Quantum statistical-mechanical iterative method in image restoration

Tanaka, Kazuyuki; Horiguchi, T.

doi:10.1002/(sici)1520-6440(200003)83:3<84::aid-ecjc9>3.0.co;2-n

Cited by 12 publications

(6 citation statements)

References 10 publications

(8 reference statements)

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“…This means that a phase transition occurs during the annealing procedure, and a quantum phase transition is known to be characterized by a vanishing energy gap in the thermodynamic limit [94]. + Several papers had proposed the term 'quantum annealing' [89,90,91] (see also [92,93]) before Ref. [18] formulated quantum annealing in its current style.…”

Section: Energy Gap and Computational Complexitymentioning

confidence: 99%

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Perspectives of quantum annealing: methods and implementations

et al. 2020

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Quantum annealing is a computing paradigm that has the ambitious goal of efficiently solving large-scale combinatorial optimization problems of practical importance. However, many challenges have yet to be overcome before this goal can be reached. This perspectives article first gives a brief introduction to the concept of quantum annealing, and then highlights new pathways that may clear the way towards feasible and large scale quantum annealing. Moreover, since this field of research is to a strong degree driven by a synergy between experiment and theory,

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Section: Energy Gap and Computational Complexitymentioning

confidence: 99%

“…+ Several papers had proposed the term 'quantum annealing' [89,90,91] (see also [92,93]) before Ref. [18] formulated quantum annealing in its current style.…”

Section: Energy Gap and Computational Complexitymentioning

confidence: 99%

Perspectives of quantum annealing: methods and implementations

et al. 2020

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“…called the target Hamiltonian. In QA, we utilize the transverse field Hamiltonian V = − N i=1 σx i as a source of quantum fluctuations to find the ground state of the target Hamiltonian ĤT [2][3][4][33][34][35][36]. We change the Hamiltonian as…”

mentioning

confidence: 99%

Shortcuts to adiabatic classical spin dynamics mimicking quantum annealing

Hatomura

Mori

2018

Phys. Rev. E

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We propose a simple construction of shortcuts to adiabaticity tracking instantaneous stationary states in classical spin systems without knowing tracked stationary states. In our construction, control fields of counter-diabatic driving are constituted by state-dependent magnetic fields, which can be easily determined with an aid of numerical calculations. Easiness of our construction is a remarkable feature since it is usually a hard task to determine explicit expression of required counter-diabatic terms in many-body systems. We also argue that our method can be applied to solve combinatorial optimization problems by considering classical spin dynamics under a timedependent Hamiltonian, which mimics the procedure of quantum annealing.

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“…In this section, on the other hand, we explain a deterministic method based on mean-field approximation according to Refs. [87,88]. Before we consider the quantum annealing based on the mean-field approximation, we treat the Ising model with random interactions and site-dependent longitudinal fields given by…”

Section: Deterministic Methods Based On Mean-field Approximationmentioning

confidence: 99%

Quantum Annealing: From Viewpoints of Statistical Physics, Condensed Matter Physics, and Computational Physics

Tanaka

2012

Kinki University Series on Quantum Computing

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In this paper, we review some features of quantum annealing and related topics from viewpoints of statistical physics, condensed matter physics, and computational physics. We can obtain a better solution of optimization problems in many cases by using the quantum annealing. Actually the efficiency of the quantum annealing has been demonstrated for problems based on statistical physics. Then the quantum annealing has been expected to be an efficient and generic solver of optimization problems. Since many implementation methods of the quantum annealing have been developed and will be proposed in the future, theoretical frameworks of wide area of science and experimental technologies will be evolved through studies of the quantum annealing.

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Quantum statistical-mechanical iterative method in image restoration

Cited by 12 publications

References 10 publications

Perspectives of quantum annealing: methods and implementations

Perspectives of quantum annealing: methods and implementations

Shortcuts to adiabatic classical spin dynamics mimicking quantum annealing

Quantum Annealing: From Viewpoints of Statistical Physics, Condensed Matter Physics, and Computational Physics

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