The quantum adiabatic algorithm applied to random optimization problems: The quantum spin glass perspective

Bapst, Victor; Foini, Laura; Krząkała, Florent; Semerjian, Guilhem; Zamponi, Francesco

doi:10.1016/j.physrep.2012.10.002

Cited by 144 publications

(181 citation statements)

References 312 publications

(779 reference statements)

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“…After a brief introduction to quantum annealing (see e.g., [8,16,17] for some recent reviews), we have proposed here an annealing scheme to reach the exact ground state of disordered spin systems with a satisfactory probability by tuning of both transverse and longitudinal fields. Here, we have applied the scheme on a small-size (N = 8) long-range interacting spin glass system.…”

Section: Resultsmentioning

confidence: 99%

Quantum annealing search of Ising spin glass ground state(s) with tunable transverse and longitudinal fields

Rajak

Chakrabarti

2014

Indian J Phys

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Here we first discuss briefly the quantum annealing technique. We then study the quantum annealing of Sherrington-Kirkpatrick spin glass model with the tuning of both transverse and longitudinal fields. Both the fields are time-dependent and vanish adiabatically at the same time, starting from high values. We solve, for rather small systems, the time-dependent Schrodinger equation of the total Hamiltonian by employing a numerical technique. At the end of annealing we obtain the final state having high overlap with the exact ground state(s) of classical spin glass system (obtained independently).

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Section: Resultsmentioning

confidence: 99%

Quantum annealing search of Ising spin glass ground state(s) with tunable transverse and longitudinal fields

Rajak

Chakrabarti

2014

Indian J Phys

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“…Mézard and Parisi [21] introduced this quantity in the study of disordered systems, calling the complexity, or configurational entropy. An equivalent quantity is used in the study of random optimization problems by means of statistical physics techniques [22].By following the analysis in [23], we shall call Eq. (1) Einstein's likelihood principle; it is a fundamental relation in Einstein's theory of fluctuations [20].…”

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confidence: 99%

Groups, information theory, and Einstein's likelihood principle

Sicuro

Tempesta

2016

Phys. Rev. E

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We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts. DOI: 10.1103/PhysRevE.93.040101 The study of the relations among statistical mechanics, information theory and the notion of entropy is at the heart of the science of complexity, and in the last decades has been widely explored. After the seminal works of Shannon and Tsallis [7], has been the prototype of the nonadditive entropies studied in the last decades [8][9][10][11][12][13]. These functionals are generalizations of the BG entropy; they depend on one or more parameters, in such a way that the BG entropy is recovered as a particular limit. Generalized entropies have been successfully adopted for the study of both classical and quantum systems. Rényi's entropy, for example, plays a central role in information theory and in the study of multifractality [14]; along with the von Neumann entropy, it has been also used extensively in the evaluation of the entanglement entropy of quantum systems [15][16][17][18].The study of new entropic forms has led to a new flow of ideas regarding the old problem of the probabilistic versus the dynamical foundations of the notion of entropy. It is well known [19] that Einstein's approach was very different with respect to the probabilistic methodology of Boltzmann (which eventually emerged as the predominant one). Indeed, Einstein argued that the probabilities of occupation of the various regions of the phase space associated with a physical system cannot be postulated a priori. Instead, only a knowledge of * sicuro@cbpf.br † p.tempesta@fis.ucm.es dynamics, obtained by solving the equations of motion, could provide this information. For this reason, in his theory of fluctuations, Einstein [20] introduced the likelihood function W ∝ exp (S BG ) as a fundamental statistical quantity (for the sake of simplicity, here and in the following, we put k B ≡ 1, k B being the Boltzmann constant). He observed that by composing two independent systems A and B, the fundamental relationholds. Equation (1) is epistemologically crucial: it expresses the fact that the physical description of system A does not depend on the physical description of system B, and vice versa. Moreover, it is related to the additivity requirement of the information content of ind...

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“…Landau-Zener transition problem which describes the population transfer between quantum states in a two level system has many different applications in today's atomic and molecular physics, quantum information science, quantum optics and other related fields [1][2][3][4][5][6]. This is while, Landau-Zener (LZ) transition model is being used extensively by experimentalists for preparation, manipulation and reading out of quantum states in two level systems (qubits) [2,6].…”

Section: Introductionmentioning

confidence: 99%

Investigation of Temperature Effect in Landau-Zener Avoided Crossing

Hosseini

Sarreshtedari

2017

IJOP

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ABSTRACT-Considering a temperature dependent two-level quantum system, we have numerically solved the Landau-Zener transition problem.The method includes the incorporation of temperature effect as a thermal noise added Schrödinger equation for the construction of the Hamiltonian. Here, the obtained results which describe the changes in the system including the quantum states and the transition probabilities are investigated and discussed. The results successfully describe the behavior of the transition probabilities by sweeping the temperature.

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The quantum adiabatic algorithm applied to random optimization problems: The quantum spin glass perspective

Cited by 144 publications

References 312 publications

Quantum annealing search of Ising spin glass ground state(s) with tunable transverse and longitudinal fields

Quantum annealing search of Ising spin glass ground state(s) with tunable transverse and longitudinal fields

Groups, information theory, and Einstein's likelihood principle

Investigation of Temperature Effect in Landau-Zener Avoided Crossing

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