2017/05/09 by Takuya Hatomura · 23 citations
Computer Science · Mathematics · Physics and Astronomy · #Adiabatic process #Adiabatic quantum computation #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Covariant Hamiltonian field theory #Diabatic #Hamiltonian (control theory) #Hamiltonian system #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum computer #Quantum many-body systems #Quantum mechanics #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.7566/jpsj.86.094002
published in Journal of the Physical Society of Japan 86(9), 094002 (Physical Society of Japan)
arxiv created 2017/05/09 · openalex created_date 2017/05/19 · openalex publication_date 2017/08/23 · arxiv updated 2017/08/24 · openalex updated_date 2026/08/05
The strategy of shortcuts to adiabaticity enables us to realize adiabatic dynamics in finite time. In the counter-diabatic driving approach, an auxiliary Hamiltonian which is called the counter-diabatic Hamiltonian is appended to an original Hamiltonian to cancel out diabatic transitions. The counter-diabatic Hamiltonian is constructed by using the eigenstates of the original Hamiltonian. Therefore, it is in general difficult to construct the counter-diabatic Hamiltonian for quantum many-body systems. Even if the counter-diabatic Hamiltonian for quantum many-body systems is obtained, it is generally non-local and even diverges at critical points. We construct an approximated counter-diabatic Hamiltonian for the infinite-range Ising model by making use of the mean-field approximation. An advantage of this method is that the mean-field counter-diabatic Hamiltonian is constructed by only local operators. We numerically demonstrate the effectiveness of this method through quantum annealing processes going the vicinity of the critical point. It is also confirmed that the mean-field counter-diabatic Hamiltonian is still well-defined in the limit to the critical point. The present method can take higher order contributions into account and is consistent with the variational approach for local counter-diabatic driving.