Quantum Diffusion Monte Carlo Method for Josephson Junction Arrays

Well, to be specific i am not that ambitious. What i focus on at the moment is more on using computatoinal technique to solve the Josephson Junction Array (JJA) quantum circuit's Shroedinger equation. Specifically i am trying to first solve the ground state (GS) energy of a generic JJA circuits. In the next step i have to use excited state Monte Carlo (MC)to solve the excited state energies as well. If one knows the energy spectrum of the JJA circuit (at least the first few excited energies) and can ascertain that provides avenue as a two-level quantum system, then such a JJA is a possible qubit. With the code I am developing, I can evaluate the energy spectrum of the JJA and see how to control the energy spectrum via its explicit dependence on the control elements in the JJA (e.g. external magnetic field, voltage source, relative coupling strengths of the JJ, etc). In other words the code allow me to know how to control the qubit. the next step is to investigate the time evolution of the quantum state of the qubit, i.e. to solve the JJA TIME DEPENDENT schrodinger equation.

It is a `simple' project in the sense that this is a computational project that can be quite straight forwardly done get the results published relatively easy. To a certain extent it is not that trivial because one have to know how to use the right computational technique to solve the Schrodinger equation of the JJA system. It is not a trivial task because the number of degree of freedom (dof) is `large' (N=9), and most usual computational techniques can't handle it. We found that Quantum Monte Carlo (QMC) methods are suitable in the sense that it allow the solution to be found very fast. With the other methods, e.g. the Lanzcos method, a single value takes ~ 30 mins, whereas with Diffusioin MC, it takes only around 5 - 10 mins.