Portfolio Asset Identification Using Graph Algorithms on a Quantum Annealer

Kalra, Angad; Qureshi, Faisal Z.; Tisi, Michael

doi:10.2139/ssrn.3333537

Cited by 8 publications

(4 citation statements)

References 16 publications

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“…Graphs offer a convenient framework to model portfolio management problems in finance. Specifically, here we outline a risk diversification strategy, but similar considerations apply for the implementation of hedging strategies [108]. We consider a (potentially very large) universe of n assets, for which we are given a vector µ ∈ R n describing expected future returns, and the covariance matrix Σ ∈ R n×n capturing volatility through the correlations among assets.…”

Section: Applications In Industrymentioning

confidence: 99%

“…Correlations can be described in graph form, either by directly taking the cross-correlation matrix as a weighted adjacency matrix, or by creating a binary adjacency matrix A through thresholding. We set A i,j = 1 if and only if the absolute value of the correlation between assets i and j is greater than some user-specific threshold parameter λ, and A i,j = 0 otherwise [108]. Accordingly, in our model pairs of assets are classified as correlated or uncorrelated, based on whether or not the corresponding correlation coefficient exceeds a minimum level.…”

Section: Applications In Industrymentioning

confidence: 99%

See 1 more Smart Citation

Combinatorial optimization with physics-inspired graph neural networks

Schuetz

Brubaker²,

Katzgraber

2022

Nat Mach Intell

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Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical physics is still outstanding. Here we demonstrate how graph neural networks can be used to solve combinatorial optimization problems. Our approach is broadly applicable to canonical NP-hard problems in the form of quadratic unconstrained binary optimization problems, such as maximum cut, minimum vertex cover, maximum independent set, as well as Ising spin glasses and higher-order generalizations thereof in the form of polynomial unconstrained binary optimization problems. We apply a relaxation strategy to the problem Hamiltonian to generate a differentiable loss function with which we train the graph neural network and apply a simple projection to integer variables once the unsupervised training process has completed. We showcase our approach with numerical results for the canonical maximum cut and maximum independent set problems. We find that the graph neural network optimizer performs on par or outperforms existing solvers, with the ability to scale beyond the state of the art to problems with millions of variables.

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Section: Applications In Industrymentioning

confidence: 99%

Section: Applications In Industrymentioning

confidence: 99%

Combinatorial optimization with physics-inspired graph neural networks

Schuetz

Brubaker²,

Katzgraber

2022

Nat Mach Intell

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“…This problem can be modified to include budget constraints. With regard to this problem, Kalra et al used a time-indexed correlation graph such that the vertices represent assets and an edge between vertices represents the existence of a significant correlation between them [183]. The price changes are modeled by data collected daily.…”

Section: Combinatorial Formulations the First Combinatorial Formulati...mentioning

confidence: 99%

A Survey of Quantum Computing for Finance

Herman¹,

Googin²,

Liu³

et al. 2022

Preprint

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Quantum computers are expected to surpass the computational capabilities of classical computers during this decade and have transformative impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from quantum computing, not only in the medium and long terms, but even in the short term. This survey paper presents a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on Monte Carlo integration, optimization, and machine learning, showing how these solutions, adapted to work on a quantum computer, can help solve more efficiently and accurately problems such as derivative pricing, risk analysis, portfolio optimization, natural language processing, and fraud detection. We also discuss the feasibility of these algorithms on near-term quantum computers with various hardware implementations and demonstrate how they relate to a wide range of use cases in finance. We hope this article will not only serve as a reference for academic researchers and industry practitioners but also inspire new ideas for future research.

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“…Recent QUBO quantum computing applications, complementing earlier applications on classical computing systems, include those for graph partitioning problems in Mniszewski et al (2016) and Ushijima-Mwesigwa et al (2017); graph clustering (quantum community detection problems) in Negre et al (2018Negre et al ( , 2019; traffic-flow optimization in Neukart et al (2017); vehicle routing problems in Feld et al (2018), Clark et al (2019) and Ohzeki et al(2018); maximum clique problems in Chapuis et al (2018); cybersecurity problems in Munch et al (2018) and Reinhardt et al(2018); predictive health analytics problems in De Oliveira et al (2018) and Sahner et al (2018); and financial portfolio management problems in Elsokkary et al (2017) and Kalra et al (2018). In another recent development, QUBO models are being studied using the IBM neuromorphic computer at as reported in Alom et al (2017) and Aimone et al (2018).…”

Section: Section 6: Connections To Quantum Computing and Machine Lear...mentioning

confidence: 99%

Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

Glover

Kochenberger²,

Du³

2019

4OR-Q J Oper Res

201

139

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The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in physics, the QUBO model has emerged as an underpinning of the quantum computing area known as quantum annealing and Fujitsu's digital annealing, and has become a subject of study in neuromorphic computing. Through these connections, QUBO models lie at the heart of experimentation carried out with quantum computers developed by D-Wave Systems and neuromorphic computers developed by IBM. The consequences of these new computational technologies and their links to QUBO models are being explored in initiatives by organizations such as Google, Amazon and Lockheed Martin in the commercial realm and Los Alamos National Laboratory, Oak Ridge National Laboratory, Lawrence Livermore National Laboratory and NASA's Ames Research Center in the public sector. Computational experience is being amassed by both the classical and the quantum computing communities that highlights not only the potential of the QUBO model but also its effectiveness as an alternative to traditional modeling and solution methodologies.

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Portfolio Asset Identification Using Graph Algorithms on a Quantum Annealer

Cited by 8 publications

References 16 publications

Combinatorial optimization with physics-inspired graph neural networks

Combinatorial optimization with physics-inspired graph neural networks

A Survey of Quantum Computing for Finance

Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

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