We present the analog analogue of Grover's problem as an example of the time-independent Hamiltonian for applying the speed limit of the imaginary-time Schrödinger equation derived by Okuyama and Ohzeki and t...We present the analog analogue of Grover's problem as an example of the time-independent Hamiltonian for applying the speed limit of the imaginary-time Schrödinger equation derived by Okuyama and Ohzeki and the new class of energy-time uncertainty relation proposed by Kieu. It is found that the computational time of the imaginary-time quantum annealing of this Grover search can be exponentially small, while the counterpart of the quantum evolution driven by the real-time Schrödinger equation could only provide square root speedup, compared with classic search. The present results are consistent with the cases of the time-dependent quantum evolution of the natural Grover problem in previous works. We once again emphasize that the logarithm and square root algorithmic performances are generic in imaginary-time quantum annealing and quantum evolution driven by real-time Schrödinger equation, respectively. Also, we provide evidences to search deep reasons why the imaginary-time quantum annealing can lead to exponential speedup and the real-time quantum annealing can make square root speedup.展开更多
In this paper,we introduce a novel approach in quantum field theories to estimate actions using artificial neural networks(ANNs).The actions are estimated by learning system configurations governed by the Boltzmann fa...In this paper,we introduce a novel approach in quantum field theories to estimate actions using artificial neural networks(ANNs).The actions are estimated by learning system configurations governed by the Boltzmann factor,e^(-s),at different temperatures within the imaginary time formalism of thermal field theory.Specifically,we focus on the 0+1 dimensional quantum field with kink/anti-kink configurations to demonstrate the feasibility of the method.Continuous-mixture autoregressive networks(CANs)enable the construction of accurate effective actions with tractable probability density estimation.Our numerical results demonstrate that this methodology not only facilitates the construction of effective actions at specified temperatures but also adeptly estimates the action at intermediate temperatures using data from both lower and higher temperature ensembles.This capability is especially valuable for detailed exploration of phase diagrams.展开更多
We re-examine physical causal propagators for scalar and pseudoscalar bound states at finite temperature in a chiral NJL model, defined by four-point amputated functions subtracted through the gap equation, and prove...We re-examine physical causal propagators for scalar and pseudoscalar bound states at finite temperature in a chiral NJL model, defined by four-point amputated functions subtracted through the gap equation, and prove that they are completely equivalent in the imaginary-time and real-time formalisms by separating carefully the imaginary part of the zero-temperature loop integral. It is shown that the same thermal transformation matrix of the matrix propagators for these bound states in the real-time formalism is precisely the one of the matrix propagator for an elementary scalar particle and this fact shows the similarity of thermodynamic property between a composite and elementary scalar particle. The retarded and advanced propagators for these bound states are also given explicitly from the imaginary-time formalism.展开更多
We give an explicit proof of equivalence of the two-point function to one-loop order in the two formalisms of thermal theory based on the expressions in the real-time formalism and indicate that the key point of comp...We give an explicit proof of equivalence of the two-point function to one-loop order in the two formalisms of thermal theory based on the expressions in the real-time formalism and indicate that the key point of completing the proof is to separate carefully the imaginary part of the zero-temperature loop integral from relevant expressions and this fact will certainly be very useful for examination of the equivalent problem of two formalisms of thermal field theory in other theories, including the one of the propagators for scalar bound states in an NJL model.展开更多
The derivation of the quantum lattice Boltzmann model is reviewed with special emphasis on recent developments of the model,namely,the extension to a multi-dimensional formulation and the application to the computatio...The derivation of the quantum lattice Boltzmann model is reviewed with special emphasis on recent developments of the model,namely,the extension to a multi-dimensional formulation and the application to the computation of the ground state of the Gross-Pitaevskii equation(GPE).Numerical results for the linear and nonlinear Schr odinger equation and for the ground state solution of the GPE are also presented and validated against analytical results or other classical schemes such as Crank-Nicholson.展开更多
基金Project supported by the China Postdoctoral Science Foundation (Grant No. 2017M620322)the Priority Fund for the Postdoctoral Scientific and Technological Program of Hubei Province in 2017, the Seed Foundation of Huazhong University of Science and Technology (Grant No. 2017KFYXJJ070)the Science and Technology Program of Shenzhen of China (Grant No. JCYJ 20180306124612893).
文摘We present the analog analogue of Grover's problem as an example of the time-independent Hamiltonian for applying the speed limit of the imaginary-time Schrödinger equation derived by Okuyama and Ohzeki and the new class of energy-time uncertainty relation proposed by Kieu. It is found that the computational time of the imaginary-time quantum annealing of this Grover search can be exponentially small, while the counterpart of the quantum evolution driven by the real-time Schrödinger equation could only provide square root speedup, compared with classic search. The present results are consistent with the cases of the time-dependent quantum evolution of the natural Grover problem in previous works. We once again emphasize that the logarithm and square root algorithmic performances are generic in imaginary-time quantum annealing and quantum evolution driven by real-time Schrödinger equation, respectively. Also, we provide evidences to search deep reasons why the imaginary-time quantum annealing can lead to exponential speedup and the real-time quantum annealing can make square root speedup.
基金Supported by the National Natural Science Foundation of China(12375131(YJ),12375136(LH))the CUHK-Shenzhen university development Fund(UDF01003041)the BMBF funded KISS consortium(05D23RI1)in the ErUM-Data action plan(KZ).
文摘In this paper,we introduce a novel approach in quantum field theories to estimate actions using artificial neural networks(ANNs).The actions are estimated by learning system configurations governed by the Boltzmann factor,e^(-s),at different temperatures within the imaginary time formalism of thermal field theory.Specifically,we focus on the 0+1 dimensional quantum field with kink/anti-kink configurations to demonstrate the feasibility of the method.Continuous-mixture autoregressive networks(CANs)enable the construction of accurate effective actions with tractable probability density estimation.Our numerical results demonstrate that this methodology not only facilitates the construction of effective actions at specified temperatures but also adeptly estimates the action at intermediate temperatures using data from both lower and higher temperature ensembles.This capability is especially valuable for detailed exploration of phase diagrams.
文摘We re-examine physical causal propagators for scalar and pseudoscalar bound states at finite temperature in a chiral NJL model, defined by four-point amputated functions subtracted through the gap equation, and prove that they are completely equivalent in the imaginary-time and real-time formalisms by separating carefully the imaginary part of the zero-temperature loop integral. It is shown that the same thermal transformation matrix of the matrix propagators for these bound states in the real-time formalism is precisely the one of the matrix propagator for an elementary scalar particle and this fact shows the similarity of thermodynamic property between a composite and elementary scalar particle. The retarded and advanced propagators for these bound states are also given explicitly from the imaginary-time formalism.
文摘We give an explicit proof of equivalence of the two-point function to one-loop order in the two formalisms of thermal theory based on the expressions in the real-time formalism and indicate that the key point of completing the proof is to separate carefully the imaginary part of the zero-temperature loop integral from relevant expressions and this fact will certainly be very useful for examination of the equivalent problem of two formalisms of thermal field theory in other theories, including the one of the propagators for scalar bound states in an NJL model.
文摘The derivation of the quantum lattice Boltzmann model is reviewed with special emphasis on recent developments of the model,namely,the extension to a multi-dimensional formulation and the application to the computation of the ground state of the Gross-Pitaevskii equation(GPE).Numerical results for the linear and nonlinear Schr odinger equation and for the ground state solution of the GPE are also presented and validated against analytical results or other classical schemes such as Crank-Nicholson.
