Quantum information with semiconductor electron spins

The study of quantum information science has brought a wealth of open questions into the view of the scientific community: it is the aim of this work to address three of these questions.; The first question is: can quantum algorithms be extended for efficient simulation of "classical" physics, such as electromagnetics simulations? Existing quantum algorithms, particularly Shor's number factorization and Lloyd's quantum many-body emulator, make use of efficient eigenvalue estimation. We show that a quantum algorithm can be extended to eigenvalue estimation of linear, partial differential operators. It is found that scaling better than existing classical algorithms can be achieved only for problems defined over domains of high dimensionality (>4 for second order differentials). The answer is thus negative for electromagnetics; the fundamental reason is the unitarity of quantum mechanics and hence the inability to "erase"' errors during convergence.; The second question is: what are the tolerable error rates for a quantum computer constructed from qubits that only exhibit nearest neighbour interactions? In many solid state qubit proposals, including electron spins in semiconductor quantum dots, the communication scheme may very well be limited to nearest neighbour interactions. We find that in the worst case scenario---with regards to communication---of a linear stripe of qubits of negligible width, the impact on the error correction threshold for the concatenated [[7,1,3]] Calderbank-Shor-Steane code is merely one order of magnitude in the amplitude or timing of control signals compared to idealized error-free communication models. The overhead associated with error correction itself is substantial enough to limit the impact of additional nearest-neighbour communication operations.; The third and final question is: is it experimentally feasible to implement long distance communication with semiconductor electron spin qubits. A critical component for long distance communication of qubits is a spin coherent photodetector that maps the arbitrary spin state of an incident photon to the spin state of a photoelectron in a fully quantum coherent fashion. The trapping and storage of single photoelectrons is reported here, a significant step towards realizing spin coherent photodetection.