Abstract
Quantum annealing is a generic solver of the optimization problem that uses fictitious quantum fluctuation. Its simulation in classical computing is often performed using the quantum Monte Carlo simulation via the Suzuki–Trotter decomposition. However, the negative sign problem sometimes emerges in the simulation of quantum annealing with an elaborate driver Hamiltonian, since it belongs to a class of non-stoquastic Hamiltonians. In the present study, we propose an alternative way to avoid the negative sign problem involved in a particular class of the non-stoquastic Hamiltonians. To check the validity of the method, we demonstrate our method by applying it to a simple problem that includes the anti-ferromagnetic XX interaction, which is a typical instance of the non-stoquastic Hamiltonians.
Highlights
Quantum annealing (QA) is a generic algorithm aimed at solving optimization problems by exploiting the quantum tunneling effect
We remark that the convergence of the estimations is relatively slow compared to the ordinary quantum Monte Carlo simulation because we have to estimate the expectation of the thermodynamic quantities as the effective transverse field f ′(mx) depending on the tentative value of the transverse magnetization
Substantial slowing down of the equilibration is not observed in the simple model, the computational time to correctly estimate the thermodynamic quantities might become longer depending on the model that is related to its complexity
Summary
Quantum annealing (QA) is a generic algorithm aimed at solving optimization problems by exploiting the quantum tunneling effect. The QA system with the transverse field is in a class of the stoquastic Hamiltonian, which can be straightforwardly simulated by use of the quantum Monte Carlo simulation in a classical computer[21]. The other type of quantum driver may be used for improving the performance of quantum annealing, a successful instance of which is the implementation of the anti-ferromagnetic XX interaction[22,23] This is a typical example of the non-stoquastic Hamiltonian, which cannot be straightforwardly simulated in a classical computer. We show a method to simulate a particular class of the non-stoquastic Hamiltonians including the anti-ferromagnetic XX interaction in the quantum Monte Carlo simulation. The future development of hardware devices to perform quantum annealing aims at implementing the non-stoquastic Hamiltonian such as the anti-ferromagnetic XX interaction beyond the classically simulatable world. Seki and Nishimori successfully avoided the first order phase transition by utilizing additional fluctuations, anti-ferromagnetic XX interactions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
