Minor Embedding in Broken Chimera and Pegasus Graphs is NP-complete

Lobe, Elisabeth; Lutz, Annette

doi:10.48550/arxiv.2110.08325

Cited by 5 publications

(6 citation statements)

References 18 publications

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“…That means several hardware vertices are combined to form a logical vertex to simulate an arbitrary problem connectivity. As we base the following work on it, we repeat and slightly extend the definition of [18] here for completeness:…”

Section: Graph Embeddingmentioning

confidence: 99%

“…Interesting applications, however, do usually not match those graphs straightforwardly but require what is known as an embedding [6], where each vertex of the original problem is mapped to several vertices in the hardware graph to represent the desired connectivity. Unfortunately, the problem of finding such an embedding is itself an NP-hard problem [18]. Although the connectivity is increased with every new hardware release, it is apparent that all of the graphs yield some kind of locality due to physical restrictions.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Sufficient Requirements on the Embedded Ising Problem in Polynomial Time

Lobe¹,

Kaibel²

2023

Preprint

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One of the central applications for quantum annealers is to find the solutions of Ising problems. Suitable Ising problems, however, need to be formulated such that they, on the one hand, respect the specific restrictions of the hardware and, on the other hand, represent the original problems which shall actually be solved. We evaluate sufficient requirements on such an embedded Ising problem analytically and transform them into a linear optimization problem. With an objective function aiming to minimize the maximal absolute problem parameter, the precision issues of the annealers are addressed. Due to the redundancy of several constraints, we can show that the formally exponentially large optimization problem can be reduced and finally solved in polynomial time for the standard embedding setting where the embedded vertices induce trees. This allows to formulate provably equivalent embedded Ising problems in a practical setup.

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Section: Graph Embeddingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Sufficient Requirements on the Embedded Ising Problem in Polynomial Time

Lobe¹,

Kaibel²

2023

Preprint

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“…This limitation restricts the correlations between optimization variables that can be represented by the Hamiltonian. Finding a suitable representation with these constraints is an NP-hard problem 55 that has to be solved classically to configure the quantum annealer for a certain problem. In practice, the quantum annealer can typically only be used for QUBOs with much less than 5000 optimization variables.…”

Section: Quantum and Classical Solversmentioning

confidence: 99%

An optimization case study for solving a transport robot scheduling problem on quantum-hybrid and quantum-inspired hardware

Leib,

Seidel,

Jäger

et al. 2023

Sci Rep

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We present a comprehensive case study comparing the performance of D-Waves’ quantum-classical hybrid framework, Fujitsu’s quantum-inspired digital annealer, and Gurobi’s state-of-the-art classical solver in solving a transport robot scheduling problem. This problem originates from an industrially relevant real-world scenario. We provide three different models for our problem following different design philosophies. In our benchmark, we focus on the solution quality and end-to-end runtime of different model and solver combinations. We find promising results for the digital annealer and some opportunities for the hybrid quantum annealer in direct comparison with Gurobi. Our study provides insights into the workflow for solving an application-oriented optimization problem with different strategies, and can be useful for evaluating the strengths and weaknesses of different approaches.

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“…These devices have limited connectivity resulting in extra qubits being needed to encode arbitrary QUBO problems (i.e., Ising models with interactions at arbitrary distances). Finding such an embedding, however, is in general a hard problem [221]. Thus heuristic algorithms [68] or precomputed templates [146] are typically used.…”

Section: Quantum Annealingmentioning

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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Minor Embedding in Broken Chimera and Pegasus Graphs is NP-complete

Cited by 5 publications

References 18 publications

Optimal Sufficient Requirements on the Embedded Ising Problem in Polynomial Time

Optimal Sufficient Requirements on the Embedded Ising Problem in Polynomial Time

An optimization case study for solving a transport robot scheduling problem on quantum-hybrid and quantum-inspired hardware

A Survey of Quantum Computing for Finance

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