Quantum dots: Coulomb blockade, mesoscopic fluctuations, and qubit decoherence

The continuous minituarization of the integrated circuits is going to affect the underlying physics of the future computers. This new physics first came into play as the effect of Coulomb blockade in the electron transport through the small conducting island. Then, as the size of the island L continued to shrink further, quantum phase coherence length became larger than L leading to the mesoscopic fluctuations---fluctuations of the island's quantum mechanical properties upon small external perturbations. Quantum coherence of the mesoscopic systems is essential for building reliable quantum computer. Unfortunately, one can not completely isolate the system from the environment and its coupling to the environment inevitably leads to the loss of coherence or decoherence. All these effects are to be thoroughly investigated as the potential of the future applications is enormous.; In this thesis I find an analytic expression for the conductance of a single electron transistor in the regime when temperature, level spacing, and charging energy of an island are all of the same order. I also study the correction to the spacing between Coulomb blockade peaks due to finite dot-lead tunnel couplings. I find analytic expressions for both correction to the spacing averaged over mesoscopic fluctuations and rms of the correction fluctuations.; In the second part of the thesis I discuss the feasibility of the quantum dot based spin- and charge-qubits. Firstly, I study the effect of mesoscopic fluctuations on the magnitude of errors that can occur in exchange operations on quantum dot spin-qubits. Mid-size double quantum dots, with an odd number of electrons in the range of a few tens in each dot, are investigated through the constant interaction model using realistic parameters. It is found that the number of independent parameters per dot that one should tune depends on the configuration and ranges from one to four. Then, I study decoherence of a quantum dot charge qubit due to coupling to piezoelectric acoustic phonons in the Born-Markov approximation. After including appropriate form factors, I find that phonon decoherence rates are one to two orders of magnitude weaker than was previously predicted. My results suggest that mechanisms other than phonon decoherence play a more significant role in current experimental setups.