This thesis focuses on two aspects of Quantum Information Processing (QIP) and contains experimental implementation by Nuclear Magnetic Resonance (NMR) spectroscopy. The two aspects are: (i) development of novel methodologies for improved or fault tolerant QIP using longer lived states and geometric phases and (ii) implementation of certain quantum algorithms and theorems by NMR. In the first chapter a general introduction to Quantum Information Processing and its implementation using NMR as well as a description of NMR Hamiltonians and NMR relaxation using Redfield theory and magnetization modes are given. The second chapter contains a study of relaxation of Pseudo Pure States (PPS). PPS are specially prepared initial states from where computation begins. These states, being non-equilibrium states, relax with time and hence introduce error in computation. In this chapter we have studied the role of Cross-Correlations in relaxation of PPS. The third and fourth chapters, respectively report observation of cyclic and non-cyclic geometric phases. When the state of a qubit is subjected to evolution either adiabatically or non-adiabatically along the surface of the Bloch sphere, the qubit sometimes gain a phase factor apart from the dynamic phase. This is known as the Geometric phase, as it depends only on the geometry of the path of evolution. Geometric phase is used in Fault tolerant QIP. In these two chapters we have demonstrated how geometric phases of a qubit can be measured using NMR. The fifth and sixth chapters contain the implementations of “No Deletion” and “No Cloning” (quantum triplicator for partially known states) theorems. No Cloning and No Deletion theorems are closely related. The former states that an unknown quantum states can not be copied perfectly while the later states that an unknown state can not be deleted perfectly either. In these two chapters we have discussed about experimental implementation of the two theorems. The last chapter contains implementation of “Deutsch-Jozsa” algorithm in strongly dipolar coupled spin systems. Dipolar couplings being larger than the scalar couplings provide better opportunity for scaling up to larger number of qubits. However, strongly coupled systems offer few experimental challenges as well. This chapter demonstrates how a strongly coupled system can be used in NMR QIP.

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The work presented in this thesis investigates transitions between quantum states in superconducting double dots (SDDs), a nanoscale device consisting of two aluminium superconducting islands coupled together by a Josephson junction, with each dot connected to a normal state lead. The energy landscape consists of a two level manifold of even charge parity Cooper pair states, and continuous bands corresponding to charge states with single quasiparticles in one or both islands. These devices are fabricated using shadow mask evaporation, and are measured at sub Kelvin temperatures using a dilution refrigerator. We use radio frequency reflectometry to measure quantum capacitance, which is dependent on the quantum state of the device. We measure the quantum capacitance as a function of gate voltage, and observe capacitance maxima corresponding to the Josephson coupling between even parity states. We also perform charge sensing and detect odd parity states. These measurements support the theoretical model of the energy landscape of the SDD. By measuring the quantum capacitance in the time domain, we observe random switching of capacitance between two levels. We determine this to be the stochastic breaking and recombination of single Cooper pairs. By carrying out spectroscopy of the bath responsible for the pair breaking we attribute it to black-body radiation in the cryogenic environment. We also drive the breaking process with a continuous microwave signal, and find that the rate is linearly proportional to incident power. This suggests that a single photon process is responsible, and demonstrates the potential of the SDD as a single photon microwave detector. We investigate this mechanism further, and design an experiment in which the breaking rate is enhanced when the SDD is in the antisymmetric state rather than the symmetric state. We also measure the quantum capacitance of a charge isolated double dot. We observe 2e periodicity, indicating the tunnelling of Cooper pairs and the lack of occupation of quasiparticle states. This work is relevant to the range of experiments investigating the effect of non-equilibrium quasiparticles on the operation of superconducting qubits and other superconducting devices.