A case study of variational quantum algorithms for a job shop scheduling problem

Amaro, David; Rosenkranz, Matthias; Fitzpatrick, Nathan; Hirano, Kōji; Fiorentini, Mattia

doi:10.1140/epjqt/s40507-022-00123-4

Cited by 32 publications

(14 citation statements)

References 35 publications

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“…In particular, the VQE has been proposed to solve combinatorial optimization problems [26][27][28]. Contrary to strongly-correlated quantum many-body systems, for combinatorial optimization problems the problem Hamiltonian is diagonal and the possible solutions correspond to basis states.…”

Section: Variational Quantum Eigensolver Using the Conditional Value ...mentioning

confidence: 99%

Towards Finding an Optimal Flight Gate Assignment on a Digital Quantum Computer

Chai¹,

Funcke²,

Hartung³

et al. 2023

Preprint

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We investigate the performance of the variational quantum eigensolver (VQE) for the optimal flight gate assignment problem. This problem is a combinatorial optimization problem that aims at finding an optimal assignment of flights to the gates of an airport, in order to minimize the passenger travel time. To study the problem, we adopt a qubit-efficient binary encoding with a cyclic mapping, which is suitable for a digital quantum computer. Using this encoding in conjunction with the Conditional Value at Risk (CVaR) as an aggregation function, we systematically explore the performance of the approach by classically simulating the CVaR-VQE. Our results indicate that the method allows for finding a good solution with high probability, and the method significantly outperforms the naive VQE approach. We examine the role of entanglement for the performance, and find that ansätze with entangling gates allow for better results than pure product states. Studying the problem for various sizes, our numerical data show that the scaling of the number of cost function calls for obtaining a good solution is not exponential for the regimes we investigate in this work.

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Section: Variational Quantum Eigensolver Using the Conditional Value ...mentioning

confidence: 99%

Towards Finding an Optimal Flight Gate Assignment on a Digital Quantum Computer

Chai¹,

Funcke²,

Hartung³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…In recent years, quantum computing has emerged as a promising platform on which to apply heuristic approaches to solve computationally expensive combinatorial optimization tasks [1][2][3][4][5][6][7][8]. Most of these approaches have in common that they consider a Quadratic Unconstrained Binary Optimization (QUBO) problem.…”

Section: Introductionmentioning

confidence: 99%

Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection

Zoufal

Mishmash

Sharma

et al. 2023

Quantum

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We introduce a variational quantum algorithm to solve unconstrained black box binary optimization problems, i.e., problems in which the objective function is given as black box. This is in contrast to the typical setting of quantum algorithms for optimization where a classical objective function is provided as a given Quadratic Unconstrained Binary Optimization problem and mapped to a sum of Pauli operators. Furthermore, we provide theoretical justification for our method based on convergence guarantees of quantum imaginary time evolution.To investigate the performance of our algorithm and its potential advantages, we tackle a challenging real-world optimization problem: feature selection. This refers to the problem of selecting a subset of relevant features to use for constructing a predictive model such as fraud detection. Optimal feature selection---when formulated in terms of a generic loss function---offers little structure on which to build classical heuristics, thus resulting primarily in ‘greedy methods’. This leaves room for (near-term) quantum algorithms to be competitive to classical state-of-the-art approaches. We apply our quantum-optimization-based feature selection algorithm, termed VarQFS, to build a predictive model for a credit risk data set with 20 and 59 input features (qubits) and train the model using quantum hardware and tensor-network-based numerical simulations, respectively. We show that the quantum method produces competitive and in certain aspects even better performance compared to traditional feature selection techniques used in today's industry.

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“…Due to this potential, there has been a rapid development in the study of the QAOA algo-rithm and its components, including (but not limited to) theoretical observations and limitations [13][14][15][16][17][18][19][20], variations on the circuit structure (ansatz) [21][22][23][24][25] used, the cost function [26][27][28] and initialisation and optimisation methods [29][30][31][32][33][34] used for finding optimal solutions. Since the algorithm is suitable for near-term devices, there has also been substantial progress in experimental or numerical benchmarks [34][35][36][37][38] and the effect of quantum noise on the algorithm [39,40].…”

Section: Introductionmentioning

confidence: 99%

Graph neural network initialisation of quantum approximate optimisation

Jain

Coyle

Kashefi

et al. 2022

Quantum

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Approximate combinatorial optimisation has emerged as one of the most promising application areas for quantum computers, particularly those in the near term. In this work, we focus on the quantum approximate optimisation algorithm (QAOA) for solving the MaxCut problem. Specifically, we address two problems in the QAOA, how to initialise the algorithm, and how to subsequently train the parameters to find an optimal solution. For the former, we propose graph neural networks (GNNs) as a warm-starting technique for QAOA. We demonstrate that merging GNNs with QAOA can outperform both approaches individually. Furthermore, we demonstrate how graph neural networks enables warm-start generalisation across not only graph instances, but also to increasing graph sizes, a feature not straightforwardly available to other warm-starting methods. For training the QAOA, we test several optimisers for the MaxCut problem up to 16 qubits and benchmark against vanilla gradient descent. These include quantum aware/agnostic and machine learning based/neural optimisers. Examples of the latter include reinforcement and meta-learning. With the incorporation of these initialisation and optimisation toolkits, we demonstrate how the optimisation problems can be solved using QAOA in an end-to-end differentiable pipeline.

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A case study of variational quantum algorithms for a job shop scheduling problem

Cited by 32 publications

References 35 publications

Towards Finding an Optimal Flight Gate Assignment on a Digital Quantum Computer

Towards Finding an Optimal Flight Gate Assignment on a Digital Quantum Computer

Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection

Graph neural network initialisation of quantum approximate optimisation

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