dorsal/arxiv
View SchemaConvergence of Quantum Annealing with Real-Time Schrodinger Dynamics
| Authors | Satoshi Morita, Hidetoshi Nishimori |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0702252 |
| URL | https://arxiv.org/abs/quant-ph/0702252 |
| DOI | 10.1143/JPSJ.76.064002 |
| Journal | J. Phys. Soc. Jpn. 76 (2007) 064002 |
Abstract
Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or transverse ferromagnetic interactions, and the time evolution follows the real-time Schrodinger equation. It is shown that the system stays arbitrarily close to the instantaneous ground state, finally reaching the target optimal state, if the strength of quantum fluctuations decreases sufficiently slowly, in particular inversely proportionally to the power of time in the asymptotic region. This is the same condition as the other implementations of quantum annealing, quantum Monte Carlo and Green's function Monte Carlo simulations, in spite of the essential difference in the type of dynamics. The method of analysis is an application of the adiabatic theorem in conjunction with an estimate of a lower bound of the energy gap based on the recently proposed idea of Somma et. al. for the analysis of classical simulated annealing using a classical-quantum correspondence.
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"abstract": "Convergence conditions for quantum annealing are derived for optimization\nproblems represented by the Ising model of a general form. Quantum fluctuations\nare introduced as a transverse field and/or transverse ferromagnetic\ninteractions, and the time evolution follows the real-time Schrodinger\nequation. It is shown that the system stays arbitrarily close to the\ninstantaneous ground state, finally reaching the target optimal state, if the\nstrength of quantum fluctuations decreases sufficiently slowly, in particular\ninversely proportionally to the power of time in the asymptotic region. This is\nthe same condition as the other implementations of quantum annealing, quantum\nMonte Carlo and Green\u0027s function Monte Carlo simulations, in spite of the\nessential difference in the type of dynamics. The method of analysis is an\napplication of the adiabatic theorem in conjunction with an estimate of a lower\nbound of the energy gap based on the recently proposed idea of Somma et. al.\nfor the analysis of classical simulated annealing using a classical-quantum\ncorrespondence.",
"arxiv_id": "quant-ph/0702252",
"authors": [
"Satoshi Morita",
"Hidetoshi Nishimori"
],
"categories": [
"quant-ph",
"cond-mat.dis-nn"
],
"doi": "10.1143/JPSJ.76.064002",
"journal_ref": "J. Phys. Soc. Jpn. 76 (2007) 064002",
"title": "Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics",
"url": "https://arxiv.org/abs/quant-ph/0702252"
},
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