FAST FORWARD OF ADIABATIC QUANTUM SPIN DYNAMICS - SETIAWAN (NIM : 30214004), IWAN
A method has been developed to accelerate adiabatic quantum dynamics on spin systems. This method is used to get the desired wave function in a shorter time. The adiabatic concept is used so that the system does not change the state during the speeding process. The adiabatic wave function is a wave function whose time parameter involves a very small adiabatic parameter ε and adds the regularization phase θ. In order for the system to satisfy the Schrodinger equation, the regularization term is also performed on the Hamiltonian system by adding the correction term to the initial Hamiltonian. This adiabatic speeding effort begins with obtaining the eigen state of the system through the original Hamiltonian. Furthermore, by examining only one eigen state, the regularization Hamiltonian and driving Hamiltonian are specified which involves the time-multiplication α leading to infinity and the adiabatic parameter ϵ leading to zero and through the concept αÃ‚Â·ϵ = finite . Regularization term and driving Hamiltonian that guarantee adiabatic accelerated systems are obtained by assuming the candidate of Hamiltonian regularization term which involves all possible interactions in the spin system i.e interactions between spins, three body interaction that only appear on the three spin system, as well as the magnetic field. This method is applied to single spin systems, two spin systems and three spin clusters. In a single spin system, a rotating spin model and a two-state Landau-Zener model are used. Applications on two-spin systems using transversal Ising models, XY model, quantum annealing model and general model of entanglement. The method of acceleration on a three-spin system is applied to transverse Ising model and quantum annealing model. In the case of a single spin, there is one regularization term and driving Hamiltonian that does not depend on eigenstate being reviewed (state-independent). In the two-spin system of the quantum annealing and the general model of entanglement each obtained three and two regularization terms and driving Hamiltonian that depend on the eigenstate (state-dependent) whereas in transverse Ising model and XY model we get only one solution that is state-independent. Three-spin system application in transverse Ising model obtained two solutions of regularization term whereas in quantum annealing model four solutions of regularization term were obtained. All solutions on this three-spin system are state-dependent. This method provides several advantages: a simpler calculation in determining the regularization term because it only consider one eigen state. In addition, the involvement of all possible interactions in the candidate of regularization term makes accelerating efforts more optimum as demonstrated by high fidelity values. The resulting diverse regularization term solutions will also add flexibility to this method.