In a classical computer information is stored as 'bits', the state of which is either 0 or 1, which are manipulated by Boolean logic gates. The quantum analogue of a classical bit is a 'qubit', which can exist not only as 0s or 1s but as superpositions of the two states. For any system to be considered a viable candidate for quantum computing it must be possible to realise a set of universal quantum logic gates, from which any quantum logic operation can be constructed (or at least simulated). This requires the implementation of at least one multi-qubit gate, the simplest of which are two-qubit operations such as CNOT, CPHASE, and √SWAP gates. It must also be possible to detect the quantum state of the qubits, which can be accomplished by quantum state tomography, in which the expectation values of a set of operators which form a complete basis of the Hilbert space are measured. All useful two-qubit gates can be implemented by a combination of an 'entangling gate', by which a separable state is converted to a maximally entangled state, and single-qubit gates. Thus the demonstration of single qubit gates, an entangling gate, and subsequent quantum state tomography is sufficient to demonstrate a universal set of gates. The intrinsic spins of nuclei and electrons makes them natural candidates for the physical realisation of qubits, and quantum logic operations can be realised by manipulation of their spin states by Nuclear Magnetic Resonance (NMR) and Electron Paramagnetic Resonance (EPR), respectively. The implementation of an entangling gate between nuclear spins by NMR was first demonstrated in liquid solutions of chloroform and cytosine ensembles, and in the case of chloroform the density matrix of the coupled 1 H and C nuclear spins was determined by quantum state tomography. However, the large identity component of the density matrix, arising from working in the high temperature limit, meant that only "pseudoentangled" states were accessible. Pseudo-entanglement was also demonstrated in an electron-nuclear ensemble system generated by x-ray irradiation of a malonic acid crystal. By working at low temperatures and introducing a polarisation transfer step between the electron and nuclear spins, it was possible to initiate a sufficiently pure starting state that real electron-nuclear entanglement was confirmed in an ensemble of phosphorus donors in silicon. Interest in identifying systems in which all qubits are electron spins is motivated by the observation that, owing to their larger Zeeman couplings compared to nuclear spins, a sufficiently pure starting state may be obtained in thermal equilibrium at readily achievable temperatures.