Revisiting physics of quantum bits

Advancements in the technology of quantum bits invoke more precise calculations for decoherence and dissipative effects. In this thesis, the physics of truncated two level systems is revisited and it is shown that in some systems, such as in triple-junction superconducting flux qubit, environmental noises that are usually recognized to only have dissipative effects and the trivial resultant dephasing, can also cause pure dephasing. Furthermore, it is demonstrated that, in the current domain of interest for quantum computation purposes, the effective Hamiltonian of single molecule magnets in interaction with a spin bath differs from the commonly quoted result in the literature. It is also shown that the topological effects in such problems are as small as transitional effects to higher excited states beyond the two-level picture. Finally, a simulation of the quantum noise by the classical noise and a simulation of spin bath by oscillator bath for a quantum bit as the principal system are presented

Constraint propagation equations of the 3+1 decomposition of f(R) gravity

Theories of gravity other than general relativity (GR) can explain the observed cosmic acceleration without a cosmological constant. One such class of theories of gravity is f(R). Metric f(R) theories have been proven to be equivalent to Brans-Dicke (BD) scalar-tensor gravity without a kinetic term. Using this equivalence and a 3+1 decomposition of the theory it has been shown that metric f(R) gravity admits a well-posed initial value problem. However, it has not been proven that the 3+1 evolution equations of metric f(R) gravity preserve the (hamiltonian and momentum) constraints. In this paper we show that this is indeed the case. In addition, we show that the mathematical form of the constraint propagation equations in BD-equilavent f(R) gravity and in f(R) gravity in both the Jordan and Einstein frames, is exactly the same as in the standard ADM 3+1 decomposition of GR. Finally, we point out that current numerical relativity codes can incorporate the 3+1 evolution equations of metric f(R) gravity by modifying the stress-energy tensor and adding an additional scalar field evolution equation. We hope that this work will serve as a starting point for relativists to develop fully dynamical codes for valid f(R) models.Comment: 25 pages, matches published version in CQG, references update