslav Gajdacz, Klaus Mølmer, Andreas Lieberoth, Jacob F. Sherson
2016 Nature  
These studies show why traditional optimization methods fail near the quantum speed limit, and they bring promise that combined analyses of optimization landscapes and heuristic solution strategies may  ...  The numerical complexity associated with time-optimal solutions increases for shorter process durations.  ...  Correspondence and requests for materials should be addressed to J.F.S. (  ... 
doi:10.1038/nature17620 pmid:27075097 fatcat:m6gxrxqanjbi5ek73n4pcqfwgq

Lyapunov control-inspired strategies for quantum combinatorial optimization [article]

Alicia B. Magann, Kenneth M. Rudinger, Matthew D. Grace, Mohan Sarovar
2021 arXiv   pre-print
The prospect of using quantum computers to solve combinatorial optimization problems via the quantum approximate optimization algorithm (QAOA) has attracted considerable interest in recent years.  ...  Here, we provide an expanded description of Lyapunov control-inspired strategies for quantum optimization, as first presented in arXiv:2103.08619, that do not require any classical optimization effort.  ...  More recently, the quantum approximate optimization algorithm (QAOA) [6] was proposed in 2014, as a method for leveraging quantum computers to solve combinatorial optimization problems.  ... 
arXiv:2108.05945v1 fatcat:6ruderyrpnavlfqmrmdiispq5u

Hessian-based optimization of constrained quantum control [article]

Mogens Dalgaard and Felix Motzoi and Jesper Hasseriis Mohr Jensen and Jacob Sherson
2020 arXiv   pre-print
Efficient optimization of quantum systems is a necessity for reaching fault tolerant thresholds.  ...  A standard tool for optimizing simulated quantum dynamics is the gradient-based grape algorithm, which has been successfully applied in a wide range of different branches of quantum physics.  ...  The x-axis is the Hessian-based optimized solutions while the y-axis is for the gradient-only method.  ... 
arXiv:2006.00935v2 fatcat:hx4hn54myvbynfrzbmwmimikbu

Quantum algorithm for molecular properties and geometry optimization

Ivan Kassal, Alán Aspuru-Guzik
2009 Journal of Chemical Physics  
For that purpose, we discuss the benefits of quantum techniques for Newton's method and Householder methods.  ...  Finally, global minima for the proposed optimizations can be found using the quantum basin hopper algorithm, which offers an additional quadratic reduction in cost over classical multi-start techniques  ...  For that purpose, we discuss the benefits of quantum techniques for Newton's method and Householder methods.  ... 
doi:10.1063/1.3266959 pmid:20001019 fatcat:p3iswwtayjavxjdvbgq5mrjpjm

The fixed angle conjecture for QAOA on regular MaxCut graphs [article]

Jonathan Wurtz, Danylo Lykov
2021 arXiv   pre-print
The quantum approximate optimization algorithm (QAOA) is a near-term combinatorial optimization algorithm suitable for noisy quantum devices.  ...  In this work, we provide numerical evidence for this fixed angle conjecture for p<12. We compute and provide these angles via numerical optimization and tensor networks.  ...  INTRODUCTION Near-term quantum computers have the potential for advantage in the field of combinatorial optimization.  ... 
arXiv:2107.00677v2 fatcat:u73tn32sjnba7lu2haruvfmerq

Evaluating Quantum Approximate Optimization Algorithm: A Case Study [article]

Ruslan Shaydulin, Yuri Alexeev
2019 arXiv   pre-print
Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum algorithms for the Noisy Intermediate-Scale Quantum (NISQ) era.  ...  We find that optimal QAOA parameters concentrate for instances in out benchmark, confirming the previous findings for a different class of problems.  ...  Clemson University is acknowledged for generous allotment of compute time on Palmetto cluster.  ... 
arXiv:1910.04881v1 fatcat:gtwv2qwo3bh3xn4a3fsjtbrlvq

Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers [article]

Xiaoyuan Liu, Anthony Angone, Ruslan Shaydulin, Ilya Safro, Yuri Alexeev, Lukasz Cincio
2021 arXiv   pre-print
We evaluate quantum optimization heuristics on the problem of detecting multiple communities in networks, for which we introduce a novel qubit-frugal formulation.  ...  We numerically compare L-VQE with Quantum Approximate Optimization Algorithm (QAOA) and demonstrate that QAOA achieves lower approximation ratios while requiring significantly deeper circuits.  ...  ACKNOWLEDGMENTS We thank Jeffrey Larson for help with tuning APOSMM for QAOA parameter optimization. Clemson University is acknowledged for generous allotment of compute time on the Palmetto cluster.  ... 
arXiv:2102.05566v2 fatcat:c3px2u3qhrcelejrnmu2ytru24

Non-Convex Optimization by Hamiltonian Alternation [article]

Anuj Apte, Kunal Marwaha, Arvind Murugan
2022 arXiv   pre-print
A major obstacle to non-convex optimization is the problem of getting stuck in local minima.  ...  We demonstrate this technique by using it to find the ground state for instances of a Sherrington-Kirkpatrick spin glass.  ...  Practitioners often use quasi-Newton methods [9] and stochastic gradient descent [10] to approximately solve non-convex optimization problems.  ... 
arXiv:2206.14072v1 fatcat:wmgkeeldxjhfnn7s7btuo2pptq
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