Physics – Quantum Physics
Scientific paper
2004-09-06
Physical Review E 70 (2004) 056218
Physics
Quantum Physics
Scientific paper
10.1103/PhysRevE.70.056218
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting phenomena such as fractal spectra, mixed phase space, dynamical localization, anomalous diffusion, or partial delocalization, and can describe electrons in a magnetic field. Three different quantum algorithms are presented and analyzed, enabling to simulate efficiently the evolution operator of this system with different precision using different resources. Depending on the parameters chosen, the system is near-integrable, localized, or partially delocalized. In each case we identify transport or spectral quantities which can be obtained more efficiently on a quantum computer than on a classical one. In most cases, a polynomial gain compared to classical algorithms is obtained, which can be quadratic or less depending on the parameter regime. We also present the effects of static imperfections on the quantities selected, and show that depending on the regime of parameters, very different behaviors are observed. Some quantities can be obtained reliably with moderate levels of imperfection, whereas others are exponentially sensitive to imperfection strength. In particular, the imperfection threshold for delocalization becomes exponentially small in the partially delocalized regime. Our results show that interesting behavior can be observed with as little as 7-8 qubits, and can be reliably measured in presence of moderate levels of internal imperfections.
Georgeot Bertrand
Lévi Benjamin
No associations
LandOfFree
Quantum Computation of a Complex System : the Kicked Harper Model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum Computation of a Complex System : the Kicked Harper Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Computation of a Complex System : the Kicked Harper Model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-375231