Basics and Applications of Quantum Annealing

Tanaka, Shu; Tanahashi, Kôtarô; Motohashi, Tomomitsu; Takayanagi, Shinichi

doi:10.2221/jcsj.53.287

Cited by 2 publications

(3 citation statements)

References 17 publications

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“…The problem is converted to quadratic unconstrained binary optimization (QUBO) (e.g., [26], [27]) for computation using Digital Annealer. For the solution search, we use Digital Annealer inspired by quantum computing.…”

Section: Methodsmentioning

confidence: 99%

Formulation of Mindfulness States as a Network Optimization Problem and an Attempt to Identify Key Brain Pathways Using Digital Annealer

Nakamura

Tawatsuji

Matsui

et al. 2022

IEICE Trans. Inf. & Syst.

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Although intervention practices like mindfulness meditation have proven effective in treating psychosis, there is no clarity on the mechanism of information propagation in the brain. In this study, we formulated a network optimization problem and searched for the optimal solution using Digital Annealer developed by Fujitsu Ltd. This is inspired by quantum computing and is effective in solving large-scale combinatorial optimization problems to find the information propagation pathway in the brain that contributes to the realization of mindfulness. Specifically, we defined the optimal network state as the state of the brain network that is considered to be associated with the mindfulness state. We formulated the problem into two network optimization problems-the minimum vertexcover problem and the maximum-flow problem-to search for the information propagation pathway that is important for realizing the state. In the minimum vertex-cover problem, we aimed to identify brain regions that are important for the realization of the mindfulness state, and identified eight regions, including four that were suggested to be consistent with previous studies. We formulated the problem as a maximum-flow problem to identify the information propagation pathways in the brain that contribute to the activation of these four identified regions. As a result, approximately 30% of the connections in the brain network structure of this study were identified, and the pathway with the highest flow rate was considered to characterize the bottom-up emotion regulation during mindfulness. The findings of this study could be useful for more direct interventions in the context of mindfulness, which are being investigated by neurofeedback and other methods. This is because existing studies have not clarified the information propagation pathways that contribute to the realization of the brain network states that characterize mindfulness states. In addition, this approach may be useful as a methodology to identify information propagation pathways in the brain that contribute to the realization of higher-order human cognitive activities, such as mindfulness, within large-scale brain networks.

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Section: Methodsmentioning

confidence: 99%

Formulation of Mindfulness States as a Network Optimization Problem and an Attempt to Identify Key Brain Pathways Using Digital Annealer

Nakamura

Tawatsuji

Matsui

et al. 2022

IEICE Trans. Inf. & Syst.

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“…This method minimizes the number of edges added with node elimination. The function H cost , which minimizes the number of added edges, is defined in (2).…”

Section: B Quantum Minimum Fill-in Algorithmmentioning

confidence: 99%

“…Quantum annealing (QA) is an optimization technique that utilizes transitions between states due to quantum fluctuation effects to search for solutions [1], [2]. Since the development of QA machines with superconducting integrated circuits [3], [4], QA has attracted attention as a metaheuristic solution method for combinatorial optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Problem Relaxation Methods for Quantum Minimum Fill-in Algorithm

Komiyama,

Suzuki

2023

IEEE Access

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Current quantum annealing and quantum-inspired annealing devices have many usage limitations and are difficult to apply to real-scale problems. In particular, a major hardware limitation is the limited number of available variables (qubits). This paper proposes a problem relaxation method for the Quantum Minimum Fill-in (QMF) algorithm. QMF finds the ordering of matrix rows and columns that minimizes the incidence of fill-ins that occur when a direct solver is used to solve linear equations with sparse matrices. In general, the first few steps in the forward elimination of sparse matrices add the most fill-ins. Therefore, QMF was relaxed to order the rows and columns in only the first few steps. The results obtained using the Fixstars Amplify Annealing Engine, a quantum-inspired annealing device, show that the problem relaxation can be computed with 20%-60% of the qubits for the original problem and that relaxation can be applied to larger problems. Furthermore, it is found that more solutions that satisfy the constraints can be obtained with problem relaxation and that the number of fill-ins is reduced. These results confirm that the proposed problem relaxation is effective for QMF.

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Basics and Applications of Quantum Annealing

Cited by 2 publications

References 17 publications

Formulation of Mindfulness States as a Network Optimization Problem and an Attempt to Identify Key Brain Pathways Using Digital Annealer

Formulation of Mindfulness States as a Network Optimization Problem and an Attempt to Identify Key Brain Pathways Using Digital Annealer

Problem Relaxation Methods for Quantum Minimum Fill-in Algorithm

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