采用横向铁磁交互作用的随机场伊辛模型的量子退火算法
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摘要
通过数值对角化分析瞬时基态和第一激发态,提出基于横向铁磁交互的量子退火的优势.采用贝特近似作为实际执行的算法,给出相应的模拟结果,并对传统量子退火、基于横向铁磁交互作用的量子退火和模拟退火算法的剩余误差进行比较.结果表明:所提算法能有效提高传统量子退火在随机场伊辛模型中的收敛速度;利用量子波动的选择空间可以有效实现量子退火的最佳性能.
Through the numerical analysis of the instantaneous ground state and the first excited state,the advantages of quantum annealing based on the transverse ferromagnetic interactions are presented.Using the Bethe approximation as an algorithm for practical implementation,the simulation results are given accordingly.Then the residual errors of conventional quantum annealing,quantum annealing by transverse ferromagnetic interactions,and simulated annealing are compared.The results show that the proposed algorithm can effectively improve the convergence speed of traditional quantum annealing in the random-field Ising model.And the best performance of quantum annealing can be achieved by using the choice space of the quantum fluctuation.
Through the numerical analysis of the instantaneous ground state and the first excited state,the advantages of quantum annealing based on the transverse ferromagnetic interactions are presented.Using the Bethe approximation as an algorithm for practical implementation,the simulation results are given accordingly.Then the residual errors of conventional quantum annealing,quantum annealing by transverse ferromagnetic interactions,and simulated annealing are compared.The results show that the proposed algorithm can effectively improve the convergence speed of traditional quantum annealing in the random-field Ising model.And the best performance of quantum annealing can be achieved by using the choice space of the quantum fluctuation.
引文
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[17]CAO Huaixin,GUO Zhihua,CHEN Zhengli.CPT-frames for non-Hermitian Hamiltonians[J].Commun TheorPhys,2013,60(9):328-334.
[18]SEMKIN S V,SMAGIN V P.Bethe approximation in the Ising model with mobile impurities[J].Physics of the Solid State,2015,57(5):943-948.
[19]MEILIKHOV E Z,FARZETDINOVA R M.Effective field theory for disordered magnetic alloys[J].Physics of the Solid State,2014,56(4):707-714.
[20]ALAVAl M,DUXBURY P,MOUKARAEL C,et al.Exact combinatorial algorithms:Ground states of disordered systems[M].New York:Phase Transitions and Critial Phenomena,2001:143-317.
[2]王凌.智能优化算法及其应用[M].北京:清华大学出版社,2004:17-35.
[3]张德富,彭煜,朱文兴,等.求解三维装箱问题的混合模拟退火算法[J].计算机学报,2009,32(11):2147-2156.
[4]KIRKPATRICK S C,GELATT C D,VECCHI M P,et al.Optimizationby simulated annealing[J].Science,1983,220(4598):671-680.
[5]HOPFIELD J J,TANK D W.Computation of decisions:A model[J].Science,1986,233(4764):625-633.
[6]KADOWAKI T.Study of optimization problems by quantum annealing[D].Tokyo:Tokyo Institute of Technology,2002:15-40.
[7]MARTONAK R,SANTORO G E,TOSATTI E.Quantum annealing by the path-integral Monte carlo method:The two-dimensional random Ising model[J].Physical Review B,2002,66(9):351-363.
[8]LORENZO S,SANTORO G E.Quantum annealing of an Ising spin-glass by Green′s function Monte carlo[J].Physical Review E,2007,75(3):036703.
[9]SARJALA M,PETAJA V,ALAVA M.Optimization in random field Ising models by quantum annealing[J].Journal of Statistical Mechanics:Theory and Experiment,2006,16(1):79-107.
[10]KADOWAKI T,NISHIMORI H.Quantum annealing in the transverse Ising model[J].Physical Review E,1998,58(5):5355.
[11]BOIXO S,ALBASH T,SPEDALIERI F M,et al.Experimental signature of programmable quantum annealing[J].Nature Communications,2012,4(3):131-140.
[12]BOIXO S,RONNOW T F,ISAKO S V,et al.Evidence for quantum annealing with more than one hundred qubits[J].Nature Physics,2014,10(3):218-224.
[13]FYTAS N G,MARTIN-MAYOR V.Universality in the three-dimensional random-field Ising model[J].Phys Rev Lett,2013,110(1):019903.
[14]黄纯青,邓绍军.三维Ising模型的蒙特卡罗模拟[J].计算物理,2009,26(6):937-941.
[15]张映玉,付樟华.绝热量子优化算法研究进展[J].计算机工程与科学,2015,37(3):429-433.
[16]曹怀信,王素媛.量子绝热定理研究[J].纺织高校基础科学学报,2015,28(2):131-138.
[17]CAO Huaixin,GUO Zhihua,CHEN Zhengli.CPT-frames for non-Hermitian Hamiltonians[J].Commun TheorPhys,2013,60(9):328-334.
[18]SEMKIN S V,SMAGIN V P.Bethe approximation in the Ising model with mobile impurities[J].Physics of the Solid State,2015,57(5):943-948.
[19]MEILIKHOV E Z,FARZETDINOVA R M.Effective field theory for disordered magnetic alloys[J].Physics of the Solid State,2014,56(4):707-714.
[20]ALAVAl M,DUXBURY P,MOUKARAEL C,et al.Exact combinatorial algorithms:Ground states of disordered systems[M].New York:Phase Transitions and Critial Phenomena,2001:143-317.